UNITS(1)

NAME
units - unit conversion program

OVERVIEW OF `UNITS'
The `units' program converts quantities expressed in various scales to their equivalents in other scales. The `units' program can handle multiplicative scale changes as well as nonlinear conversions such as Fahrenheit to Celsius.

The units are defined in an external data file. You can use the extensive data file that comes with this program, or you can provide your own data file to suit your needs.

You can use the program interactively with prompts, or you can use it from the command line.

INTERACTING WITH `UNITS'
To invoke units for interactive use, type `units' at your shell prompt. The program will print something like this:

    2131 units, 53 prefixes, 24 functions

    You have:

At the `You have:' prompt, type the quantity and units that you are converting 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 type of units you want to convert to. To convert to feet, you would type `feet'.

The answer 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 factor. 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 meters. It also tells you that 1/32.8 is about .03.

The `units' program prints the inverse because sometimes it is a more convenient number. In the example above, for example, the inverse value is an exact conversion: a foot is exactly .03048 dekameters. But the number given the other direction is inexact.

If you try to 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 using the `--verbose' option:

    You have: grain
    You want: aeginamina
            grain = 0.00010416667 aeginamina
            grain = (1 / 9600) aeginamina

If you request a conversion between units which measure reciprocal dimensions, 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 message 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 return 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, meters, and hertz. The fully reduced (and in this case somewhat more cryptic) form appears on the far right.

If you want a list of options you can type `?' at the `You want:' prompt. The program will display a list of named units which are conformable with the unit that you entered at the `You have:' prompt above. Note that conformable unit combinations will not appear on this list.

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 data base at the point where that unit is defined. You can read the definition and comments that may give more details or historical information about the unit.

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 units expression, and type the new units you want. You will probably need to protect the units expressions from interpretation by the shell using single 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.

If the conversion is successful, then `units' will return success (0) to the calling environment. If `units' is given non-conformable units to convert, it will print a message giving the reduced form of each unit and it will return failure (nonzero) to the calling environment.

When `units' is invoked with only one argument, it will print out the definition of the specified unit. It will return failure if the unit is not defined and success if the unit is defined.

UNIT EXPRESSIONS
In order to enter more complicated units or fractions, you will need to use operations such as powers, products and division. Powers of units can be specified using the `^' character as shown in the following example, or by simple concatenation: `cm3' is equivalent to `cm^3'. If the exponent is more than one digit, the `^' is required.

    You have: cm^3
    You want: gallons
            * 0.00026417205
            / 3785.4118
    You have: arabicfoot-arabictradepound-force
    You want: ft lbf
            * 0.7296
            / 1.370614

Multiplication of units can be specified by using spaces, a hyphen (`-') or an asterisk (`*'). Division of units is indicated by the slash (`/') or by `per'.

    You have: furlongs per fortnight
    You want: m/s
            * 0.00016630986
            / 6012.8727

Multiplication has a higher precedence than division and is evaluated left to right, so `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 reciprocal length equivalent to .5/meter, which is probably not what you would intend if you entered that expression. You can indicate division of numbers with the vertical dash (`|'). This operator has very high precedence, higher even than the exponent operator.

    You have: 1|2 inch
    You want: cm
            * 1.27
            / 0.78740157

Parentheses can be used for grouping as desired.

    You have: (1/2) kg / (kg/meter)
    You want: league
            * 0.00010356166
            / 9656.0833

Prefixes are defined separately from base units. In order to get centimeters, the units database defines `centi-' and `c-' as prefixes. Prefixes can appear alone with no unit following them. An exponent applies only to the immediately preceding unit and its prefix so that `cm^3' or `centimeter^3' refer to cubic centimeters but `centi-meter^3' refers to hundredths of cubic meters. Only one prefix is permitted per unit, so `micromicrofarad' will fail, but `micro-microfarad' will work.

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 which 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 dollars^5.

Outside of the SI system, it is often desirable to add values of different units together. Sums of conformable units are written 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 which are added together must reduce to identical expressions in primitive units, or an error message will be displayed:

    You have: 12 printerspoint + 4 heredium
                                          ^
    Illegal sum of non-conformable units

Because `-' is used for products, it cannot also be used to form differences of units. If a `-' appears after `(' or after `+' then it will act as a negation operator. So you can compute 20 degrees minus 12 minutes by entering `20 degrees + -12 arcmin'. The `+' character is sometimes used 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 `+' as part of an exponent if possible.

Several built in functions are provided: `sin', `cos', `tan', `ln', `log', `log2', `exp', `acos', `atan' and `asin'. The `sin', `cos', and `tan' 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 inverse trigonometric functions return arguments with dimensions of angle.

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. Higher roots can be obtained 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

Unit functions can be used for nonlinear unit conversions such as Fahrenheit to Celsius:

    You have: tempF(45)
    You want: tempC
            7.2222222

In this case, think of `tempF(x)' not as a function but as a notation which indicates that `x' should have units of `tempF' attached to it. @xref{Defining functions}.

INVOKING `UNITS'
You invoke `units' like this:

    units OPTIONS [FROM-UNIT [TO-UNIT]]

If the FROM-UNIT and TO-UNIT are omitted, then the program will use interactive prompts to determine which conversions to perform. 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 will need to be quoted to protect them from shell interpretation and to group them into two arguments. @xref{Command line use}.

The following options allow you to read in an alternative units file, check your units file, or change the output format:

-c, --check
    Check that all units and prefixes defined in the units data file reduce to primitive units. Print a list of all units that cannot be reduced. Also display some other diagnostics about suspicious definitions in the units data file.

--check-verbose
    Like the `-check' option, this option prints a list of units that cannot be reduced. But to help find unit definitions that cause endless loops, it lists the units as they are checked. If `units' hangs, then the last unit to be printed has a bad definition.

-o format, --output-format format
    Use the specified format for numeric output. Format is the same as that for the printf function in the ANSI C standard. For example, if you want more precision you might use `-o %.15g'.

-f filename, --file filename
    Use filename as the units data file rather than the default units data file. This option overrides the `UNITSFILE' environment variable.

-h, --help
    Print out a summary of the options for `units'.

-q, --quiet, --silent
    Suppress prompting of the user for units and the display of statistics about the number of units loaded.

-s, --strict
    Suppress conversion of units to their reciprocal units.

-v, --verbose
    Give slightly more verbose output when converting units. When combined with the `-c' option this gives the same effect as `--check-verbose'.

-V, --version
    Print program version number, tell whether the readline library has been included, and give the location of the default units data file.

UNIT DEFINITIONS
The conversion information is read from a units data file which is called `units.dat' and is probably located in the `/usr/local/share' directory. If you invoke `units' with the `-V' option, it will print the location of this file. The default file includes definitions for all familiar units, abbreviations and metric prefixes. It also includes many obscure or archaic units.

Many constants of nature are defined, including these:
pi	ratio of circumference to 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	permitivity of vacuum
G	gravitational constant
mach	speed of sound
The database includes atomic masses for all of the elements and 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 definitions that are used.

The unit `pound' is a unit of mass. To get force, multiply by the force conversion 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'. British capacity units that differ from their US counterparts, such as the British Imperial gallon, are prefixed with `br'. Currency is prefixed with its country name: `belgiumfranc', `britainpound'.

The US Survey foot, yard, and mile can be obtained by using the `US' prefix. These units differ slightly from the international length units. They were in general use until 1959, and are still used for geographic surveys. The acre is officially defined in terms of the US Survey foot. If you want an acre defined according to the international foot, use `intacre'. The difference between these units is about 4 parts per million. The British also used a slightly different length measure before 1959. These can be obtained with the prefix `UK'.

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' or a trailing `es'. If that fails, `units' will check for a prefix. All of the standard metric prefixes are defined.

To find out what units and prefixes are available, read the standard units data file.

DEFINING NEW UNITS
All of the units and prefixes that `units' can convert are defined in the units data file. If you want to add your own units, you can supply your own file.

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 appears as the last character on a line, making it possible to spread definitions out over several lines if desired.

Unit names must not contain any of the operator characters `+', `-', `*', `/', `|', `^' or the parentheses. They cannot begin with a digit or a decimal point (`.'), nor can they end with a digit (except for zero). 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. When adding new units, be sure to use the `-c' option to check that the new units reduce properly. If you define any units which contain `+' characters, carefully check them because the `-c' option will not catch non-conformable sums. If you create a loop in the units definitions, then `units' will hang when invoked with the `-c' options. You will need to use the `--check-verbose' option which prints out each unit as it checks them. The program will still hang, but the last unit printed will be the unit which caused the infinite loop.

Here is an example of a short units file that defines some basic units:
m	!	# The meter is a primitive unit
sec	!	# The second is a 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	0.0254 m	# Inch defined in terms of meters
ft	12 inches	# The foot defined in terms of inches
mile	5280 ft	# And the mile

A unit which 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 meter'.

DEFINING FUNCTIONS
Functions can be useful for performing nonlinear unit conversions. For example, temperature conversions between the Fahrenheit and Celsius scales cannot be done by simply multiplying by conversions factors.

When you give a linear unit definition such as `inch 2.54 cm' you are providing information that `units' uses to convert values in inches into primitive units of meters. For nonlinear units, you must provide a functional definition that provides the same information.

When using a function to perform a conversion, the function is best regarded 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. But internally, the unit function is defined as a function which converts to other units in the data file, so that an eventual conversion to primitive units is possible. It is also necessary to specify the inverse conversion from some linear units to the new units.

Here is an example function definition:

tempF(x) [1;K] (x+(-32)) degF + stdtemp ; (tempF+(-stdtemp))/degF + 32

A function definition begins with the function name followed immediately (with no spaces) by a `(' character. In parentheses is the name of the parameter. Next is an optional specification of what units this function requires. In the example above, the `tempF' function requires an input argument conformable with `1'. The inverse function requires an input argument conformable with `K'. The sole purpose of the expression in brackets to enable `units' to perform error checking on function arguments.

Next the function definition appears. In the example above, the `tempF' function is defined by

    tempF(x) = (x+(-32)) degF + stdtemp

This means that the `tempF' function regards its argument as a temperature in Fahrenheit and converts it to an absolute temperature.

In order to make conversions to Fahrenheit possible, you must also specify the inverse. The inverse will be `x(tempF)' and its definition appears after 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, but then conversions to the unit will be impossible.

If you wish to make synonyms for functions, you still need to define both the forward and inverse functions. Inverse functions can be obtained using the `~' operator. So to create a synonym for `tempF' you could do

    fahrenheit(x) [1;K] tempF(x); ~tempF(fahrenheit)

Sometimes you may be interested in a piecewise linear unit such as wire gauge. Piecewise linear functions can be defined by specifying the function's value on a list of points. The function will be evaluated using 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 function. The definition of such a function is indicated by the embedded `[' character. After the bracket, you should indicate the units to be attached to this function. No spaces can appear before the `]' character, so a definition like `foo[kg meters]' is illegal; instead write `foo[kg*meters]'. The definition of the function consists of a list of pairs optionally separated by commas. 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 line 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 preceeding 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 function that is not strictly monotonic, then the inverse will not be well defined. If the inverse is requested for such a function, `units' will return the smallest inverse.

ENVIRONMENT VARIABLES
The `units' programs uses the following environment variables.

PAGER
    Specifies the pager to use for help and for displaying the conformable units. The help function browses the units database and calls the pager using the `+nn' syntax for specifying a line number. The default pager is `more', but `less', `emacs', or `vi' are possible alternatives.

UNITSFILE
    Specifies the units database file to use (instead of the default). This will be overridden by the `-f' option.

READLINE SUPPORT
If the `readline' package has been compiled in, then when `units' is used interactively, numerous command line editing features are available. To check if your version of `units' includes the 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 commands.

If you type a few characters and then hit `ESC' followed by the `?' key then `units' will display a list of all the units which 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 unitname, 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.

FILES
/usr/local/share/units.dat - the standard units data file

AUTHOR
Adrian Mariano (adrian@cam.cornell.edu)