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units - unit conversion program
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.
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.
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.
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}.
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:
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 soundThe 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.
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'.
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.
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.
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