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(units.info)Unit expressions
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
Nonlinear units are represented using functional notation. They
make possible nonlinear unit conversions such temperature. This is
different from the linear units that convert temperature differences.
Note the difference below. The absolute temperature conversions are
handled by units starting with `temp', and you must use functional
notation. The temperature differences are done using units starting
with `deg' and they do not require functional notation.
You have: tempF(45)
You want: tempC
7.2222222
You have: 45 degF
You want: degC
* 25
/ 0.04
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. Note: Nonlinear units.
Some other examples of nonlinears units are ring size and wire gauge.
There are numerous different gauges and ring sizes. See the units
database for more details. Note that wire gauges with multiple zeroes
are signified using negative numbers where two zeroes is -1.
Alternatively, you can use the synonyms `g00', `g000', and so on that
are defined in the units database.
You have: wiregauge(11)
You want: inches
* 0.090742002
/ 11.020255
You have: brwiregauge(g00)
You want: inches
* 0.348
/ 2.8735632
You have: 1 mm
You want: wiregauge
18.201919
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