Units are objects that have 2 separate parts: the value and the unit per se. The value is usually a real number, but units may be attached to other numerical objects as well, for example complex numbers and vectors or matrices can have associated units. The unit part is entered using the underscore _, which acts as both a separator and an operator.

The unit is an algebraic expression combining one or more unit symbols, and may be optionally surrounded by square brackets. The brackets are optional for stack input, but mandatory when units are used within a symbolic expression (to separate the unit from other algebraic operations). The _ key will always add the brackets regardless of whether the user is typing an algebraic expression or not, the use of the brackets is encouraged.

Examples of valid unit objects are:
1_m
3_m/s^2
3_[m/s^2]
[1 2 3]_kg
'3_[m]+2_[ft]'
in all cases above, the underscore is being used as a separator, but can be used as an operator as well:
_[m]
[1 2 3] _[kg]
in the first case, the operator _[] will apply the unit to some value previously left on the stack. In the second case, the value (a vector) is separated with a space, therefore it will be compiled as a separate object, put on the stack, and then the underscore operator will apply the unit.

Exponents within a unit expression can be integer numbers, real numbers or fractional exponents. The use of fractional exponents is always preferred over real numbers because they can be simplified in an exact way.
3_[m^(2/3)] is always preferred to 3_[m^0.666667]

Multiples and submultiples of many units are obtained by prefixing them with the standard SI prefixes. Therefore, 1_dal is equivalent to 10_l and 3.5_MHz is equivalent to 3500000_Hz.

SI prefixes can be used with all SI units and many non-SI units where SI prefixes are common usage. Other non-SI units do not accept prefixes.

Unit objects can be operated upon normally, and the system will perform all the necessary unit conversions in the background. Unit consistency is strictly enforced for addition and subtraction, therefore if one variable uses units in an algebraic expression, all variables should have proper units attached.

Results of an addition or subtraction between consistent units will produce a result with the units of the first argument (argument in level 2 of the stack at the time of the operation, or the left argument in an algebraic expression).

Unit conversions can be performed directly using the CONVERT command, which is accessible directly from the keyboard (LS-6). For example to convert 100 ml into m^3 simply place the original unit and the new unit on the stack: 100_ml 1_m^3 CONVERT.

To reduce a unit to its base components, use the command UBASE. For example 1_N UBASE will return 1_kg*m/s^2.

To extract the value part of a unit object, use the UVAL command, which will return the object without its unit.

Units in newRPL can be arbitrary symbols, not just the ones predefined in the system. For example, adding 3_apples and 2_apples will produce 5_apples as expected. In this case, apples is a custom unit without a definition. Units without a definition are considered base units. The system already includes base units for mass, length, time, etc. but any number of new base units can be added simply by using new symbols.

Custom units can also be defined as derived units, in terms of other base units. This is done with the UDEFINE command. For example typing 750_ml 'mug' UDEFINE would define a unit named mug as 750 ml. From that moment mug can be used in the exact same way as any system-defined unit, and it will be considered consistent with all other volume units.

Custom units may also accept SI prefixes, but this needs to be explicitly enabled during the unit definition. To create a custom unit that accepts SI prefixes, the name of the unit needs to be preceded by a question mark ? when the unit is defined. For example, following the previous example, for the unit mug to accept SI prefixes, the definition should be done typing 750_ml '?mug' UDEFINE creates a unit mug exactly as before, except now 1_[Mmug] UBASE will produce 750_m^3, as expected.

New units can also be defined in terms of new (unknown) base units. For example typing 3_apples 'oranges' UDEFINE will define oranges as equivalent to 3 apples, where apples is a base unit (amount of fruit?) that may or may not have been explicitly defined before. From that moment the addition 2_[oranges]+3_[apples] will result in 3_oranges since the units of the result will match the units of the left operand, and the 3 apples were automatically converted to 1 orange.

Custom units work systemwide, the command ULIST returns a list of all the custom units that are defined in the system. To remove a unit definition use the UPURGE command. Following the previous example, typing 'oranges' UPURGE will undefine the unit. Notice that the unit oranges definition was removed, which means this symbol now represents an unknown base unit, then 2_[oranges]+3_[apples] cannot proceed since oranges and apples are now considered as unrelated base units.

This is a list of the units available in the Units menu on newRPL. All the conversion factors are meant to be exact, not approximated.