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UNITS(1) General Commands Manual UNITS(1) NAME units -- unit conversion and calculation program SYNOPSIS units [from-unit [to-unit]] units [-hcemnSpqsv1trUVI] [-d digits] [-f units file] [-L logfile] [-l locale] [-o format] [-u unit system] [from-unit [to-unit]] units [--help] [--check] [--check-verbose] [--verbose-check] [--list-units] [--digits digits] [--exponential] [--file units file] [--log logfile] [--locale locale] [--minus] [--oldstar] [--newstar] [--nolists] [--show-factor] [--conformable] [--output-format format] [--product] [--quiet] [--silent] [--strict] [--verbose] [--compact] [--one-line] [--terse] [--round] [--unitsfile] [--units units system] [--version] [--info] [from-unit [to-unit]] DESCRIPTION The units program converts quantities expressed in various systems of mea- surement to their equivalents in other systems of measurement. Like many similar programs, it can handle multiplicative scale changes. It can also handle nonlinear conversions such as Fahrenheit to Celsius; see Temperature Conversions. The program can also perform conversions from and to sums of units, such as converting between meters and feet plus inches. But Fahrenheit to Celsius is linear, you insist. Not so. A transformation T is linear if T(x + y) = T(x) + T(y) and this fails for T(x) = ax + b. This transformation is affine, but not linear--see https://en.wikipedia.org/wiki/Linear_map. Basic operation is simple: you enter the units that you want to convert from and the units that you want to convert to. You can use the program interactively with prompts, or you can use it from the command line. Beyond simple unit conversions, units can be used as a general-purpose sci- entific calculator that keeps track of units in its calculations. You can form arbitrary complex mathematical expressions of dimensions including sums, products, quotients, powers, and even roots of dimensions. Thus you can ensure accuracy and dimensional consistency when working with long ex- pressions that involve many different units that may combine in complex ways; for an illustration, see Complicated Unit Expressions. The units are defined in several external data files. You can use the ex- tensive data files that come with the program, or you can provide your own data file to suit your needs. You can also use your own data file to sup- plement the standard data files. You can change the default behavior of units with various options given on the command line. See Invoking Units for a description of the available op- tions. ADDITIONAL DOCUMENTATION This manual is also available in PDF and HTML: https://www.gnu.org/software/units/manual/units.pdf https://www.gnu.org/software/units/manual/units.html INTERACTING WITH UNITS To invoke units for interactive use, type units at your shell prompt. The program will print something like this: Currency exchange rates from FloatRates (USD base) on 2023-07-08 3612 units, 109 prefixes, 122 nonlinear units You have: At the `You have:' prompt, type the quantity and units that you are con- verting from. For example, if you want to convert ten meters to feet, type 10 meters. Next, units will print `You want:'. You should type the units you want to convert to. To convert to feet, you would type feet. If the readline library was compiled in, then tab will complete unit names. See Readline Support for more information about readline. To quit the program type quit or exit at either prompt. The result will be displayed in two ways. The first line of output, which is marked with a `*' to indicate multiplication, gives the result of the conversion you have asked for. The second line of output, which is marked with a `/' to indicate division, gives the inverse of the conversion fac- tor. If you convert 10 meters to feet, units will print * 32.808399 / 0.03048 which tells you that 10 meters equals about 32.8 feet. The second number gives the conversion in the opposite direction. In this case, it tells you that 1 foot is equal to about 0.03 dekameters since the dekameter is 10 me- ters. It also tells you that 1/32.8 is about 0.03. The units program prints the inverse because sometimes it is a more conve- nient number. In the example above, for example, the inverse value is an exact conversion: a foot is exactly 0.03048 dekameters. But the number given the other direction is inexact. If you convert grains to pounds, you will see the following: You have: grains You want: pounds * 0.00014285714 / 7000 From the second line of the output, you can immediately see that a grain is equal to a seven thousandth of a pound. This is not so obvious from the first line of the output. If you find the output format confusing, try us- ing the `--verbose' option: You have: grain You want: aeginamina grain = 0.00010416667 aeginamina grain = (1 / 9600) aeginamina If you request a conversion between units that measure reciprocal dimen- sions, then units will display the conversion results with an extra note indicating that reciprocal conversion has been done: You have: 6 ohms You want: siemens reciprocal conversion * 0.16666667 / 6 Reciprocal conversion can be suppressed by using the `--strict' option. As usual, use the `--verbose' option to get more comprehensible output: You have: tex You want: typp reciprocal conversion 1 / tex = 496.05465 typp 1 / tex = (1 / 0.0020159069) typp You have: 20 mph You want: sec/mile reciprocal conversion 1 / 20 mph = 180 sec/mile 1 / 20 mph = (1 / 0.0055555556) sec/mile If you enter incompatible unit types, the units program will print a mes- sage indicating that the units are not conformable and it will display the reduced form for each unit: You have: ergs/hour You want: fathoms kg^2 / day conformability error 2.7777778e-11 kg m^2 / sec^3 2.1166667e-05 kg^2 m / sec If you only want to find the reduced form or definition of a unit, simply press Enter at the `You want:' prompt. Here is an example: You have: jansky You want: Definition: fluxunit = 1e-26 W/m^2 Hz = 1e-26 kg / s^2 The output from units indicates that the jansky is defined to be equal to a fluxunit which in turn is defined to be a certain combination of watts, me- ters, and hertz. The fully reduced (and in this case somewhat more cryp- tic) form appears on the far right. If the ultimate definition and the fully reduced form are identical, the latter is not shown: You have: B You want: Definition: byte = 8 bit The fully reduced form is shown if it and the ultimate definition are equivalent but not identical: You have: N You want: Definition: newton = kg m / s^2 = 1 kg m / s^2 Some named units are treated as dimensionless in some situations. These units include the radian and steradian. These units will be treated as equal to 1 in units conversions. Power is equal to torque times angular velocity. This conversion can only be performed if the radian is dimen- sionless. You have: (14 ft lbf) (12 radians/sec) You want: watts * 227.77742 / 0.0043902509 It is also possible to compute roots and other non-integer powers of dimen- sionless units; this allows computations such as the altitude of geosyn- chronous orbit: You have: cuberoot(G earthmass / (circle/siderealday)^2) - earthradius You want: miles * 22243.267 / 4.4957425e-05 Named dimensionless units are not treated as dimensionless in other con- texts. They cannot be used as exponents so for example, `meter^radian' is forbidden. If you want a list of options you can type ? at the `You want:' prompt. The program will display a list of named units that are conformable with the unit that you entered at the `You have:' prompt above. Conformable unit combinations will not appear on this list. Interactive Commands Typing help at either prompt displays a short help message. You can also type help followed by a unit name. This will invoke a pager on the units database at the point where that unit is defined. You can read the defini- tion and comments that may give more details or historical information about the unit. If your pager allows, you may want to scroll backwards, e.g., with `b', because sometimes a longer comment about a unit or group of units will appear before the definition. You can generally quit out of the pager by pressing `q'. Typing search text will display a list of all units whose names contain text as a substring along with their definitions. This may help in the case where you aren't sure of the right unit name. Typing search . will display a list of all units; this can be helpful if you aren't sure of an appropriate substring, though examining the output can be tedious. Here `.' is a special argument to the search command, not a regular expression. If you want to use a regular expression to search units and their defini- tions, the `--list-units' option will display a list of all units, which can be sent to a filter such as grep. Typing search _ will display a list of all assigned runtime variables--whose names begin with `_'--without in- cluding all units whose names simply contain `_'. See Variables Assigned at Run Time for more information on runtime variables. Typing version will display the units version number; unlike the `--ver- sion' option, only the version number is shown, regardless of any other settings. Full information is available with the info command. Typing info will display the same information as the `--info' option, de- scribed in Invoking Units. Many values set by command-line options can also be set interactively by typing set option=value; typing set option will show the value for that op- tion. Typing set will show a list of options that can be set; options set to other than default values will have a prepended `*'. See Setting Op- tions Interactively for more information. USING UNITS NON-INTERACTIVELY The units program can perform units conversions non-interactively from the command line. To do this, type the command, type the original unit expres- sion, and type the new units you want. If a units expression contains non- alphanumeric characters, you may need to protect it from interpretation by the shell using single or double quote characters. If you type units "2 liters" quarts then units will print * 2.1133764 / 0.47317647 and then exit. The output tells you that 2 liters is about 2.1 quarts, or alternatively that a quart is about 0.47 times 2 liters. units does not require a space between a numerical value and the unit, so the previous example can be given as units 2liters quarts to avoid having to quote the first argument. If the conversion is successful, units will return success (zero) to the calling environment. If you enter non-conformable units, then units will print a message giving the reduced form of each unit and it will return failure (nonzero) to the calling environment. If the `--conformable' option is given, only one unit expression is al- lowed, and units will print all units conformable with that expression; it is equivalent to giving ? at the `You want:' prompt. For example, units --conformable gauss B_FIELD tesla Gs gauss T tesla gauss abvolt sec / cm^2 stT stattesla statT stattesla stattesla statWb/cm^2 tesla Wb/m^2 If you give more than one unit expression with the `--conformable' option, the program will exit with an error message and return failure. This op- tion has no effect in interactive mode. If the `--terse' (`-t') option is given with the `--conformable' option, conformable units are shown without definitions; with the previous example, this would give units --terse --conformable gauss B_FIELD Gs T gauss stT statT stattesla tesla When the `--conformable' option is not given and you invoke units with only one argument, units will print the definition of the specified unit. It will return failure if the unit is not defined and success if the unit is defined. Finding Units The units database includes many units, and it can sometimes be difficult to remember every name. The interactive search command examines only unit names, so it cannot be used to find units whose definitions contain a pat- tern. If units is invoked with the `--list-units' option, the output can be sent to a filter such as grep, examining the unit name and the defini- tion. For example, units --list-units | grep ';' dms deg;arcmin;arcsec ftin ft;in;1|8 in ftin16 ft;in;1|16 in ftin32 ft;in;1|32 in ftin4 ft;in;1|4 in ftin64 ft;in;1|64 in ftin8 ft;in;1|8 in hms hr;min;sec inchfine in;1|8 in;1|16 in;1|32 in;1|64 in time year;day;hr;min;sec uswt lb;oz . . . could find all unit lists, which include at least one semicolon in their definitions. The search command doesn't support regular expressions, but with the `--list-units' option the output can be sent to a filter such as grep, which does. If you expect a long list of results, you can send the output of the filter to a pager. For example, units --list-units | grep 'paper[[:space:]]' | more A0paper 841 mm 1189 mm A10paper 26 mm 37 mm A1paper 594 mm 841 mm A2paper 420 mm 594 mm A3paper 297 mm 420 mm A4paper 210 mm 297 mm A5paper 148 mm 210 mm A6paper 105 mm 148 mm A7paper 74 mm 105 mm A8paper 52 mm 74 mm A9paper 37 mm 52 mm . . . could show a list of all defined paper sizes. UNIT DEFINITIONS The conversion information is read from several units data files: `definitions.units', `elements.units', `currency.units', and `cpi.units', which are usually located in the `/usr/share/units' directory. If you in- voke units with the `-V' option, it will print the location of these files. The default main file includes definitions for all familiar units, abbrevi- ations and metric prefixes. It also includes many obscure or archaic units. Many common spelled-out numbers (e.g., `seventeen') are recognized. Physical Constants Many constants of nature are defined, including these: pi ratio of circumference of a circle to its diameter c speed of light e charge on an electron force acceleration of gravity mole Avogadro's number water pressure per unit height of water Hg pressure per unit height of mercury au astronomical unit k Boltzman's constant mu0 permeability of vacuum epsilon0 permittivity of vacuum G Gravitational constant mach speed of sound The standard data file includes numerous other constants. Also included are the densities of various ingredients used in baking so that `2 cups flour_sifted' can be converted to `grams'. This is not an exhaustive list. Consult the units data file to see the complete list, or to see the defini- tions that are used. Atomic Masses of the Elements The data file `elements.units' includes atomic masses for most elements and most known isotopes. If the mole fractions of constituent isotopes are known, an elemental mass is calculated from the sum of the products of the mole fractions and the masses of the constituent isotopes. If the mole fractions are not known, the mass of the most stable isotope--if known--is given as the elemental mass. For radioactive elements with atomic numbers 95 or greater, the mass number of the most stable isotope is not specified, because the list of studied isotopes is still incomplete. If no stable isotope is known, no elemental mass is given, and you will need to choose the most appropriate isotope. The data are obtained from the US National Institute for Standards and Technology (NIST): https://physics.nist.gov/cgi-bin/Composi- tions/stand_alone.pl?ele=&all=all&ascii=ascii2&isotype=all. The `elements.units' file can be generated from these data using the elemcvt command included with the distribution. Currency Exchange Rates and Consumer Price Index The data files `currency.units', `crypto.units', and `metal_prices.units' include currency conversion rates, cryptocurrency prices, and the prices of precious metals. The file `cpi.units' includes the US Consumer Price Index (CPI), published by the US Bureau of Labor Statistics; the data are updated monthly by the BLS. See Updating Currency Exchange Rates and CPI for in- formation on updating `currency.units', `crypto.units', `metal_prices.units', and `cpi.units'. English Customary Units English customary units differ in various ways among different regions. In Britain a complex system of volume measurements featured different gallons for different materials such as a wine gallon and ale gallon that different by twenty percent. This complexity was swept away in 1824 by a reform that created an entirely new gallon, the British Imperial gallon defined as the volume occupied by ten pounds of water. Meanwhile in the USA the gallon is derived from the 1707 Winchester wine gallon, which is 231 cubic inches. These gallons differ by about twenty percent. By default if units runs in the `en_GB' locale you will get the British volume measures. If it runs in the `en_US' locale you will get the US volume measures. In other locales the default values are the US definitions. If you wish to force different definitions, then set the environment variable UNITS_ENGLISH to either `US' or `GB' to set the desired definitions independent of the locale. Before 1959, the value of a yard (and other units of measure defined in terms of it) differed slightly among English-speaking countries. In 1959, Australia, Canada, New Zealand, the United Kingdom, the United States, and South Africa adopted the Canadian value of 1 yard = 0.9144 m (exactly), which was approximately halfway between the values used by the UK and the US; it had the additional advantage of making 1 inch = 2.54 cm (exactly). This new standard was termed the International Yard. Australia, Canada, and the UK then defined all customary lengths in terms of the International Yard (Australia did not define the furlong or rod); because many US land surveys were in terms of the pre-1959 units, the US continued to define customary surveyors' units (furlong, chain, rod, pole, perch, and link) in terms of the previous value for the foot, which was termed the US survey foot. The US defined a US survey mile as 5280 US survey feet, and defined a statute mile as a US survey mile. The US values for these units differed from the international values by about 2 ppm. The 1959 redefinition of the foot was legally binding in the US but allowed continued use of the previous definition of the foot for geodetic survey- ing. It was assumed that this use would be temporary, but use persisted, leading to confusion and errors, and it was at odds with the intent of uni- form standards. Since January 1, 2023, the US survey foot has been offi- cially deprecated (85 FR 62698), with its use limited to historical and legacy applications. The units program has always used the international values for these units; the legacy US values can be obtained by using either the `US' or the `survey' prefix. In either case, the simple familiar relationships among the units are maintained, e.g., 1 `furlong' = 660 `ft', and 1 `USfurlong' = 660 `USft', though the metric equivalents differ slightly between the two cases. The `US' prefix or the `survey' prefix can also be used to obtain the US survey mile and the value of the US yard prior to 1959, e.g., `USmile' or `surveymile' (but not `USsurveymile'). To get the US value of the statute mile, use either `USstatutemile' or `USmile'. The pre-1959 UK values for these units can be obtained with the prefix `UK'. Except for distances that extend over hundreds of miles (such as in the US State Plane Coordinate System), the differences in the miles are usually insignificant: You have: 100 surveymile - 100 mile You want: inch * 12.672025 / 0.078913984 The US acre was officially defined in terms of the US survey foot, but units has used a definition based on the international foot; the units def- inition is now the same as the official US value. If you want the previous US acre, use `USacre' and similarly use `USacrefoot' for the previous US version of that unit. The difference between these units is about 4 parts per million. Miscellaneous Notes on Unit Definitions The `pound' is a unit of mass. To get force, multiply by the force conver- sion unit `force' or use the shorthand `lbf'. (Note that `g' is already taken as the standard abbreviation for the gram.) The unit `ounce' is also a unit of mass. The fluid ounce is `fluidounce' or `floz'. When British capacity units differ from their US counterparts, such as the British Impe- rial gallon, the unit is defined both ways with `br' and `us' prefixes. Your locale settings will determine the value of the unprefixed unit. Cur- rency is prefixed with its country name: `belgiumfranc', `britainpound'. When searching for a unit, if the specified string does not appear exactly as a unit name, then the units program will try to remove a trailing `s', `es'. Next units will replace a trailing `ies' with `y'. If that fails, units will check for a prefix. The database includes all of the standard metric prefixes. Only one prefix is permitted per unit, so `micromicrofarad' will fail. However, prefixes can appear alone with no unit following them, so `micro*microfarad' will work, as will `micro micro- farad'. To find out which units and prefixes are available, read the default units data files; the main data file is extensively annotated. UNIT EXPRESSIONS Operators You can enter more complicated units by combining units with operations such as multiplication, division, powers, addition, subtraction, and paren- theses for grouping. You can use the customary symbols for these operators when units is invoked with its default options. Additionally, units sup- ports some extensions, including high priority multiplication using a space, and a high priority numerical division operator (`|') that can sim- plify some expressions. You multiply units using a space or an asterisk (`*'). The next example shows both forms: You have: arabicfoot * arabictradepound * force You want: ft lbf * 0.7296 / 1.370614 You can divide units using the slash (`/') or with `per': You have: furlongs per fortnight You want: m/s * 0.00016630986 / 6012.8727 You can use parentheses for grouping: You have: (1/2) kg / (kg/meter) You want: league * 0.00010356166 / 9656.0833 White space surrounding operators is optional, so the previous example could have used `(1/2)kg/(kg/meter)'. As a consequence, however, hyphen- ated spelled-out numbers (e.g., `forty-two') cannot be used; `forty-two' is interpreted as `40 - 2'. Multiplication using a space has a higher precedence than division using a slash and is evaluated left to right; in effect, the first `/' character marks the beginning of the denominator of a unit expression. This makes it simple to enter a quotient with several terms in the denominator: `J / mol K'. The `*' and `/' operators have the same precedence, and are evaluated left to right; if you multiply with `*', you must group the terms in the denominator with parentheses: `J / (mol * K)'. The higher precedence of the space operator may not always be advantageous. For example, `m/s s/day' is equivalent to `m / s s day' and has dimensions of length per time cubed. Similarly, `1/2 meter' refers to a unit of reci- procal length equivalent to 0.5/meter, perhaps not what you would intend if you entered that expression. The get a half meter you would need to use parentheses: `(1/2) meter'. The `*' operator is convenient for multiplying a sequence of quotients. For example, `m/s * s/day' is equivalent to `m/day'. Similarly, you could write `1/2 * meter' to get half a meter. The units program supports another option for numerical fractions: you can indicate division of numbers with the vertical bar (`|'), so if you wanted half a meter you could write `1|2 meter'. You cannot use the vertical bar to indicate division of non-numerical units (e.g., `m|s' results in an er- ror message). Powers of units can be specified using the `^' character, as shown in the following example, or by simple concatenation of a unit and its exponent: `cm3' is equivalent to `cm^3'; if the exponent is more than one digit, the `^' is required. You can also use `**' as an exponent operator. You have: cm^3 You want: gallons * 0.00026417205 / 3785.4118 Concatenation only works with a single unit name: if you write `(m/s)2', units will treat it as multiplication by 2. When a unit includes a prefix, exponent operators apply to the combination, so `centimeter3' gives cubic centimeters. If you separate the prefix from the unit with any multiplica- tion operator (e.g., `centi meter^3'), the prefix is treated as a separate unit, so the exponent applies only to the unit without the prefix. The second example is equivalent to `centi * (meter^3)', and gives a hundredth of a cubic meter, not a cubic centimeter. The units program is limited in- ternally to products of 99 units; accordingly, expressions like `meter^100' or `joule^34' (represented internally as `kg^34 m^68 / s^68') will fail. The `|' operator has the highest precedence, so you can write the square root of two thirds as `2|3^1|2'. The `^' operator has the second highest precedence, and is evaluated right to left, as usual: You have: 5 * 2^3^2 You want: Definition: 2560 With a dimensionless base unit, any dimensionless exponent is meaningful (e.g., `pi^exp(2.371)'). Even though angle is sometimes treated as dimen- sionless, exponents cannot have dimensions of angle: You have: 2^radian ^ Exponent not dimensionless If the base unit is not dimensionless, the exponent must be a rational num- ber p/q, and the dimension of the unit must be a power of q, so `gallon^2|3' works but `acre^2|3' fails. An exponent using the slash (`/') operator (e.g., `gallon^(2/3)') is also acceptable; the parentheses are needed because the precedence of `^' is higher than that of `/'. Since units cannot represent dimensions with exponents greater than 99, a fully reduced exponent must have q < 100. When raising a non-dimensionless unit to a power, units attempts to convert a decimal exponent to a rational num- ber with q < 100. If this is not possible units displays an error message: You have: ft^1.234 Base unit not dimensionless; rational exponent required A decimal exponent must match its rational representation to machine preci- sion, so `acre^1.5' works but `gallon^0.666' does not. Sums and Differences of Units You may sometimes want to add values of different units that are outside the SI. You may also wish to use units as a calculator that keeps track of units. Sums of conformable units are written with the `+' character, and differences with the `-' character. You have: 2 hours + 23 minutes + 32 seconds You want: seconds * 8612 / 0.00011611705 You have: 12 ft + 3 in You want: cm * 373.38 / 0.0026782366 You have: 2 btu + 450 ft lbf You want: btu * 2.5782804 / 0.38785542 The expressions that are added or subtracted must reduce to identical ex- pressions in primitive units, or an error message will be displayed: You have: 12 printerspoint - 4 heredium ^ Invalid sum of non-conformable units If you add two values of vastly different scale you may exceed the avail- able precision of floating point (about 15 digits). The effect is that the addition of the smaller value makes no change to the larger value; in other words, the smaller value is treated as if it were zero. You have: lightyear + cm No warning is given, however. As usual, the precedence for `+' and `-' is lower than that of the other operators. A fractional quantity such as 2 1/2 cups can be given as `(2+1|2) cups'; the parentheses are necessary because multiplication has higher precedence than addition. If you omit the parentheses, units attempts to add `2' and `1|2 cups', and you get an error message: You have: 2+1|2 cups ^ Invalid sum or difference of non-conformable units The expression could also be correctly written as `(2+1/2) cups'. If you write `2 1|2 cups' the space is interpreted as multiplication so the result is the same as `1 cup'. The `+' and `-' characters sometimes appears in exponents like `3.43e+8'. This leads to an ambiguity in an expression like `3e+2 yC'. The unit `e' is a small unit of charge, so this can be regarded as equivalent to `(3e+2) yC' or `(3 e)+(2 yC)'. This ambiguity is resolved by always interpreting `+' and `-' as part of an exponent if possible. Numbers as Units For units, numbers are just another kind of unit. They can appear as many times as you like and in any order in a unit expression. For example, to find the volume of a box that is 2 ft by 3 ft by 12 ft in steres, you could do the following: You have: 2 ft 3 ft 12 ft You want: stere * 2.038813 / 0.49048148 You have: $ 5 / yard You want: cents / inch * 13.888889 / 0.072 And the second example shows how the dollar sign in the units conversion can precede the five. Be careful: units will interpret `$5' with no space as equivalent to `dollar^5'. Built-in Functions Several built-in functions are provided: `sin', `cos', `tan', `secant', `csc', `cot', `asin', `acos', `atan', `asecant', `acsc', `acot', `sinh', `cosh', `tanh', `sech', `csch', `coth', `asinh', `acosh', `atanh', `asech', `acsch', `acoth', `exp', `ln', `log', `abs', `round', `floor', `ceil', `factorial', `Gamma', `lnGamma', `erf', and `erfc'; the function `lnGamma' is the natural logarithm of the `Gamma' function. The `sin', `cos', `tan', `secant', `csc' and `cot' functions require either a dimensionless argument or an argument with dimensions of angle. You have: sin(30 degrees) You want: Definition: 0.5 You have: sin(pi/2) You want: Definition: 1 You have: sin(3 kg) ^ Unit not dimensionless The other functions on the list require dimensionless arguments. The in- verse trigonometric functions return arguments with dimensions of angle. The `ln' and `log' functions give natural log and log base 10 respectively. To obtain logs for any integer base, enter the desired base immediately af- ter `log'. For example, to get log base 2 you would write `log2' and to get log base 47 you could write `log47'. You have: log2(32) You want: Definition: 5 You have: log3(32) You want: Definition: 3.1546488 You have: log4(32) You want: Definition: 2.5 You have: log32(32) You want: Definition: 1 You have: log(32) You want: Definition: 1.50515 You have: log10(32) You want: Definition: 1.50515 If you wish to take roots of units, you may use the `sqrt' or `cuberoot' functions. These functions require that the argument have the appropriate root. You can obtain higher roots by using fractional exponents: You have: sqrt(acre) You want: feet * 208.71074 / 0.0047913202 You have: (400 W/m^2 / stefanboltzmann)^(1/4) You have: Definition: 289.80882 K You have: cuberoot(hectare) ^ Unit not a root Previous Result You can insert the result of the previous conversion using the underscore (`_'). It is useful when you want to convert the same input to several different units, for example You have: 2.3 tonrefrigeration You want: btu/hr * 27600 / 3.6231884e-005 You have: _ You want: kW * 8.0887615 / 0.12362832 Suppose you want to do some deep frying that requires an oil depth of 2 inches. You have 1/2 gallon of oil, and want to know the largest-diame- ter pan that will maintain the required depth. The nonlinear unit `circlearea' gives the radius of the circle (see Other Nonlinear Units, for a more detailed description) in SI units; you want the diameter in inches: You have: 1|2 gallon / 2 in You want: circlearea 0.10890173 m You have: 2 _ You want: in * 8.5749393 / 0.1166189 In most cases, surrounding white space is optional, so the previous example could have used `2_'. If `_' follows a non-numerical unit symbol, however, the space is required: You have: m_ ^ Parse error You can use the `_' symbol any number of times; for example, You have: m You want: Definition: 1 m You have: _ _ You want: Definition: 1 m^2 Using `_' before a conversion has been performed (e.g., immediately after invocation) generates an error: You have: _ ^ No previous result; '_' not set Accordingly, `_' serves no purpose when units is invoked non-interactively. If units is invoked with the `--verbose' option (see Invoking Units), the value of `_' is not expanded: You have: mile You want: ft mile = 5280 ft mile = (1 / 0.00018939394) ft You have: _ You want: m _ = 1609.344 m _ = (1 / 0.00062137119) m You can give `_' at the `You want:' prompt, but it usually is not very use- ful. Complicated Unit Expressions The units program is especially helpful in ensuring accuracy and dimen- sional consistency when converting lengthy unit expressions. For example, one form of the Darcy-Weisbach fluid-flow equation is Delta P = (8 / pi)^2 (rho fLQ^2) / d^5, where Delta P is the pressure drop, rho is the mass density, f is the (di- mensionless) friction factor, L is the length of the pipe, Q is the volu- metric flow rate, and d is the pipe diameter. You might want to have the equation in the form Delta P = A1 rho fLQ^2 / d^5 that accepted the user's normal units; for typical units used in the US, the required conversion could be something like You have: (8/pi^2)(lbm/ft^3)ft(ft^3/s)^2(1/in^5) You want: psi * 43.533969 / 0.022970568 The parentheses allow individual terms in the expression to be entered nat- urally, as they might be read from the formula. Alternatively, the multi- plication could be done with the `*' rather than a space; then parentheses are needed only around `ft^3/s' because of its exponent: You have: 8/pi^2 * lbm/ft^3 * ft * (ft^3/s)^2 /in^5 You want: psi * 43.533969 / 0.022970568 Without parentheses, and using spaces for multiplication, the previous con- version would need to be entered as You have: 8 lb ft ft^3 ft^3 / pi^2 ft^3 s^2 in^5 You want: psi * 43.533969 / 0.022970568 Variables Assigned at Run Time Unit definitions are fixed once units has finished reading the units data file(s), but at run time you can assign unit expressions to variables whose names begin with an underscore, using the syntax _name = <unit expression> This can help manage a long calculation by saving intermediate quantities as variables that you can use later. For example, to determine the shot- noise-limited signal-to-noise ratio (SNR) of an imaging system using a he- lium-neon laser, you could do You have: _lambda = 632.8 nm # laser wavelength You have: _nu = c / _lambda # optical frequency You have: _photon_energy = h * _nu You have: _power = 550 uW You have: _photon_count = _power * 500 ns / _photon_energy You have: _snr = sqrt(_photon_count) You have: _snr You want: Definition: sqrt(_photon_count) = 29597.922 Except for beginning with an underscore, runtime variables follow the same naming rules as units. Because names beginning with `_' are reserved for these variables and unit names cannot begin with `_', runtime variables can never hide unit definitions. Runtime variables are undefined until you make an assignment to them, so if you give a name beginning with an under- score and no assignment has been made, you get an error message. When you assign a unit expression to a runtime variable, units checks the expression to determine whether it is valid, but the resulting definition is stored as a text string that is not reduced to primitive units. The text will be processed anew each time you use the variable in a conversion or calculation; this means that if your definition depends on other run- time variables (or the special variable `_'), the result of calculating with your variable will change if any of those variables change. A depen- dence need not be direct. Continuing the example of the laser above, suppose you have done the calcu- lation as shown. You now wonder what happens if you switch to an argon laser: You have: _lambda = 454.6 nm You have: _snr You want: Definition: sqrt(_photon_count) = 25086.651 If you then change the power: You have: _power = 1 mW You have: _snr You want: Definition: sqrt(_photon_count) = 33826.834 Instead of having to reenter or edit a lengthy expression when you perform another calculation, you need only enter values that change; in this re- spect, runtime variables are similar to a spreadsheet. The more times a variable appears in an expression that depends on it, the greater the benefit of having a calculation using that expression reflect changes to that variable. For example, the length of daylight--the time the Sun is above the horizon--at a given latitude and declination of the Sun is given by L = acos((sin h - sin <phi> sin <delta>) / (cos <phi> cos <delta>)) where L is the day length, h is the altitude, <phi> is the latitude, and <delta> is the Sun's declination. The result above is in sidereal time; the length in solar time is obtained by multiplying by siderealday / day By convention, the Sun's altitude at rise or set is -50' to allow for at- mospheric refraction and the semidiameter of its disk. At the summer sol- stice in the northern hemisphere, the Sun's declination is approximately 23.44<degree>; to find the length of the longest day of the year for a lat- itude of 55<degree>, you could do You have: _alt = -50 arcmin You have: _lat = 55 deg You have: _decl = 23.44 deg You have: _num = sin(_alt) - sin(_lat) sin(_decl) You have: _denom = cos(_lat) cos(_decl) You have: _sday = 2 (acos(_num / _denom) / circle) 24 hr You have: _day = _sday siderealday / day You have: _day You want: hms 17 hr + 19 min + 34.895151 sec At the winter solstice, the Sun's declination is approximately -23.44<degree>, so you could calculate the length of the shortest day of the year using: You have: _decl = -23.44 deg You have: _day You want: hms 7 hr + 8 min + 40.981084 sec Latitude and declination each appear twice in the expression for _day; the result in the examples above is updated by changing only the value of the declination. It may seem easier--and less subject to error--to simply specify the new value of _decl as the negative of the current value (e.g., `_decl = -_decl'). This doesn't work; when you make an assignment with the `=' operator, the definition is stored as entered, including possible de- pendencies on variables. But if you attempt an assignment that is ulti- mately self-referential, the current definition is retained, and you get an error message. For example, You have: _decl = 23.44 deg You have: _decl = -_decl Circular unit definition You can overcome this by using the `:=' operator, which reduces the right hand side to primitive units before making the assignment, eliminating any dependencies on variables. Returning to the example above, You have: _decl = 23.44 deg You have: _decl = -_decl Circular unit definition You have: _decl := -_decl You have: _decl You want: deg * -23.44 / -0.042662116 This works to much the same effect as if the assignment had been entered literally, e.g., You have: _decl = -23.44 deg but the actual definition is in primitive units--in this case, radians: You have: _decl = 23.44 deg You have: _decl := -_decl You have: _decl You want: Definition: -0.40910517666747087 radian = -0.40910518 radian Definitions are text strings, and a redefinition using `:=' is given with enough digits maintain the full precision of the current definition when converted back to a number; because it is a string, all digits are dis- played when showing the definition, regardless of the numerical display precision, so you may see more digits than expected. A runtime variable must be assigned before it can be used in an assignment; in the first of the three examples above, giving the general equation be- fore the values for _alt, _lat, and _decl had been assigned would result in an error message. You can display a list of runtime variables you have assigned by typing search _. Backwards Compatibility: `*' and `-' The original units assigned multiplication a higher precedence than divi- sion using the slash. This differs from the usual precedence rules, which give multiplication and division equal precedence, and can be confusing for people who think of units as a calculator. The star operator (`*') included in this units program has, by default, the same precedence as division, and hence follows the usual precedence rules. For backwards compatibility you can invoke units with the `--oldstar' op- tion. Then `*' has a higher precedence than division, and the same prece- dence as multiplication using the space. Historically, the hyphen (`-') has been used in technical publications to indicate products of units, and the original units program treated it as a multiplication operator. Because units provides several other ways to ob- tain unit products, and because `-' is a subtraction operator in general algebraic expressions, units treats the binary `-' as a subtraction opera- tor by default. For backwards compatibility use the `--product' option, which causes units to treat the binary `-' operator as a product operator. When `-' is a multiplication operator it has the same precedence as multi- plication with a space, giving it a higher precedence than division. When `-' is used as a unary operator it negates its operand. Regardless of the units options, if `-' appears after `(' or after `+', then it will act as a negation operator. So you can always compute 20 degrees minus 12 min- utes by entering `20 degrees + -12 arcmin'. You must use this construction when you define new units because you cannot know what options will be in force when your definition is processed. NONLINEAR UNIT CONVERSIONS Nonlinear units are represented using functional notation. They make pos- sible nonlinear unit conversions such as temperature. Temperature Conversions Conversions between temperatures are different from linear conversions be- tween temperature increments--see the example below. The absolute tempera- ture conversions are handled by units starting with `temp', and you must use functional notation. The temperature-increment conversions are done using units starting with `deg' and they do not require functional nota- tion. You have: tempF(45) You want: tempC 7.2222222 You have: 45 degF You want: degC * 25 / 0.04 Think of `tempF(x)' not as a function but as a notation that indicates that x should have units of `tempF' attached to it. See Defining Nonlinear Units. The first conversion shows that if it's 45 degrees Fahrenheit out- side, it's 7.2 degrees Celsius. The second conversion indicates that a change of 45 degrees Fahrenheit corresponds to a change of 25 degrees Cel- sius. The conversion from `tempF(x)' is to absolute temperature, so that You have: tempF(45) You want: degR * 504.67 / 0.0019814929 gives the same result as You have: tempF(45) You want: tempR * 504.67 / 0.0019814929 But if you convert `tempF(x)' to `degC', the output is probably not what you expect: You have: tempF(45) You want: degC * 280.37222 / 0.0035666871 The result is the temperature in K, because `degC' is defined as `K', the kelvin. For consistent results, use the `tempX' units when converting to a temperature rather than converting a temperature increment. The `tempC()' and `tempF()' definitions are limited to positive absolute temperatures, and giving a value that would result in a negative absolute temperature generates an error message: You have: tempC(-275) ^ Argument of function outside domain US Consumer Price Index units includes the US Consumer Price Index published by the US Bureau of Labor Statistics. Several functions that use this value are provided: `cpi', `cpi_now', `inflation_since', and `dollars_in'. The `cpi' function gives the CPI for a specified decimal year. A decimal year is given as the year plus the fractional part of the year; because of leap years and the different lengths of months, calculating an exact value for the fractional part can be tedious, but for the purposes of CPI, an ap- proximate value is usually adequate. For example, 1 January 2000 is 2000.0, 1 April 2000 is 2000.25, 1 July 2000 is 2000.4986, and 1 October 2000 is 2000.75. Note also that the CPI data update monthly; values in be- tween months are linearly interpolated. In the middle of 1975, the CPI was You have: cpi(1975.5) You want: Definition: 53.6 The value of the CPI for a month is usually published sometime around the 20th day of the following month; the latest value of the CPI is available with `cpi_now'. On 7 January 2024, the value was You have: cpi_now You want: Definition: UScpi_now = 307.051 This means that the CPI was 307.015 on 1 December 2023. The `cpi_now' variable can only present the most recent data available, so it can lag the current CPI by several weeks. The decimal year of the last update is available with `cpi_lastdate'. The `inflation_since' function provides a convenient way to determine the inflation factor from a specified decimal year to the latest value in the CPI table. For example, on 7 January 2024: You have: inflation_since(1970) You want: Definition: 8.1445889 In other words, goods that cost 1 US$ in 1970 would cost 8.14 US$ on 1 De- cember 2023. The `inflation_since' function can be used to determine an annual rate of inflation. The earliest US CPI data are from about 1913.1; the approximate time between then and 7 January 2024 is 110.9 years. The approximate an- nual inflation rate for that period is then You have: inflation_since(1913.1)^1|110.9 - 1 You want: % * 3.1548115 / 0.31697614 The inflation rate for any time period can be found from the ratio of the CPI at the end of the period to that of the beginning: You have: (cpi(1982)/cpi(1972))^1|10 - 1 You want: % * 8.6247033 / 0.11594602 The period 1972-1982 was indeed one of high inflation. The `dollars_in' function is similar to `inflation_since' but its output is in US$ rather than dimensionless: You have: dollars_in(1970) You want: Definition: 8.1445889 US$ A typical use might be You have: 250 dollars_in(1970) You want: $ * 2036.1472 / 0.00049112362 Because `dollars_in' includes the units, you should not include them at the `You have:' prompt. You can also use `dollars_in' to convert between two specified years: You have: 250 dollars_in(1970) You want: dollars_in(1950) * 156.49867 / 0.0063898305 which shows that 250 US$ in 1970 would have equivalent purchasing power to 156 US$ in 1950. Other Nonlinear Units Some other examples of nonlinear units are numerous different ring sizes and wire gauges, screw gauges, pipe and tubing sizes, the grit sizes used for abrasives, the decibel scale, shoe size, scales for the density of sugar (e.g., baume). The standard data file also supplies units for com- puting the area of a circle and the volume of a sphere. See the standard units data file for more details. Diameters of American wire sizes can be found using the `wiregauge()' func- tion or its alias `awg()': You have: wiregauge(11) You want: inches * 0.090742002 / 11.020255 You have: 1 mm You want: wiregauge 18.201919 Wire and screw gauges with multiple zeroes are signified using negative numbers, where two zeroes ("00"; "2/0") is `-1', three zeros ("000"; "3/0") is `-2', and so on. Alternatively, you can use the synonyms `g00', `g000', or `g2_0', `g3_0', and so on that are defined in the standard units data file. You have: brwiregauge(g00) You want: inches * 0.348 / 2.8735632 In North America, wire sizes larger than 0000 ("4/0") are usually given in terms of area, either in kcmil or the older initialism MCM (thousand circu- lar mils). Outside of North America, all wire sizes are usually given in terms of area in mm^2. Wire area can be obtained using `wiregaugeA()' or its alias `awgA()': You have: awgA(g6_0) You want: kcmil * 336.45718 / 0.0029721464 You have: awgA(12) You want: mm^2 * 3.3087729 / 0.30222685 The closest standard metric sizes are 2.5 mm^2 and 4 mm^2; in general, there isn't an exact correlation between American and metric wire sizes. Though based on the long-established iron pipe size (IPS) given in inches, nominal pipe size (NPS) is a dimensionless quantity that corresponds to the inch size. Pipe size can be equivalently specified using metric diametre nominal (DN), which roughly corresponds to the diameter in mm. For a given pipe size, outside diameter is constant while inside diameter varies with schedule. For example, for NPS 21/2 pipe, You have: npsOD(2+1|2) You want: in * 2.875 / 0.34782609 You have: nps40(2+1|2) You want: in * 2.469 / 0.40502228 You have: nps80(2+1|2) You want: in * 2.323 / 0.43047783 Pipe size can be given equivalently in terms of the metric DN by using the `DN()' function, which converts nominal metric size to nominal inch size: You have: npsOD(DN(65)) You want: mm * 73.025 / 0.01369394 You have: _ You want: in * 2.875 / 0.34782609 Unlike with wire sizes, actual NPS and metric DN pipe dimensions are the same. You have: grit_P(600) You want: grit_ansicoated 342.76923 The last example shows the conversion from P graded sand paper, which is the European standard and may be marked "P600" on the back, to the USA standard. You can compute the area of a circle using the nonlinear unit, `circlearea'. You can also do this using the circularinch or circleinch. The next example shows two ways to compute the area of a circle with a five inch radius and one way to compute the volume of a sphere with a radius of one meter. You have: circlearea(5 in) You want: in2 * 78.539816 / 0.012732395 You have: 10^2 circleinch You want: in2 * 78.539816 / 0.012732395 You have: spherevol(meter) You want: ft3 * 147.92573 / 0.0067601492 The inverse of a nonlinear conversion is indicated by prefixing a tilde (`~') to the nonlinear unit name: You have: ~wiregauge(0.090742002 inches) You want: Definition: 11 You can give a nonlinear unit definition without an argument or parenthe- ses, and press Enter at the `You want:' prompt to get the definition of a nonlinear unit; if the definition is not valid for all real numbers, the range of validity is also given. If the definition requires specific units this information is also displayed: You have: tempC Definition: tempC(x) = x K + stdtemp defined for x >= -273.15 You have: ~tempC Definition: ~tempC(tempC) = (tempC +(-stdtemp))/K defined for tempC >= 0 K You have: circlearea Definition: circlearea(r) = pi r^2 r has units m To see the definition of the inverse use the `~' notation. In this case the parameter in the functional definition will usually be the name of the unit. Note that the inverse for `tempC' shows that it requires units of `K' in the specification of the allowed range of values. Nonlinear unit conversions are described in more detail in Defining Nonlinear Units. Multivariate Functions The units program supports some multivariate functions for performing cal- culations with units. The `hypot' function computes the length of a hy- potenuse given two sides. It works with any pair of values that have com- patible dimensions. You have: hypot(3 m, 4 m) You want: Definition: 5 m You can compute wind chill, based on temperature and wind speed, or heat index, based on temperature and humidity, with humidity given as a frac- tion, e.g., 0.5 for a 50% relative humidity. You have: windchill(tempF(28), 14 mph) You want: tempF 16.86826 You have: heatindex(tempC(40),0.5) You want: tempC 54.767952 Both wind chill and heat index return a value that is nominally a tempera- ture, so you will want to convert it to Fahrenheit or Celsius as shown in order to get a meaningful numerical value. UNIT LISTS: CONVERSION TO SUMS OF UNITS Outside of the SI, it is sometimes desirable to convert a single unit to a sum of units--for example, feet to feet plus inches. The conversion from sums of units was described in Sums and Differences of Units, and is a sim- ple matter of adding the units with the `+' sign: You have: 12 ft + 3 in + 3|8 in You want: ft * 12.28125 / 0.081424936 Although you can similarly write a sum of units to convert to, the result will not be the conversion to the units in the sum, but rather the conver- sion to the particular sum that you have entered: You have: 12.28125 ft You want: ft + in + 1|8 in * 11.228571 / 0.089058524 The unit expression given at the `You want:' prompt is equivalent to asking for conversion to multiples of `1 ft + 1 in + 1|8 in', which is 1.09375 ft, so the conversion in the previous example is equivalent to You have: 12.28125 ft You want: 1.09375 ft * 11.228571 / 0.089058524 In converting to a sum of units like miles, feet and inches, you typically want the largest integral value for the first unit, followed by the largest integral value for the next, and the remainder converted to the last unit. You can do this conversion easily with units using a special syntax for lists of units. You must list the desired units in order from largest to smallest, separated by the semicolon (`;') character: You have: 12.28125 ft You want: ft;in;1|8 in 12 ft + 3 in + 3|8 in The conversion always gives integer coefficients on the units in the list, except possibly the last unit when the conversion is not exact: You have: 12.28126 ft You want: ft;in;1|8 in 12 ft + 3 in + 3.00096 * 1|8 in The order in which you list the units is important: You have: 3 kg You want: oz;lb 105 oz + 0.051367866 lb You have: 3 kg You want: lb;oz 6 lb + 9.8218858 oz Listing ounces before pounds produces a technically correct result, but not a very useful one. You must list the units in descending order of size in order to get the most useful result. Ending a unit list with the separator `;' has the same effect as repeating the last unit on the list, so `ft;in;1|8 in;' is equivalent to `ft;in;1|8 in;1|8 in'. With the example above, this gives You have: 12.28126 ft You want: ft;in;1|8 in; 12 ft + 3 in + 3|8 in + 0.00096 * 1|8 in in effect separating the integer and fractional parts of the coefficient for the last unit. If you instead prefer to round the last coefficient to an integer you can do this with the `--round' (`-r') option. With the pre- vious example, the result is You have: 12.28126 ft You want: ft;in;1|8 in 12 ft + 3 in + 3|8 in (rounded down to nearest 1|8 in) When you use the `-r' option, repeating the last unit on the list has no effect (e.g., `ft;in;1|8 in;1|8 in' is equivalent to `ft;in;1|8 in'), and hence neither does ending a list with a `;'. With a single unit and the `-r' option, a terminal `;' does have an effect: it causes units to treat the single unit as a list and produce a rounded value for the single unit. Without the extra `;', the `-r' option has no effect on single unit conver- sions. This example shows the output using the `-r' option: You have: 12.28126 ft You want: in * 147.37512 / 0.0067854058 You have: 12.28126 ft You want: in; 147 in (rounded down to nearest in) Each unit that appears in the list must be conformable with the first unit on the list, and of course the listed units must also be conformable with the unit that you enter at the `You have:' prompt. You have: meter You want: ft;kg ^ conformability error ft = 0.3048 m kg = 1 kg You have: meter You want: lb;oz conformability error 1 m 0.45359237 kg In the first case, units reports the disagreement between units appearing on the list. In the second case, units reports disagreement between the unit you entered and the desired conversion. This conformability error is based on the first unit on the unit list. Other common candidates for conversion to sums of units are angles and time: You have: 23.437754 deg You want: deg;arcmin;arcsec 23 deg + 26 arcmin + 15.9144 arcsec You have: 7.2319 hr You want: hr;min;sec 7 hr + 13 min + 54.84 sec Some applications for unit lists may be less obvious. Suppose that you have a postal scale and wish to ensure that it's accurate at 1 oz, but have only metric calibration weights. You might try You have: 1 oz You want: 100 g;50 g; 20 g;10 g;5 g;2 g;1 g; 20 g + 5 g + 2 g + 1 g + 0.34952312 * 1 g You might then place one each of the 20 g, 5 g, 2 g, and 1 g weights on the scale and hope that it indicates close to You have: 20 g + 5 g + 2 g + 1 g You want: oz; 0.98767093 oz Appending `;' to `oz' forces a one-line display that includes the unit; here the integer part of the result is zero, so it is not displayed. If a non-empty list item differs vastly in scale from the quantity from which the list is to be converted, you may exceed the available precision of floating point (about 15 digits), in which case you will get a warning, e.g., You have: lightyear You want: mile;100 inch;10 inch;mm;micron 5.8786254e+12 mile + 390 * 100 inch (at 15-digit precision limit) Cooking Measure In North America, recipes for cooking typically measure ingredients by vol- ume, and use units that are not always convenient multiples of each other. Suppose that you have a recipe for 6 and you wish to make a portion for 1. If the recipe calls for 2 1/2 cups of an ingredient, you might wish to know the measurements in terms of measuring devices you have available, you could use units and enter You have: (2+1|2) cup / 6 You want: cup;1|2 cup;1|3 cup;1|4 cup;tbsp;tsp;1|2 tsp;1|4 tsp 1|3 cup + 1 tbsp + 1 tsp By default, if a unit in a list begins with fraction of the form 1|x and its multiplier is an integer, the fraction is given as the product of the multiplier and the numerator; for example, You have: 12.28125 ft You want: ft;in;1|8 in; 12 ft + 3 in + 3|8 in In many cases, such as the example above, this is what is wanted, but some- times it is not. For example, a cooking recipe for 6 might call for 5 1/4 cup of an ingredient, but you want a portion for 2, and your 1-cup measure is not available; you might try You have: (5+1|4) cup / 3 You want: 1|2 cup;1|3 cup;1|4 cup 3|2 cup + 1|4 cup This result might be fine for a baker who has a 1 1/2-cup measure (and rec- ognizes the equivalence), but it may not be as useful to someone with more limited set of measures, who does want to do additional calculations, and only wants to know "How many 1/2-cup measures to I need to add?" After all, that's what was actually asked. With the `--show-factor' option, the factor will not be combined with a unity numerator, so that you get You have: (5+1|4) cup / 3 You want: 1|2 cup;1|3 cup;1|4 cup 3 * 1|2 cup + 1|4 cup A user-specified fractional unit with a numerator other than 1 is never overridden, however--if a unit list specifies `3|4 cup;1|2 cup', a result equivalent to 1 1/2 cups will always be shown as `2 * 3|4 cup' whether or not the `--show-factor' option is given. Unit List Aliases A unit list such as cup;1|2 cup;1|3 cup;1|4 cup;tbsp;tsp;1|2 tsp;1|4 tsp can be tedious to enter. The units program provides shorthand names for some common combinations: hms time: hours, minutes, seconds dms angle: degrees, minutes, seconds time time: years, days, hours, minutes and seconds usvol US cooking volume: cups and smaller uswt US weight: pounds and ounces ftin length: feet, inches and 1/8 inches ftin2 length: feet, inches and 1/2 inches ftin4 length: feet, inches and 1/4 inches ftin8 length: feet, inches and 1/8 inches ftin16 length: feet, inches and 1/16 inches ftin32 length: feet, inches and 1/32 inches ftin64 length: feet, inches and 1/64 inches inchfine length: inches subdivided to 1/64 inch Using these shorthands, or unit list aliases, you can do the following con- versions: You have: anomalisticyear You want: time 1 year + 25 min + 3.4653216 sec You have: 1|6 cup You want: usvol 2 tbsp + 2 tsp Suppose you want to drill a clearance hole for a #10 screw and have about 1/64 inch clearance; you could try You have: screwgauge(10) + 1|64 in You want: ftin64 13.16 * 1|64 in You have: _ You want: ftin32 6.58 * 1|32 in If a slightly tight fit is acceptable, a 13/64-inch drill would do the job; if not, a 7/32-inch drill would work with a slightly looser fit. You can define your own unit list aliases; see Defining Unit List Aliases. You cannot combine a unit list alias with other units: it must appear alone at the `You want:' prompt. You can display the definition of a unit list alias by entering it at the `You have:' prompt: You have: dms Definition: unit list, deg;arcmin;arcsec When you specify compact output with `--compact', `--terse' or `-t' and perform conversion to a unit list, units lists the conversion factors for each unit in the list, separated by semicolons. You have: year You want: day;min;sec 365;348;45.974678 Unlike the case of regular output, zeros are included in this output list: You have: liter You want: cup;1|2 cup;1|4 cup;tbsp 4;0;0;3.6280454 ALTERNATIVE UNIT SYSTEMS CGS Units The SI--an extension of the MKS (meter-kilogram-second) system--has largely supplanted the older CGS (centimeter-gram-second) system, but CGS units are still used in a few specialized fields, especially in physics where they lead to a more elegant formulation of Maxwell's equations. Conversions be- tween SI and CGS involving mechanical units are straightforward, involving powers of 10 (e.g., 1 m = 100 cm). Conversions involving electromagnetic units are more complicated, and units supports four different systems of CGS units: electrostatic units (ESU), electromagnetic units (EMU), the Gaussian system and the Heaviside-Lorentz system. The differences between these systems arise from different choices made for proportionality con- stants in electromagnetic equations. Coulomb's law gives electrostatic force between two charges separated by a distance delim $$ r: F = k_C q_1 q_2 / r^2. Ampere's law gives the electromagnetic force per unit length between two current-carrying conductors separated by a distance r: F/l = 2 k_A I_1 I_2 / r. The two constants, k_C and k_A, are related by the square of the speed of light: k_A = k_C / c^2. In the SI, the constants have dimensions, and an additional base unit, the ampere, measures electric current. The CGS systems do not define new base units, but express charge and current as derived units in terms of mass, length, and time. In the ESU system, the constant for Coulomb's law is chosen to be unity and dimensionless, which defines the unit of charge. In the EMU system, the constant for Ampere's law is chosen to be unity and di- mensionless, which defines a unit of current. The Gaussian system usually uses the ESU units for charge and current; it chooses another constant so that the units for the electric and magnetic fields are the same. The Heaviside-Lorentz system is "rationalized" so that factors of 4{pi} do not appear in Maxwell's equations. The SI system is similarly rationalized, but the other CGS systems are not. In the Heaviside-Lorentz (HLU) system the factor of 4{pi} appears in Coulomb's law instead; this system differs from the Gaussian system by factors of the square root of 4{pi} The dimensions of electrical quantities in the various CGS systems are dif- ferent from the SI dimensions for the same units; strictly, conversions be- tween these systems and SI are not possible. But units in different sys- tems relate to the same physical quantities, so there is a correspondence between these units. The units program defines the units so that you can convert between corresponding units in the various systems. The CGS definitions involve cm^(1/2) and g^(1/2), which is problematic be- cause units does not normally support fractional roots of base units. The `--units' (`-u') option allows selection of a CGS unit system and works around this restriction by introducing base units for the square roots of length and mass: `sqrt_cm' and `sqrt_g'. The centimeter then becomes `sqrt_cm^2' and the gram, `sqrt_g^2'. This allows working from equations using the units in the CGS system, and enforcing dimensional conformity within that system. Recognized CGS arguments to the `--units' option are `gauss[ian]', `esu', `emu', `lhu'; the argument is case insensitive. You can also give `si' which just enforces the default SI mode and displays `(SI)' at the `You have:' prompt to emphasize the units mode. Some other types of units are also supported as described below. Giving an unrecog- nized system generates a warning, and units uses SI units. The changes resulting from the `--units' option are actually controlled by the UNITS_SYSTEM environment variable. If you frequently work with one of the supported CGS units systems, you may set this environment variable rather than giving the `--units' option at each invocation. As usual, an option given on the command line overrides the setting of the environment variable. For example, if you would normally work with Gaussian units but might occasionally work with SI, you could set UNITS_SYSTEM to `gaussian' and specify SI with the `--units' option. Unlike the argument to the `--units' option, the value of UNITS_SYSTEM is case sensitive, so setting a value of `EMU' will have no effect other than to give an error message and set SI units. The CGS definitions appear as conditional settings in the standard units data file, which you can consult for more information on how these units are defined, or on how to define an alternate units system. The ESU system derives the electromagnetic units from its unit of charge, the statcoulomb, which is defined from Coulomb's law. The statcoulomb equals dyne^(1/2) cm, or cm^(3/2) g^(1/2) s^(-1). The unit of current, the statampere, is statcoulomb sec, analogous to the relationship in SI. Other electrical units are then derived in a manner similar to that for SI units; the units use the SI names prefixed by `stat-', e.g., `statvolt' or `statV'. The prefix `st-' is also recognized (e.g., `stV'). The EMU system derives the electromagnetic units from its unit of current, the abampere, which is defined in terms of Ampere's law. The abampere is equal to dyne^(1/2), or cm^(1/2) g^(1/2) s^(-1). delim off The unit of charge, the abcoulomb, is abampere sec, again analogous to the SI relation- ship. Other electrical units are then derived in a manner similar to that for SI units; the units use the SI names prefixed by `ab-', e.g., `abvolt' or `abV'. The magnetic field units include the gauss, the oersted and the maxwell. The Gaussian units system, which was also known as the Symmetric System, uses the same charge and current units as the ESU system (e.g., `statC', `statA'); it differs by defining the magnetic field so that it has the same units as the electric field. The resulting magnetic field units are the same ones used in the EMU system: the gauss, the oersted and the maxwell. The Heaviside-Lorentz system appears to lack named units. We define five basic units, `hlu_charge', `hlu_current', `hlu_volt', `hlu_efield' and `hlu_bfield' for conversions with this system. It is important to remember that with all of the CGS systems, the units may look the same but mean something different. The HLU system and Gaussian systems both measure mag- netic field using the same CGS dimensions, but the amount of magnetic field with the same units is different in the two systems. The CGS systems define units that measure the same thing but may have con- flicting dimensions. Furthermore, the dimensions of the electromagnetic CGS units are never compatible with SI. But if you measure charge in two different systems you have measured the same physical thing, so there is a correspondence between the units in the different systems, and units sup- ports conversions between corresponding units. When running with SI, units defines all of the CGS units in terms of SI. When you select a CGS system, units defines the SI units and the other CGS system units in terms of the system you have selected. (Gaussian) You have: statA You want: abA * 3.335641e-11 / 2.9979246e+10 (Gaussian) You have: abA You want: sqrt(dyne) conformability error 2.9979246e+10 sqrt_cm^3 sqrt_g / s^2 1 sqrt_cm sqrt_g / s In the above example, units converts between the current units statA and abA even though the abA, from the EMU system, has incompatible dimensions. This works because in Gaussian mode, the abA is defined in terms of the statA, so it does not have the correct definition for EMU; consequently, you cannot convert the abA to its EMU definition. One challenge of conversion is that because the CGS system has fewer base units, quantities that have different dimensions in SI may have the same dimension in a CGS system. And yet, they may not have the same conversion factor. For example, the unit for the E field and B fields are the same in the Gaussian system, but the conversion factors to SI are quite different. This means that correct conversion is only possible if you keep track of what quantity is being measured. You cannot convert statV/cm to SI without indicating which type of field the unit measures. To aid in dimensional analysis, units defines various dimension units such as `LENGTH', `TIME', and `CHARGE' to be the appropriate dimension in SI. The electromagnetic dimensions such as `B_FIELD' or `E_FIELD' may be useful aids both for con- version and dimensional analysis in CGS. You can convert them to or from CGS in order to perform SI conversions that in some cases will not work di- rectly due to dimensional incompatibilities. This example shows how the Gaussian system uses the same units for all of the fields, but they all have different conversion factors with SI. (Gaussian) You have: statV/cm You want: E_FIELD * 29979.246 / 3.335641e-05 (Gaussian) You have: statV/cm You want: B_FIELD * 0.0001 / 10000 (Gaussian) You have: statV/cm You want: H_FIELD * 79.577472 / 0.012566371 (Gaussian) You have: statV/cm You want: D_FIELD * 2.6544187e-07 / 3767303.1 The next example shows that the oersted cannot be converted directly to the SI unit of magnetic field, A/m, because the dimensions conflict. We cannot redefine the ampere to make this work because then it would not convert with the statampere. But you can still do this conversion as shown below. (Gaussian) You have: oersted You want: A/m conformability error 1 sqrt_g / s sqrt_cm 29979246 sqrt_cm sqrt_g / s^2 (Gaussian) You have: oersted You want: H_FIELD * 79.577472 / 0.012566371 Natural Units Like the CGS units, "natural" units are an alternative to the SI system used primarily physicists in different fields, with different systems tai- lored to different fields of study. These systems are "natural" because the base measurements are defined using physical constants instead of arbi- trary values such as the meter or second. In different branches of physics, different physical constants are more fundamental, which has given rise to a variety of incompatible natural unit systems. The supported systems are the "natural" units (which seem to have no better name) used in high energy physics and cosmology, the Planck units, often used by scientists working with gravity, and the Hartree atomic units are favored by those working in physical chemistry and condensed matter physics. You can select the various natural units using the `--units' option in the same way that you select the CGS units. The "natural" units come in two types, a rationalized system derived from the Heaviside-Lorentz units and an unrationalized system derived from the Gaussian system. You can select these using `natural' and `natural-gauss' respectively. For conversions in SI mode, several unit names starting with `natural' are available. This "natural" system is defined by setting {hbar}, c and the Boltzman constant to 1. Only a single base unit remains: the electron volt. The Planck units exist in a variety of forms, and units supports two. Both supported forms are rationalized, in that factors of 4{pi} do not appear in Maxwell's equations. However, Planck units can also differ based on how the gravitational constant is treated. This system is similar to the nat- ural units in that c, {hbar}, and Boltzman's constant are set to 1, but in this system, Newton's gravitational constant, G is also fixed. In the "re- duced" Planck system, delim $$ 8{pi}G = 1 whereas in the unreduced system G = 1. The reduced system eliminates factors of 8{pi} delim off from the Einstein field equations for gravitation, so this is similar to the process of forming rationalized units to simplify Maxwell's equations. To obtain the unreduced system use the name `planck' and for the reduced Planck units, `planck-red'. Units such as `planckenergy' and `planckenergy_red' enable you to convert the unreduced and reduced Planck energy unit in SI mode between the various systems. In Planck units, all measurements are dimensionless. The final natural unit system is the Hartree atomic units. Like the Planck units, all measurements in the Hartree units are dimensionless, but this system is defined by defined from completely different physical constants: the electron mass, Planck's constant, the electron charge, and the Coulomb constant are the defining physical quantities, which are all set to unity. To invoke this system with the `--units' option use the name `hartree'. Prompt Prefix If a unit system is specified with the `--units' option, the selected sys- tem's name is prepended to the `You have:' prompt as a reminder, e.g., (Gaussian) You have: stC You want: Definition: statcoulomb = sqrt(dyne) cm = 1 sqrt_cm^3 sqrt_g / s You can suppressed the prefix by including a line !prompt with no argument in a site or personal units data file. The prompt can be conditionally suppressed by including such a line within `!var' ... `!end- var' constructs, e.g., !var UNITS_SYSTEM gaussian gauss !prompt !endvar This might be appropriate if you normally use Gaussian units and find the prefix distracting but want to be reminded when you have selected a differ- ent CGS system. LOGGING CALCULATIONS The `--log' option allows you to save the results of calculations in a file; this can be useful if you need a permanent record of your work. For example, the fluid-flow conversion in Complicated Unit Expressions, is lengthy, and if you were to use it in designing a piping system, you might want a record of it for the project file. If the interactive session # Conversion factor A1 for pressure drop # dP = A1 rho f L Q^2/d^5 You have: (8/pi^2) (lbm/ft^3)ft(ft^3/s)^2(1/in^5) # Input units You want: psi * 43.533969 / 0.022970568 were logged, the log file would contain ### Log started Fri Oct 02 15:55:35 2015 # Conversion factor A1 for pressure drop # dP = A1 rho f L Q^2/d^5 From: (8/pi^2) (lbm/ft^3)ft(ft^3/s)^2(1/in^5) # Input units To: psi * 43.533969 / 0.022970568 The time is written to the log file when the file is opened. The use of comments can help clarify the meaning of calculations for the log. The log includes conformability errors between the units at the `You have:' and `You want:' prompts, but not other errors, including lack of conformability of items in sums or differences or among items in a unit list. For example, a conversion between zenith angle and elevation angle could involve You have: 90 deg - (5 deg + 22 min + 9 sec) ^ Invalid sum or difference of non-conformable units You have: 90 deg - (5 deg + 22 arcmin + 9 arcsec) You want: dms 84 deg + 37 arcmin + 51 arcsec You have: _ You want: deg * 84.630833 / 0.011816024 You have: The log file would contain From: 90 deg - (5 deg + 22 arcmin + 9 arcsec) To: deg;arcmin;arcsec 84 deg + 37 arcmin + 51 arcsec From: _ To: deg * 84.630833 / 0.011816024 The initial entry error (forgetting that minutes have dimension of time, and that arcminutes must be used for dimensions of angle) does not appear in the output. When converting to a unit list alias, units expands the alias in the log file. The `From:' and `To:' tags are written to the log file even if the `--quiet' option is given. If the log file exists when units is invoked, the new results are appended to the log file. The time is written to the log file each time the file is opened. The `--log' option is ignored when units is used non-interactively. INVOKING UNITS You invoke units like this: units [options] [from-unit [to-unit]] If the from-unit and to-unit are omitted, the program will use interactive prompts to determine which conversions to perform. See Interactive Use. If both from-unit and to-unit are given, units will print the result of that single conversion and then exit. If only from-unit appears on the command line, units will display the definition of that unit and exit. Units specified on the command line may need to be quoted to protect them from shell interpretation and to group them into two arguments. Note also that the `--quiet' option is enabled by default if you specify from-unit on the command line. See Command Line Use. The default behavior of units can be changed by various options given on the command line. In most cases, the options may be given in either short form (a single `-' followed by a single character) or long form (`--' fol- lowed by a word or hyphen-separated words). Short-form options are cryptic but require less typing; long-form options require more typing but are more explanatory and may be more mnemonic. With long-form options you need only enter sufficient characters to uniquely identify the option to the program. For example, `--out %f' works, but `--o %f' fails because units has other long options beginning with `o'. However, `--q' works because `--quiet' is the only long option beginning with `q'. Some options require arguments to specify a value (e.g., `-d 12' or `--dig- its 12'). Short-form options that do not take arguments may be concate- nated (e.g., `-erS' is equivalent to `-e -r -S'); the last option in such a list may be one that takes an argument (e.g., `-ed 12'). With short-form options, the space between an option and its argument is optional (e.g., `-d12' is equivalent to `-d 12'). Long-form options may not be concate- nated, and the space between a long-form option and its argument is re- quired. Short-form and long-form options may be intermixed on the command line. Options may be given in any order, but when incompatible options (e.g., `--output-format' and `--exponential') are given in combination, be- havior is controlled by the last option given. For example, `-o%.12f -e' gives exponential format with the default eight significant digits). Many options can be set interactively; this can be especially helpful for Windows users who start units from a shortcut. See Setting Options Inter- actively for more information. The following options are available: -c, --check Check that all units and prefixes defined in units data files reduce to primitive units. Display a list of all units that cannot be re- duced and a list of units with circular definitions. Also display some other diagnostics about suspicious definitions in the units data file. Only definitions active in the current locale are checked. You should always run units with this option after modify- ing a units data file. Some errors may hide other errors, so you should run units with this option again after correcting any errors, and keep doing so until there are no errors. --check-verbose, --verbose-check Like the `--check' option, this option displays a list of units that cannot be reduced. But it also lists the units as they are checked. Because the `--check' option now catches circular unit definitions that previously caused units to hang, this option is no longer nec- essary. It is retained only for compatibility with previous ver- sions. --list-units This option displays a list of all units and exits. With output redirected to a file, it can produce a list of all units in the database, which may comprise multiple units data files. It can also be useful if you aren't sure of the name of a unit or want to find all units of a particular type and you want a more advanced search than is available with the interactive search command. See Finding Units for some examples of how this option can be used. -d ndigits, --digits ndigits Set the number of significant digits in the output to the value specified (which must be greater than zero). For example, `-d 12' sets the number of significant digits to 12. With exponential out- put, units displays one digit to the left of the decimal point and eleven digits to the right of the decimal point. On most systems, the maximum number of internally meaningful digits is 15; if you specify a greater number than your system's maximum, units will print a warning and set the number to the largest meaningful value. To directly set the maximum value, give an argument of max (e.g., `-d max'). Be aware, of course, that "significant" here refers only to the display of numbers; if results depend on physical constants not known to this precision, the physically meaningful precision may be less than that shown. The `--digits' option is incompatible with the `--output-format' option; if you give them both, the format is controlled by the last option given. -e, --exponential Set the numeric output format to exponential (i.e., scientific nota- tion), like that used in the Unix units program. The default preci- sion is eight significant digits (seven digits to the right of the decimal point); this can be changed with the `--digits' option. The `--exponential' option is incompatible with the `--output-format' option; if you give them both, the format is controlled by the last option given. -o format, --output-format format This option affords complete control over the numeric output format using the specified format. The format is a single floating point numeric format for the printf function in the C programming lan- guage. All compilers support the format types `g' and `G' to spec- ify significant digits, `e' and `E' for scientific notation, and `f' for fixed-point decimal. The ISO C99 standard introduced the `F' type for fixed-point decimal and the `a' and `A' types for hexadeci- mal floating point; these types are allowed with compilers that sup- port them. The default format is `%.8g'; for greater precision, you could specify `-o %.15g'. Unlike with the `--digits' option, you can specify any desired precision, though not all digits may be meaningful. See Numeric Output Format and the documentation for printf for more detailed descriptions of the format specification. The `--output-format' option affords the greatest control of the output appearance, but requires at least rudimentary knowledge of the printf format syntax. If you don't want to bother with the printf syntax, you can specify greater precision more simply with the `--digits' option or select exponential format with `--exponen- tial'. The `--output-format' option is incompatible with the `--ex- ponential' and `--digits' options; if you give either in combination with `--output-format', the format is controlled by the last option given. -f filename, --file filename Instruct units to load the units file filename. You can specify up to 25 units files on the command line. When you use this option, units will load only the files you list on the command line; it will not load the standard file or your personal units file unless you explicitly list them. If filename is the empty string (`-f ""'), the default main units file (or that specified by UNITSFILE) will be loaded in addition to any others specified with `-f'. -L logfile, --log logfile Save the results of calculations in the file logfile; this can be useful if it is important to have a record of unit conversions or other calculations that are to be used extensively or in a critical activity such as a program or design project. If logfile exits, the new results are appended to the file. This option is ignored when units is used non-interactively. See Logging Calculations for a more detailed description and some examples. -H filename, --history filename Instruct units to save history to filename, so that a record of your commands is available for retrieval across different units invoca- tions. To prevent the history from being saved set filename to the empty string (`-H ""'). This option has no effect if readline is not available. -h, --help Print out a summary of the options for units. -m, --minus Causes `-' to be interpreted as a subtraction operator. This is the default behavior. -p, --product Causes `-' to be interpreted as a multiplication operator when it has two operands. It will act as a negation operator when it has only one operand: `(-3)'. By default `-' is treated as a subtrac- tion operator. --oldstar Causes `*' to have the old-style precedence, higher than the prece- dence of division so that `1/2*3' will equal `1/6'. --newstar Forces `*' to have the new (default) precedence that follows the usual rules of algebra: the precedence of `*' is the same as the precedence of `/', so that `1/2*3' will equal `3/2'. -r, --round When converting to a combination of units given by a unit list, round the value of the last unit in the list to the nearest integer. -S, --show-factor When converting to a combination of units specified in a list, al- ways show a non-unity factor before a unit that begins with a frac- tion with a unity denominator. By default, if the unit in a list begins with fraction of the form 1|x and its multiplier is an inte- ger other than 1, the fraction is given as the product of the multi- plier and the numerator (e.g., `3|8 in' rather than `3 * 1|8 in'). In some cases, this is not what is wanted; for example, the results for a cooking recipe might show `3 * 1|2 cup' as `3|2 cup'. With the `--show-factor' option, a result equivalent to 1.5 cups will display as `3 * 1|2 cup' rather than `3|2 cup'. A user-specified fractional unit with a numerator other than 1 is never overridden, however--if a unit list specifies `3|4 cup;1|2 cup', a result equiv- alent to 1 1/2 cups will always be shown as `2 * 3|4 cup' whether or not the `--show-factor' option is given. --conformable In non-interactive mode, show all units conformable with the origi- nal unit expression. Only one unit expression is allowed; if you give more than one, units will exit with an error message and return failure. -v, --verbose Give slightly more verbose output when converting units. When com- bined with the `-c' option this gives the same effect as `--check- verbose'. When combined with `--version' produces a more detailed output, equivalent to the `--info' option. -V, --version Print the program version number, tell whether the readline library has been included, tell whether UTF-8 support has been included; give the locale, the location of the default main units data file, and the location of the personal units data file; indicate if the personal units data file does not exist. When given in combination with the `--terse' option, the program prints only the version number and exits. When given in combination with the `--verbose' option, the program, the `--version' option has the same effect as the `--info' option below. -I, --info Print the information given with the `--version' option, show the pathname of the units program, show the status of the UNITSFILE and MYUNITSFILE environment variables, and additional information about how units locates the related files. On systems running Microsoft Windows, the status of the UNITSLOCALE environment variable and in- formation about the related locale map are also given. This option is usually of interest only to developers and administrators, but it can sometimes be useful for troubleshooting. Combining the `--version' and `--verbose' options has the same ef- fect as giving `--info'. -U, --unitsfile Print the location of the default main units data file and exit; if the file cannot be found, print "Units data file not found". -u units-system, --units units-system Specify a CGS units system or natural units system. The supported units systems are: gauss[ian], esu, emu, hlu, natural, natural- gauss, hartree, planck, planck-red, and si. See Alternative Unit Systems for further information about these unit systems. -l locale, --locale locale Force a specified locale such as `en_GB' to get British definitions by default. This overrides the locale determined from system set- tings or environment variables. See Locale for a description of lo- cale format. -n, --nolists Disable conversion to unit lists. -s, --strict Suppress conversion of units to their reciprocal units. For exam- ple, units will normally convert hertz to seconds because these units are reciprocals of each other. The strict option requires that units be strictly conformable to perform a conversion, and will give an error if you attempt to convert hertz to seconds. -1, --one-line Give only one line of output (the forward conversion); do not print the reverse conversion. If a reciprocal conversion is performed, then units will still print the "reciprocal conversion" line. -t, --terse Print only a single conversion factor without any clutter, or if you request a definition, prints just the definition (including its units). This option can be used when calling units from another program so that the output is easy to parse. The command units --terse mile m produces the output `1690.344'. This option has the combined effect of these options: `--strict' `--quiet' `--one-line' `--compact'. When combined with `--version' it produces a display showing only the program name and version number. --compact Give compact output featuring only the conversion factor; the multi- plication and division signs are not shown, and there is no leading whitespace. If you convert to a unit list, then the output is a semicolon separated list of factors. This turns off the `--verbose' option. -q, --quiet, --silent Suppress the display of statistics about the number of units loaded, any messages printed by the units database, and the prompting of the user for units. This option does not affect how units displays the results. This option is turned on by default if you invoke units with a unit expression on the command line. SETTING OPTIONS INTERACTIVELY Many command-line options can also be set interactively, obviating the need to quit and restart units to change the values. This can be especially helpful for Windows users who start units from a shortcut. Typing set will display a list of all options that can be set interac- tively, as well as the current and possible values; options set to other than default values have an asterisk (`*') prepended. For example, You have: set q[uiet] = no (y|n) do/don't suppress prompting o[neline] = no (y|n) do/don't suppress the second line of output st[rict] = no (y|n) do/don't suppress reciprocal unit conversion (e.g., Hz<->s) t[erse] = no (y|n) do/don't give very terse output c[ompact] = no (y|n) do/don't suppress printing tab, SETFLAG, and '/' characters in results v[erbose] = 1 (0|1|2) amount of information shown *d[igits] = 9 number of significant digits in output e[xponential] = no (y|n) do/don't use exponential ("scientific") notation *f[ormat] = %.9g printf(3) format specification u[nitlists] = yes (y|n) do/don't allow conversion to unit lists r[ound] = no (y|n) do/don't round last element of unit list output to an integer sh[owfactor] = no (y|n) do/don't show non-unity factor before 1|x in multi-unit output Characters within the square brackets are optional, so settings can be changed by entering only one or two characters. The syntax for setting options is set option = value; the spaces around the `=' sign are optional. Some settings are Boolean, enabled by entering yes (or just y) and disabled by entering no (or just n). For example, You have: set quiet = y quiet = yes Other settings take an integer value; for example, You have: set d=11 digits = 11 format = %.11g The format setting takes a string, the format specification for the printf function in the C programming language; for example, You have: set format = %.9g format = %.9g Typing set option will display the current value of option, for example You have: set u unitlists = yes You have: set d digits = 8 format = %.8g For the digits and exponential options, the value of format is also shown. SCRIPTING WITH UNITS Despite its numerous options, units cannot cover every conceivable unit- conversion task. For example, suppose we have found some mysterious scale, but cannot figure out the units in which it is reporting. We reach into our pocket, place a 3.75-gram coin on the scale, and observe the scale reading `0.120'. How do we quickly determine the units? Or we might won- der if a unit has any "synonyms," i.e., other units with the same value. The capabilities of units are easily extended with simple scripting. Both questions above involve conformable units; on a system with Unix-like util- ities, conversions to conformable units could be shown accomplished with the following script: #!/bin/sh progname=`basename $0 .sh` umsg="Usage: $progname [<number>] unit" if [ $# -lt 1 ] then echo "$progname: missing quantity to convert" echo "$umsg" exit 1 fi for unit in `units --conformable "$*" | cut -f 1 -d ' '` do echo "$*" # have -- quantity to convert echo $unit # want -- conformable unit done | units --terse --verbose When units is invoked with no non-option arguments, it reads have/want pairs, on alternating lines, from its standard input, so the task can be accomplished with only two invocations of units. This avoids the computa- tional overhead of needlessly reprocessing the units database for each con- formable unit, as well as the inherent system overhead of process invoca- tion. By itself, the script is not very useful. But it could be used in combina- tion with other commands to address specific tasks. For example, running the script through a simple output filter could help solve the scale prob- lem above. If the script is named conformable, running $ conformable 3.75g | grep 0.120 gives 3.75g = 0.1205653 apounce 3.75g = 0.1205653 fineounce 3.75g = 0.1205653 ozt 3.75g = 0.1205653 tradewukiyeh 3.75g = 0.1205653 troyounce So we might conclude that the scale is calibrated in troy ounces. We might run $ units --verbose are Definition: 100 m^2 = 100 m^2 and wonder if `are' has any synonyms, value. To find out, we could run $ conformable are | grep "= 1 " are = 1 a are = 1 are OUTPUT STYLES The output can be tweaked in various ways using command line options. With no options, the output looks like this $ units Currency exchange rates from FloatRates (USD base) on 2023-07-08 3612 units, 109 prefixes, 122 nonlinear units You have: 23ft You want: m * 7.0104 / 0.14264521 You have: m You want: ft;in 3 ft + 3.3700787 in This is arguably a bit cryptic; the `--verbose' option makes clear what the output means: $ units --verbose Currency exchange rates from FloatRates (USD base) on 2023-07-08 3612 units, 109 prefixes, 122 nonlinear units You have: 23 ft You want: m 23 ft = 7.0104 m 23 ft = (1 / 0.14264521) m You have: meter You want: ft;in meter = 3 ft + 3.3700787 in The `--quiet' option suppresses the clutter displayed when units starts, as well as the prompts to the user. This option is enabled by default when you give units on the command line. $ units --quiet 23 ft m * 7.0104 / 0.14264521 $ units 23ft m * 7.0104 / 0.14264521 The remaining style options allow you to display only numerical values without the tab or the multiplication and division signs, or to display just a single line showing the forward conversion: $ units --compact 23ft m 7.0104 0.14264521 $ units --compact m 'ft;in' 3;3.3700787 $ units --one-line 23ft m * 7.0104 $ units --one-line 23ft 1/m reciprocal conversion * 0.14264521 $ units --one-line 23ft kg conformability error 7.0104 m 1 kg Note that when converting to a unit list, the `--compact' option displays a semicolon separated list of results. Also be aware that the `one-line' op- tion doesn't live up to its name if you execute a reciprocal conversion or if you get a conformability error. The former case can be prevented using the `--strict' option, which suppresses reciprocal conversions. Similarly you can suppress unit list conversion using `--nolists'. It is impossible to prevent the three line error output. $ units --compact --nolists m 'ft;in' Error in 'ft;in': Parse error $ units --one-line --strict 23ft 1/m The various style options can be combined appropriately. The ultimate com- bination is the `--terse' option, which combines `--strict', `--quiet', `--one-line', and `--compact' to produce the minimal output, just a single number for regular conversions and a semicolon separated list for conver- sion to unit lists. This will likely be the best choice for programs that want to call units and then process its result. $ units --terse 23ft m 7.0104 $ units --terse m 'ft;in' 3;3.3700787 $ units --terse 23ft 1/m conformability error 7.0104 m 1 / m $ units --terse '1 mile' 1609.344 m $ units --terse mile 5280 ft = 1609.344 m ADDING YOUR OWN DEFINITIONS Units Data Files The units and prefixes that units can convert are defined in the units data file, typically `/usr/share/units/definitions.units'. If you can't find this file, run units --version to get information on the file locations for your installation. Although you can extend or modify this data file if you have appropriate user privileges, it's usually better to put extensions in separate files so that the definitions will be preserved if you update units. You can include additional data files in the units database using the `!in- clude' command in the standard units data file. For example !include /usr/local/share/units/local.units might be appropriate for a site-wide supplemental data file. The location of the `!include' statement in the standard units data file is important; later definitions replace earlier ones, so any definitions in an included file will override definitions before the `!include' statement in the stan- dard units data file. With normal invocation, no warning is given about redefinitions; to ensure that you don't have an unintended redefinition, run units -c after making changes to any units data file. If you want to add your own units in addition to or in place of standard or site-wide supplemental units data files, you can include them in the `.units' file in your home directory. If this file exists it is read after the standard units data file, so that any definitions in this file will re- place definitions of the same units in the standard data file or in files included from the standard data file. This file will not be read if any units files are specified on the command line. (Under Windows the personal units file is named `unitdef.units'.) Running units -V will display the location and name of your personal units file. The units program first tries to determine your home directory from the HOME environment variable. On systems running Microsoft Windows, if HOME does not exist, units attempts to find your home directory from HOMEDRIVE, HOMEPATH and USERPROFILE. You can specify an arbitrary file as your per- sonal units data file with the MYUNITSFILE environment variable; if this variable exists, its value is used without searching your home directory. The default units data files are described in more detail in Data Files. Defining New Units and Prefixes A unit is specified on a single line by giving its name and an equivalence. Comments start with a `#' character, which can appear anywhere in a line. The backslash character (`\') acts as a continuation character if it ap- pears as the last character on a line, making it possible to spread defini- tions out over several lines if desired. A file can be included by giving the command `!include' followed by the file's name. The `!' must be the first character on the line. The file will be sought in the same directory as the parent file unless you give a full path. The name of the file to be included cannot contain spaces or the comment character `#'. Unit names cannot begin or end with an underscore (`_') or a decimal point (`.'), and cannot contain any of the operator characters `+', `-', `*', `/', `|', `^', `;', `~', a comma (`,'), the comment character `#', or parentheses. To facilitate copying and pasting from documents, several ty- pographical characters are converted to operators: the figure dash (U+2012), minus (`-'; U+2212), and en dash (`-'; U+2013) are converted to the operator `-'; the multiplication sign (`x'; U+00D7), N-ary times opera- tor (U+2A09), dot operator (`.'; U+22C5), and middle dot (`.'; U+00B7) are converted to the operator `*'; the division sign (`/'; U+00F7) is converted to the operator `/'; and the fraction slash (U+2044) is converted to the operator `|'; accordingly, none of these characters can appear in unit names. Names cannot begin with a digit, and if a name ends in a digit other than zero or one, then the name must end with an underscore followed by a string consisting only of digits and decimal points. For example, `foo_2', `foo_3.14', and `foo_3...\&9' are valid names but `foo2' or `foo_a2' are invalid. The underscore is necessary because without it, units cannot de- termine whether `foo2' is a unit name or represents `foo^2'. Zero and one are exceptions because units never interprets them as exponents. You could define nitrous oxide as N2O nitrogen 2 + oxygen but would need to define nitrogen dioxide as NO_2 nitrogen + oxygen 2 Be careful to define new units in terms of old ones so that a reduction leads to the primitive units, which are marked with `!' characters. Di- mensionless units are indicated by using the string `!dimensionless' for the unit definition. When adding new units, be sure to use the `-c' option to check that the new units reduce properly and that there are no circular definitions that lead to endless loops. Because some errors may hide other errors, you should run units with the `-c' option again after correcting any errors, and keep doing so until no errors are displayed. If you define any units that contain `+' characters in their definitions, carefully check them because the `-c' option will not catch non-conformable sums. Be careful with the `-' operator as well. When used as a binary op- erator, the `-' character can perform addition or multiplication depending on the options used to invoke units. To ensure consistent behavior use `-' only as a unary negation operator when writing units definitions. To mul- tiply two units leave a space or use the `*' operator with care, recalling that it has two possible precedence values and may require parentheses to ensure consistent behavior. To compute the difference of `foo' and `bar' write `foo+(-bar)' or even `foo+-bar'. You may wish to intentionally redefine a unit. When you do this, and use the `-c' option, units displays a warning message about the redefinition. You can suppress these warnings by redefining a unit using a `+' at the be- ginning of the unit name. Do not include any white space between the `+' and the redefined unit name. Here is an example of a short data file that defines some basic units: m ! # The meter is a primitive unit sec ! # The second is a primitive unit rad !dimensionless # A dimensionless primitive unit micro- 1e-6 # Define a prefix minute 60 sec # A minute is 60 seconds hour 60 min # An hour is 60 minutes inch 72 m # Inch defined incorrectly terms of meters ft 12 inches # The foot defined in terms of inches mile 5280 ft # And the mile +inch 0.0254 m # Correct redefinition, warning suppressed A unit that ends with a `-' character is a prefix. If a prefix definition contains any `/' characters, be sure they are protected by parentheses. If you define `half- 1/2', then `halfmeter' would be equivalent to `1 / (2 me- ter)'. Defining Nonlinear Units Some unit conversions of interest are nonlinear; for example, temperature conversions between the Fahrenheit and Celsius scales cannot be done by simply multiplying by conversion factors. When you give a linear unit definition such as `inch 2.54 cm' you are pro- viding information that units uses to convert values in inches into primi- tive units of meters. For nonlinear units, you give a functional defini- tion that provides the same information. Nonlinear units are represented using a functional notation. It is best to regard this notation not as a function call but as a way of adding units to a number, much the same way that writing a linear unit name after a number adds units to that number. Internally, nonlinear units are defined by a pair of functions that convert to and from linear units in the database, so that an eventual conversion to primitive units is possible. Here is an example nonlinear unit definition: tempF(x) units=[1;K] domain=[-459.67,) range=[0,) \ (x+(-32)) degF + stdtemp ; (tempF+(-stdtemp))/degF + 32 A nonlinear unit definition comprises a unit name, a formal parameter name, two functions, and optional specifications for units, the domain, and the range (the domain of the inverse function). The functions tell units how to convert to and from the new unit. To produce valid results, the argu- ments of these functions need to have the correct dimensions and be within the domains for which the functions are defined. The definition begins with the unit name followed immediately (with no spaces) by a `(' character. In the parentheses is the name of the formal parameter. Next is an optional specification of the units required by the functions in the definition. In the example above, the `units=[1;K]' spec- ification indicates that the `tempF' function requires an input argument conformable with `1' (i.e., the argument is dimensionless), and that the inverse function requires an input argument conformable with `K'. For nor- mal nonlinear units definition, the forward function will always take a di- mensionless argument; in general, the inverse function will need units that match the quantity measured by your nonlinear unit. Specifying the units enables units to perform error checking on function arguments, and also to assign units to domain and range specifications, which are described later. Next the function definitions appear. In the example above, the `tempF' function is defined by tempF(x) = (x+(-32)) degF + stdtemp This gives a rule for converting `x' in the units `tempF' to linear units of absolute temperature, which makes it possible to convert from tempF to other units. To enable conversions to Fahrenheit, you must give a rule for the inverse conversions. The inverse will be `x(tempF)' and its definition appears af- ter a `;' character. In our example, the inverse is x(tempF) = (tempF+(-stdtemp))/degF + 32 This inverse definition takes an absolute temperature as its argument and converts it to the Fahrenheit temperature. The inverse can be omitted by leaving out the `;' character and the inverse definition, but then conver- sions to the unit will not be possible. If the inverse definition is omit- ted, the `--check' option will display a warning. It is up to you to cal- culate and enter the correct inverse function to obtain proper conversions; the `--check' option tests the inverse at one point and prints an error if it is not valid there, but this is not a guarantee that your inverse is correct. With some definitions, the units may vary. For example, the definition square(x) x^2 can have any arbitrary units, and can also take dimensionless arguments. In such a case, you should not specify units. If a definition takes a root of its arguments, the definition is valid only for units that yield such a root. For example, squirt(x) sqrt(x) is valid for a dimensionless argument, and for arguments with even powers of units. Some definitions may not be valid for all real numbers. In such cases, units can handle errors better if you specify an appropriate domain and range. You specify the domain and range as shown below: baume(d) units=[1;g/cm^3] domain=[0,130.5] range=[1,10] \ (145/(145-d)) g/cm^3 ; (baume+-g/cm^3) 145 / baume In this example the domain is specified after `domain=' with the two numer- ical endpoints given in brackets. No spaces can appear before the `='. In accord with mathematical convention, square brackets indicate a closed in- terval (one that includes its endpoints), and parentheses indicate an open interval (one that does not include its endpoints). An interval can be open or closed on one or both ends; an interval that is unbounded on either end is indicated by omitting the limit on that end. For example, a quan- tity to which decibel (dB) is applied may have any value greater than zero, so the range is indicated by `(0,)': decibel(x) units=[1;1] range=(0,) 10^(x/10); 10 log(decibel) If the domain or range is given, the second endpoint must be greater than the first. The intervals given for the domain and range must be numbers and cannot include units or any calculations. The domain and range specifications can appear independently and in any or- der along with the units specification. The values for the domain and range endpoints are attached to the units given in the units specification, and if necessary, the parameter value is adjusted for comparison with the endpoints. For example, if a definition includes `units=[1;ft]' and `range=[3,)', the range will be taken as 3 ft to infinity. If the function is passed a parameter of `900 mm', that value will be adjusted to 2.9527559 ft, which is outside the specified range. If you omit the units specification from the previous example, units can not tell whether you in- tend the lower endpoint to be 3 ft or 3 microfurlongs, and can not adjust the parameter value of 900 mm for comparison. Without units, numerical values other than zero or plus or minus infinity for domain or range end- points are meaningless, and accordingly they are not allowed. If you give other values without units, then the definition will be ignored and you will get an error message. Although the units, domain, and range specifications are optional, it's best to give them when they are applicable; doing so allows units to per- form better error checking and give more helpful error messages. Giving the domain and range also enables the `--check' option to find a point in the domain to use for its point check of your inverse definition. You can make synonyms for nonlinear units by providing both the forward and inverse functions; inverse functions can be obtained using the `~' opera- tor. So to create a synonym for `tempF' you could write fahrenheit(x) units=[1;K] tempF(x); ~tempF(fahrenheit) This is useful for creating a nonlinear unit definition that differs slightly from an existing definition without having to repeat the original functions. For example, dBW(x) units=[1;W] range=[0,) dB(x) W ; ~dB(dBW/W) If you wish a synonym to refer to an existing nonlinear unit without modi- fication, you can do so more simply by adding the synonym with appended parentheses as a new unit, with the existing nonlinear unit--without paren- theses--as the definition. So to create a synonym for `tempF' you could write fahrenheit() tempF The definition must be a nonlinear unit; for example, the synonym fahrenheit() meter will result in an error message when units starts. You may occasionally wish to define a function that operates on units. This can be done using a nonlinear unit definition. For example, the defi- nition below provides conversion between radius and the area of a circle. This definition requires a length as input and produces an area as output, as indicated by the `units=' specification. Specifying the range as the nonnegative numbers can prevent cryptic error messages. circlearea(r) units=[m;m^2] range=[0,) pi r^2 ; sqrt(circlearea/pi) Defining Piecewise Linear Units Sometimes you may be interested in a piecewise linear unit such as many wire gauges. Piecewise linear units can be defined by specifying conver- sions to linear units on a list of points. Conversion at other points will be done by linear interpolation. A partial definition of zinc gauge is zincgauge[in] 1 0.002, 10 0.02, 15 0.04, 19 0.06, 23 0.1 In this example, `zincgauge' is the name of the piecewise linear unit. The definition of such a unit is indicated by the embedded `[' character. Af- ter the bracket, you should indicate the units to be attached to the num- bers in the table. No spaces can appear before the `]' character, so a de- finition like `foo[kg meters]' is invalid; instead write `foo[kg*meters]'. The definition of the unit consists of a list of pairs optionally separated by commas. This list defines a function for converting from the piecewise linear unit to linear units. The first item in each pair is the function argument; the second item is the value of the function at that argument (in the units specified in brackets). In this example, we define `zincgauge' at five points. For example, we set `zincgauge(1)' equal to `0.002 in'. Definitions like this may be more readable if written using continuation characters as zincgauge[in] \ 1 0.002 \ 10 0.02 \ 15 0.04 \ 19 0.06 \ 23 0.1 With the preceding definition, the following conversion can be performed: You have: zincgauge(10) You want: in * 0.02 / 50 You have: .01 inch You want: zincgauge 5 If you define a piecewise linear unit that is not strictly monotonic, then the inverse will not be well defined. If the inverse is requested for such a unit, units will return the smallest inverse. After adding nonlinear units definitions, you should normally run `units --check' to check for errors. If the `units' keyword is not given, the `--check' option checks a nonlinear unit definition using a dimension- less argument, and then checks using an arbitrary combination of units, as well as the square and cube of that combination; a warning is given if any of these tests fail. For example, Warning: function 'squirt(x)' defined as 'sqrt(x)' failed for some test inputs: squirt(7(kg K)^1): Unit not a root squirt(7(kg K)^3): Unit not a root Running `units --check' will print a warning if a non-monotonic piecewise linear unit is encountered. For example, the relationship between ANSI coated abrasive designation and mean particle size is non-monotonic in the vicinity of 800 grit: ansicoated[micron] \ . . . 600 10.55 \ 800 11.5 \ 1000 9.5 \ Running `units --check' would give the error message Table 'ansicoated' lacks unique inverse around entry 800 Although the inverse is not well defined in this region, it's not really an error. Viewing such error messages can be tedious, and if there are enough of them, they can distract from true errors. Error checking for nonlinear unit definitions can be suppressed by giving the `noerror' keyword; for the examples above, this could be done as squirt(x) noerror domain=[0,) range=[0,) sqrt(x); squirt^2 ansicoated[micron] noerror \ . . . Use the `noerror' keyword with caution. The safest approach after adding a nonlinear unit definition is to run `units --check' and confirm that there are no actual errors before adding the `noerror' keyword. Defining Multivariate Functions Some common dimensional calculations such as wind chill or body mass index have more than one parameter. To support these calculations, units allows multivariate functions as unit definitions. Unlike the nonlinear units de- scribed above, multivariate functions provide only a forward evaluation and are not invertible: it is impossible to convert a wind chill output back to the temperature and wind speed that generated it. A multivariate function definition is similar to that for other nonlinear units. For example, you could define `bmi' like this, starting with the unit's name followed immediately without white space by a comma-separated parameter list: bmi(ht,wt) units=[m,kg] domain=(0,)(0,) (wt/kg)/(ht/m)^2 This defines a new unit, `bmi', that has two parameters, `height', and `weight'. You are allowed to use white space in the parameter list. The optional `units=' specification (with no space before the `=') provides a comma-separated list in square brackets of units that provide the dimen- sions of the parameters. If you list fewer units than the number of para- meters, the remaining parameters will allow any unit. For univariate non- linear units, a semicolon introduces the units of the inverse. The semi- colon is not permitted in the `units=' list for multivariate functions. You specify the domain, if desired, using `domain=', followed (without white space) by the intervals defining the domain of each parameter, either juxtaposed or separated by commas. The above example requires that both arguments be strictly positive. As usual, use square brackets to indicate closed intervals. The rules for domain intervals are the same as those de- scribed above for nonlinear units. If you need to indicate an uncon- strained input give the interval `(,)'. The intervals in the domain speci- fication must use numerical values; you cannot use units or calculations in the domain. The final part of the definition is the expression that defines the unit. Since inverses are not well-defined for multivariate units, you cannot pro- vide an inverse. Since you cannot provide an inverse, you also cannot pro- vide a range, so the `range=' specification is invalid for multivariate functions. If you need to specify that a particular unit is of arbitrary dimension when units appearing after it in the parameter list are of specified dimen- sion, you can do this using the special dimension specification, `*'. Here is a toy example: func(a,b) units=[*,1] domain=(,),[-1,1] a asin(b) In this example the first argument is permitted to be of any dimension, but the second argument must be dimensionless. The first argument has no do- main bounds, but the second one must lie in the domain of the arcsine func- tion. Defining Unit List Aliases Unit list aliases are treated differently from unit definitions, because they are a data entry shorthand rather than a true definition for a new unit. A unit list alias definition begins with `!unitlist' and includes the alias and the definition; for example, the aliases included in the standard units data file are !unitlist hms hr;min;sec !unitlist time year;day;hr;min;sec !unitlist dms deg;arcmin;arcsec !unitlist ftin ft;in;1|8 in !unitlist usvol cup;3|4 cup;2|3 cup;1|2 cup;1|3 cup;1|4 cup;\ tbsp;tsp;1|2 tsp;1|4 tsp;1|8 tsp Unit list aliases are only for unit lists, so the definition must include a `;'. Unit list aliases can never be combined with units or other unit list aliases, so the definition of `time' shown above could not have been short- ened to `year;day;hms'. As usual, be sure to run `units --check' to ensure that the units listed in unit list aliases are conformable. NUMERIC OUTPUT FORMAT By default, units shows results to eight significant digits in general num- ber format. You can change this with the `--exponential', `--digits', and `--output-format' options. The first sets an exponential format (i.e., scientific notation) like that used in the original Unix units program, the second allows you to specify a different number of significant digits, and the last allows you to control the output appearance using the format for the printf function in the C programming language. If you only want to change the number of significant digits or specify exponential format type, use the `--digits' and `--exponential' options. The `--output-format' op- tion affords the greatest control of the output appearance, but requires at least rudimentary knowledge of the printf format syntax. See Invoking Units for descriptions of these options. Format Specification The format specification recognized with the `--output-format' option is a subset of that for printf. The format specification has the form %[flags][width][.precision]type; it must begin with `%', and must end with a floating-point type specifier: `g' or `G' to specify the number of sig- nificant digits, `e' or `E' for scientific notation, and `f' for fixed- point decimal. The ISO C99 standard added the `F' type for fixed-point decimal and the `a' and `A' types for hexadecimal floating point; these types are allowed with compilers that support them. Type length modifiers (e.g., `L' to indicate a long double) are inapplicable and are not allowed. The default format for units is `%.8g'; for greater precision, you could specify `-o %.15g'. The `g' and `G' format types use exponential format whenever the exponent would be less than -4, so the value 0.000013 displays as `1.3e-005'. These types also use exponential notation when the exponent is greater than or equal to the precision, so with the default format, the value 5 x 10^7 displays as `50000000' and the value 5 x 10^8 displays as `5e+008'. If you prefer fixed-point display, you might specify `-o %.8f'; however, small numbers will display very few significant digits, and values less than 5 x 10^-8 will show nothing but zeros. The format specification may include one or more optional flags: `+', ` ' (space), `#', `-', or `0' (the digit zero). The digit-grouping flag `'' is allowed with compilers that support it. Flags are followed by an optional value for the minimum field width, and an optional precision specification that begins with a period (e.g., `.6'). The field width includes the dig- its, decimal point, the exponent, thousands separators (with the digit- grouping flag), and the sign if any of these are shown. Flags The `+' flag causes the output to have a sign (`+' or `-'). The space flag ` ' is similar to the `+' flag, except that when the value is positive, it is prefixed with a space rather than a plus sign; this flag is ignored if the `+' flag is also given. The `+' or ` ' flag could be useful if conver- sions might include positive and negative results, and you wanted to align the decimal points in exponential notation. The `#' flag causes the output value to contain a decimal point in all cases; by default, the output con- tains a decimal point only if there are digits (which can be trailing ze- ros) to the right of the point. With the `g' or `G' types, the `#' flag also prevents the suppression of trailing zeros. The digit-grouping flag `'' shows a thousands separator in digits to the left of the decimal point. This can be useful when displaying large numbers in fixed-point decimal; for example, with the format `%f', You have: mile You want: microfurlong * 8000000.000000 / 0.000000 the magnitude of the first result may not be immediately obvious without counting the digits to the left of the decimal point. If the thousands separator is the comma (`,'), the output with the format `%'f' might be You have: mile You want: microfurlong * 8,000,000.000000 / 0.000000 making the magnitude readily apparent. Unfortunately, few compilers sup- port the digit-grouping flag. With the `-' flag, the output value is left aligned within the specified field width. If a field width greater than needed to show the output value is specified, the `0' (zero) flag causes the output value to be left padded with zeros until the specified field width is reached; for example, with the format `%011.6f', You have: troypound You want: grain * 5760.000000 / 0000.000174 The `0' flag has no effect if the `-' (left align) flag is given. Field Width By default, the output value is left aligned and shown with the minimum width necessary for the specified (or default) precision. If a field width greater than this is specified, the value shown is right aligned, and padded on the left with enough spaces to provide the specified field width. A width specification is typically used with fixed-point decimal to have columns of numbers align at the decimal point; this arguably is less useful with units than with long columnar output, but it may nonetheless assist in quickly assessing the relative magnitudes of results. For example, with the format `%12.6f', You have: km You want: in * 39370.078740 / 0.000025 You have: km You want: rod * 198.838782 / 0.005029 You have: km You want: furlong * 4.970970 / 0.201168 Precision The meaning of "precision" depends on the format type. With `g' or `G', it specifies the number of significant digits (like the `--digits' option); with `e', `E', `f', or `F', it specifies the maximum number of digits to be shown after the decimal point. With the `g' and `G' format types, trailing zeros are suppressed, so the results may sometimes have fewer digits than the specified precision (as indicated above, the `#' flag causes trailing zeros to be displayed). The default precision is 6, so `%g' is equivalent to `%.6g', and would show the output to six significant digits. Similarly, `%e' or `%f' would show the output with six digits after the decimal point. The C printf function allows a precision of arbitrary size, whether or not all of the digits are meaningful. With most compilers, the maximum inter- nal precision with units is 15 decimal digits (or 13 hexadecimal digits). With the `--digits' option, you are limited to the maximum internal preci- sion; with the `--output-format' option, you may specify a precision greater than this, but it may not be meaningful. In some cases, specifying excess precision can result in rounding artifacts. For example, a pound is exactly 7000 grains, but with the format `%.18g', the output might be You have: pound You want: grain * 6999.9999999999991 / 0.00014285714285714287 With the format `%.25g' you might get the following: You have: 1/3 You want: Definition: 0.333333333333333314829616256247 In this case the displayed value includes a series of digits that represent the underlying binary floating-point approximation to 1/3 but are not mean- ingful for the desired computation. In general, the result with excess precision is system dependent. The precision affects only the display of numbers; if a result relies on physical constants that are not known to the specified precision, the number of physically meaningful digits may be less than the number of digits shown. See the documentation for printf for more detailed descriptions of the for- mat specification. The `--output-format' option is incompatible with the `--exponential' or `--digits' options; if the former is given in combination with either of the latter, the format is controlled by the last option given. LOCALIZATION Some units have different values in different locations. The localization feature accommodates this by allowing a units data file to specify defini- tions that depend on the user's locale. Locale A locale is a subset of a user's environment that indicates the user's lan- guage and country, and some attendant preferences, such as the formatting of dates. The units program attempts to determine the locale from the POSIX setlocale function; if this cannot be done, units examines the envi- ronment variables LC_CTYPE and LANG. On POSIX systems, a locale is of the form language_country, where language is the two-character code from ISO 639-1 and country is the two-character code from ISO 3166-1; language is lower case and country is upper case. For example, the POSIX locale for the United Kingdom is en_GB. On systems running Microsoft Windows, the value returned by setlocale is different from that on POSIX systems; units attempts to map the Windows value to a POSIX value by means of a table in the file `locale_map.txt' in the same directory as the other data files. The file includes entries for many combinations of language and country, and can be extended to include other combinations. The `locale_map.txt' file comprises two tab-separated columns; each entry is of the form Windows-locale POSIX-locale where POSIX-locale is as described above, and Windows-locale typically spells out both the language and country. For example, the entry for the United States is English_United States en_US You can force units to run in a desired locale by using the `-l' option. In order to create unit definitions for a particular locale you begin a block of definitions in a unit datafile with `!locale' followed by a locale name. The `!' must be the first character on the line. The units program reads the following definitions only if the current locale matches. You end the block of localized units with `!endlocale'. Here is an example, which defines the British gallon. !locale en_GB gallon 4.54609 liter !endlocale Additional Localization Sometimes the locale isn't sufficient to determine unit preferences. There could be regional preferences, or a company could have specific prefer- ences. Though probably uncommon, such differences could arise with the choice of English customary units outside of English-speaking countries. To address this, units allows specifying definitions that depend on envi- ronment variable settings. The environment variables can be controlled based on the current locale, or the user can set them to force a particular group of definitions. A conditional block of definitions in a units data file begins with either `!var' or `!varnot' following by an environment variable name and then a space separated list of values. The leading `!' must appear in the first column of a units data file, and the conditional block is terminated by `!endvar'. Definitions in blocks beginning with `!var' are executed only if the environment variable is exactly equal to one of the listed values. Definitions in blocks beginning with `!varnot' are executed only if the en- vironment variable does not equal any of the list values. The inch has long been a customary measure of length in many places. The word comes from the Latin uncia meaning "one twelfth," referring to its re- lationship with the foot. By the 20th century, the inch was officially de- fined in English-speaking countries relative to the yard, but until 1959, the yard differed slightly among those countries. In France the customary inch, which was displaced in 1799 by the meter, had a different length based on a french foot. These customary definitions could be accommodated as follows: !var INCH_UNIT usa yard 3600|3937 m !endvar !var INCH_UNIT canada yard 0.9144 meter !endvar !var INCH_UNIT uk yard 0.91439841 meter !endvar !var INCH_UNIT canada uk usa foot 1|3 yard inch 1|12 foot !endvar !var INCH_UNIT france foot 144|443.296 m inch 1|12 foot line 1|12 inch !endvar !varnot INCH_UNIT usa uk france canada !message Unknown value for INCH_UNIT !endvar When units reads the above definitions it will check the environment vari- able INCH_UNIT and load only the definitions for the appropriate section. If INCH_UNIT is unset or is not set to one of the four values listed, then units will run the last block. In this case that block uses the `!message' command to display a warning message. Alternatively that block could set default values. In order to create default values that are overridden by user settings the data file can use the `!set' command, which sets an environment variable only if it is not already set; these settings are only for the current units invocation and do not persist. So if the example above were preceded by `!set INCH_UNIT france', then this would make `france' the default value for INCH_UNIT. If the user had set the variable in the environment before invoking units, then units would use the user's value. To link these settings to the user's locale you combine the `!set' command with the `!locale' command. If you wanted to combine the above example with suitable locales you could do by preceding the above definition with the following: !locale en_US !set INCH_UNIT usa !endlocale !locale en_GB !set INCH_UNIT uk !endlocale !locale en_CA !set INCH_UNIT canada !endlocale !locale fr_FR !set INCH_UNIT france !endlocale !set INCH_UNIT france These definitions set the overall default for INCH_UNIT to `france' and set default values for four locales appropriately. The overall default setting comes last so that it only applies when INCH_UNIT was not set by one of the other commands or by the user. If the variable given after `!var' or `!varnot' is undefined, then units prints an error message and ignores the definitions that follow. Use `!set' to create defaults to prevent this situation from arising. The `-c' option only checks the definitions that are active for the current environ- ment and locale, so when adding new definitions take care to check that all cases give rise to a well defined set of definitions. ENVIRONMENT VARIABLES The units program uses the following environment variables: HOME Specifies the location of your home directory; it is used by units to find a personal units data file `.units'. On systems running Mi- crosoft Windows, the file is `unitdef.units', and if HOME does not exist, units tries to determine your home directory from the HOMEDRIVE and HOMEPATH environment variables; if these variables do not exist, units finally tries USERPROFILE--typically `C:\Users\username' (Windows Vista and Windows 7) or `C:\Documents and Settings\username' (Windows XP). LC_CTYPE, LANG Checked to determine the locale if units cannot obtain it from the operating system. Sections of the default main units data file are specific to certain locales. MYUNITSFILE Specifies your personal units data file. If this variable exists, units uses its value rather than searching your home directory for `.units'. The personal units file will not be loaded if any data files are given using the `-f' option. PAGER Specifies the pager to use for help and for displaying the con- formable units. The help function browses the units database and calls the pager using the `+n'n syntax for specifying a line number. The default pager is more; PAGER can be used to specify alternatives such as less, pg, emacs, or vi. UNITS_ENGLISH Set to either `US' or `GB' to choose United States or British volume definitions, overriding the default from your locale. UNITSFILE Specifies the units data file to use (instead of the default). You can only specify a single units data file using this environment variable. If units data files are given using the `-f' option, the file specified by UNITSFILE will be not be loaded unless the `-f' option is given with the empty string (`units -f ""'). UNITSLOCALEMAP Windows only; this variable has no effect on Unix-like systems. Specifies the units locale map file to use (instead of the default). This variable seldom needs to be set, but you can use it to ensure that the locale map file will be found if you specify a location for the units data file using either the `-f' option or the UNITSFILE environment variable, and that location does not also contain the locale map file. UNITS_SYSTEM This environment variable is used in the default main data file to select CGS measurement systems. Currently supported systems are `esu', `emu', `gauss[ian]', `hlu', `natural', `natural-gauss', `planck', `planck-red', `hartree' and `si'. The default is `si'. DATA FILES The units program uses six default data files: the main data file, `definitions.units'; the atomic masses of the elements, `elements.units'; currency exchange rates, `currency.units', cryptocurrency prices, `crypto.units'; precious metals prices, `metal_prices.units'; and the US Consumer Price Index, `cpi.units'. The last five files are loaded by means of `!include' directives in the main file (see Database Command Syntax). The program can also use an optional personal units data file `.units' (- `unitdef.units' under Windows) located in the user's home directory. The personal units data file is described in more detail in Units Data Files. On Unix-like systems, the data files are typically located in `/usr/share/units' if units is provided with the operating system, or in `/usr/local/share/units' if units is compiled from the source distribution. The files `currency.units', `crypto.units', `metal_prices.units', and `cpi.units' are symbolic links to another location. On systems running Microsoft Windows, the files may be in the same loca- tions if Unix-like commands are available, a Unix-like file structure is present (e.g., `C:/usr/local'), and units is compiled from the source dis- tribution. If Unix-like commands are not available, a more common location is `C:\Program Files (x86)\GNU\units' (for 64-bit Windows installations) or `C:\Program Files\GNU\units' (for 32-bit installations). If units is obtained from the GNU Win32 Project (http://gnuwin32.source- forge.net/), the files are commonly in `C:\Program Files\GnuWin32\share\units'. If the default main units data file is not an absolute pathname, units will look for the file in the directory that contains the units program; if the file is not found there, units will look in a directory ../share/units rel- ative to the directory with the units program. You can determine the location of the files by running `units --version'. Running `units --info' will give you additional information about the files, how units will attempt to find them, and the status of the related environment variables. UNICODE SUPPORT The standard units data file is in Unicode, using UTF-8 encoding. Most de- finitions use only ASCII characters (i.e., code points U+0000 through U+007F); definitions using non-ASCII characters appear in blocks beginning with `!utf8' and ending with `!endutf8'. The non-ASCII definitions are loaded only if the platform and the locale support UTF-8. Platform support is determined when units is compiled; the locale is checked at every invocation of units. To see if your version of units includes Unicode support, invoke the program with the `--version' op- tion. When Unicode support is available, units checks every line within UTF-8 blocks in all of the units data files for invalid or non-printing UTF-8 se- quences; if such sequences occur, units ignores the entire line. In addi- tion to checking validity, units determines the display width of non-ASCII characters to ensure proper positioning of the pointer in some error mes- sages and to align columns for the `search' and `?' commands. Microsoft Windows supports UTF-8 in console applications running in Windows Terminal; UTF-8 is not supported in applications running in the older Win- dows Console Host--see Unicode Support on Windows. The UTF-16 and UTF-32 encodings are not supported on any platforms. If Unicode support is available and definitions that contain non-ASCII UTF-8 characters are added to a units data file, those definitions should be enclosed within `!utf8' ... `!endutf8' to ensure that they are only loaded when Unicode support is available. As usual, the `!' must appear as the first character on the line. As discussed in Units Data Files, it's usually best to put such definitions in supplemental data files linked by an `!include' command or in a personal units data file. When Unicode support is not available, units makes no assumptions about character encoding, except that characters in the range 00-7F hexadecimal correspond to ASCII encoding. Non-ASCII characters are simply sequences of bytes, and have no special meanings; for definitions in supplementary units data files, you can use any encoding consistent with this assumption. For example, if you wish to use non-ASCII characters in definitions when run- ning units under Windows, you can use a character set such as Windows "ANSI" (code page 1252 in the US and Western Europe); if this is done, the console code page must be set to the same encoding for the characters to display properly. You can even use UTF-8, though some messages may be im- properly aligned, and units will not detect invalid UTF-8 sequences. If you use UTF-8 encoding when Unicode support is not available, you should place any definitions with non-ASCII characters outside `!utf8' ... `!en- dutf8' blocks--otherwise, they will be ignored. Except for code examples, typeset material usually uses the Unicode symbols for mathematical operators. To facilitate copying and pasting from such sources, several typographical characters are converted to the ASCII opera- tors used in units: the figure dash (U+2012), minus (`-'; U+2212), and en dash (`-'; U+2013) are converted to the operator `-'; the multiplication sign (`x'; U+00D7), N-ary times operator (U+2A09), dot operator (`.'; U+22C5), and middle dot (`.'; U+00B7) are converted to the operator `*'; the division sign (`/'; U+00F7) is converted to the operator `/'; and the fraction slash (U+2044) is converted to the operator `|'. Unicode Support on Windows Microsoft Windows supports UTF-8 in console applications running in Windows Terminal but not in applications running in the older Windows Console Host. In Windows Terminal, the code page must be set to 65001 for UTF-8 to be en- abled. With the UTF-8 code page, running units -V might show GNU Units version 2.24 Without readline, with UTF-8, locale English_United States (en_US) Two values are shown for the locale: the first is the one returned by the system; the second is the POSIX value to which the system value is mapped. With a different code page, the result might be GNU Units version 2.24 Without readline, with UTF-8 (disabled), locale English_United States (en_US) To enable UTF-8: set code page to 65001 If units is running in Windows Console Host, regardless of the code page, the result might be GNU Units version 2.24 Without readline, with UTF-8 (disabled), locale English_United States (en_US) To enable UTF-8: run in Windows Terminal and set code page to 65001 The UTF-8 code page can be set by running chcp 65001. As of late 2024, the Windows build of units does not identify characters-- typically East Asian--that occupy more than one column, and error messages involving those characters may not be properly aligned. READLINE SUPPORT If the readline package has been compiled in, then when units is used in- teractively, numerous command line editing features are available. To check if your version of units includes readline, invoke the program with the `--version' option. For complete information about readline, consult the documentation for the readline package. Without any configuration, units will allow editing in the style of emacs. Of particular use with units are the completion com- mands. If you type a few characters and then hit ESC followed by ?, then units will display a list of all the units that start with the characters typed. For example, if you type metr and then request completion, you will see something like this: You have: metr metre metriccup metrichorsepower metrictenth metretes metricfifth metricounce metricton metriccarat metricgrain metricquart metricyarncount You have: metr If there is a unique way to complete a unit name, you can hit the TAB key and units will provide the rest of the unit name. If units beeps, it means that there is no unique completion. Pressing the TAB key a second time will print the list of all completions. The readline library also keeps a history of the values you enter. You can move through this history using the up and down arrows. The history is saved to the file `.units_history' in your home directory so that it will persist across multiple units invocations. If you wish to keep work for a certain project separate you can change the history filename using the `--history' option. You could, for example, make an alias for units to units --history .units_history so that units would save separate history in the current directory. The length of each history file is limited to 5000 lines. Note also that if you run several concurrent copies of units each one will save its new history to the history file upon exit. UPDATING CURRENCY EXCHANGE RATES AND CPI Currency Exchange Rates The units program database includes currency exchange rates and prices for some precious metals. Of course, these values change over time, sometimes very rapidly, and units cannot provide real-time values. To update the ex- change rates, run units_cur, which rewrites the file containing the cur- rency rates, typically `/var/lib/units/currency.units' or `/usr/local/com/ units/currency.units' on a Unix-like system or `C:\Program Files (x86)\GNU\ units\definitions.units' on a Windows system. This program requires Python 3 (https://www.python.org). The program must be run with suitable permissions to write the file. To keep the rates up- dated automatically, run it using a cron job on a Unix-like system, or a similar scheduling program on a different system. Reliable free sources of currency exchange rates have been annoyingly ephemeral. The program currently supports several sources: * ExchangeRate-API.com (https://www.exchangerate-api.com). The default currency server. Allows open access without an API key, with unlimited API requests. Rates update once a day, the US dollar (- `USD') is the default base currency, and you can choose your base cur- rency with the `-b' option described below. You can optionally sign up for an API key to access paid benefits such as faster data update rates. * FloatRates (https://www/floatrates.com). The US dollar (`USD') is the default base currency. You can change the base currency with the `-b' option described below. Allowable base currencies are listed on the FloatRates website. Exchange rates update daily. * The European Central Bank (https://www.ecb.europa.eu). The base currency is always the euro (`EUR'). Exchange rates update daily. This source offers a more limited list of currencies than the others. * Fixer (https://fixer.io). Registration for a free API key is required. With a free API key, base currency is the euro; exchange rates are updated hourly, the service has a limit of 1,000 API calls per month, and SSL encryption (https protocol) is not available. Most of these restrictions are eliminated or reduced with paid plans. * open exchange rates (https://openexchangerates.org). Registration for a free API key is required. With a free API key, the base currency is the US dollar; exchange rates are updated hourly, and there is a limit of 1,000 API calls per month. Most of these restric- tions are eliminated or reduced with paid plans. The default source is FloatRates; you can select a different one using `-s' option described below. Crypto and Precious Metals Prices Cryptocurrency prices are obtained from coingecko (coingecko.com). Pre- cious metals pricing is obtained from Packetizer (www.packetizer.com); this site updates once per day. US Consumer Price Index The units program includes the US Consumer Price Index (CPI) published by the US Bureau of Labor Statistics: specifically, the Consumer Price Index for All Urban Consumers (CPI-U), not seasonally adjusted--Series CUUR0000SA0. The units_cur command updates the CPI and saves the result in `cpi.units' in the same location as `currency.units'. The data are ob- tained via the BLS Public Data API (https://www.bls.gov/developers/). These data update once a month. When units_cur runs it will only attempt to update the CPI data if the current CPI data file is from a previous month, or if the current date is after the 18th of the month. Invoking units_cur You invoke units_cur like this: units_cur [options] [currency_file] [crypto_file] [metals_file] [cpi_file] By default, the output is written to the default currency, crypto, metals, and CPI files described above; this is usually what you want, because this is where units looks for the files. If you wish, you can specify different filenames on the command line and units_cur will write the data to those files. If you give `-' for a file it will write to standard output. The special filename `.' skips the update for that file. The following options are available: -h, --help Print a summary of the options for units_cur. -V, --version Print the units_cur version number. -v, --verbose Give slightly more verbose output when attempting to update currency exchange rates. -c coingecko,packetizer, --crypto coingecko,packetizer Set crypto data source (default: coingecko). -s source, --source source Specify the source for currency exchange rates; currently supported values are `floatrates' (for FloatRates), `eubank' (for the European Central Bank), `fixer' (for Fixer), and `openexchangerates' (for open exchange rates); the last two require an API key to be given with the `-k' option. -b base, --base base Set the base currency (when allowed by the site providing the data). base should be a 3-letter ISO currency code, e.g., `USD'. The spec- ified currency will be the primitive currency unit used by units. You may find it convenient to specify your local currency. Conver- sions may be more accurate and you will be able to convert to your currency by simply hitting Enter at the `You want:' prompt. This option is ignored if the source does not allow specifying the base currency. (Currently only floatrates supports this option.) -k key, --key key Set the API key to key for currency sources that require it. --blskey BLSkey Set the US Bureau of Labor Statistics (BLS) key for fetching CPI data. Without a BLS key you should be able to fetch the CPI data exactly one time per day. If you want to use a key you must request a personal key from BLS. DATABASE COMMAND SYNTAX unit definition Define a regular unit. prefix- definition Define a prefix. funcname(var) noerror units=[in-units,out-units] domain=[x1,x2] range=[y1,y2] definition(var) ; inverse(funcname) Define a nonlinear unit or unit function. The four optional key- words noerror, `units=', `range=' and `domain=' can appear in any order. The definition of the inverse is optional. tabname[out-units] noerror pair-list Define a piecewise linear unit. The pair list gives the points on the table listed in ascending order. The noerror keyword is op- tional. !endlocale End a block of definitions beginning with `!locale' !endutf8 End a block of definitions begun with `!utf8' !endvar End a block of definitions begun with `!var' or `!varnot' !include file Include the specified file. !locale value Load the following definitions only of the locale is set to value. !message text Display text when the database is read unless the quiet option (`-q') is enabled. If you omit text, then units will display a blank line. Messages will also appear in the log file. !prompt text Prefix the `You have:' prompt with the specified text. If you omit text, then any existing prefix is canceled. !set variable value Sets the environment variable, variable, to the specified value only if it is not already set. !unitlist alias definition Define a unit list alias. !utf8 Load the following definitions only if units is running with UTF-8 enabled. !var envar value-list Load the block of definitions that follows only if the environment variable envar is set to one of the values listed in the space-sepa- rated value list. If envar is not set, units prints an error mes- sage and ignores the block of definitions. !varnot envar value-list Load the block of definitions that follows only if the environment variable envar is set to value that is not listed in the space-sepa- rated value list. If envar is not set, units prints an error mes- sage and ignores the block of definitions. FILES /usr/local/share/units/definitions.units -- the standard units data file AUTHOR units was written by Adrian Mariano 29 March 2026 UNITS(1)
NAME | SYNOPSIS | DESCRIPTION | ADDITIONAL DOCUMENTATION | USING UNITS NON-INTERACTIVELY | UNIT DEFINITIONS | UNIT EXPRESSIONS | NONLINEAR UNIT CONVERSIONS | UNIT LISTS: CONVERSION TO SUMS OF UNITS | ALTERNATIVE UNIT SYSTEMS | LOGGING CALCULATIONS | SETTING OPTIONS INTERACTIVELY | OUTPUT STYLES | ADDING YOUR OWN DEFINITIONS | NUMERIC OUTPUT FORMAT | LOCALIZATION | ENVIRONMENT VARIABLES | DATA FILES | UNICODE SUPPORT | READLINE SUPPORT | UPDATING CURRENCY EXCHANGE RATES AND CPI | DATABASE COMMAND SYNTAX | FILES | AUTHOR
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