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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 simple 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 conversion 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 previous 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 conversions. 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

In North America, recipes for cooking typically measure ingredients by
volume, 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 sometimes 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 recognizes 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.

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.

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 hours, minutes, seconds dms angle: degrees, minutes, seconds time years, days, hours, minutes and seconds usvol US cooking volume: cups and smaller

Using these shorthands, or *unit list aliases*,
you can do the following conversions:

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

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

Next: Logging Calculations, Previous: Nonlinear Conversions, Up: Top [Contents][Index]