Using Standard Unit Prefixes and Syntax

For SI units you can scale data using the standard prefixes for powers of 10 — kilo, mega, milli, or micro, for example. Either the full prefix or the symbol can be used, but you must use the same form for the prefix and the unit — that is, [milliampere] and [mA] are valid but not [mampere] or [milliA]). In the windows for plotting and numerical results, the list contains the SI unit for the quantity, including the most common prefixes. The lists also contain applicable non-SI units, which in some cases also support these prefixes — for example, for g (gram), G (gauss), and M (molar).

Use Table 3-7 as a guide for the format to enter.

Table 3-7: SI prefixes
Full prefix	Symbol	Factor
yotta	Y	1024
zetta	Z	1021
exa	E	1018
peta	P	1015
tera	T	1012
giga	G	109
mega	M	106
kilo	k	103
hekto	h	102
deca	da	101
deci	d	10-1
centi	c	10-2
milli	m	10-3
micro	u	10-6
nano	n	10-9
pico	p	10-12
femto	f	10-15
atto	a	10-18
zepto	z	10-21
yocto	y	10-24

Standard Unit Syntax

You can use the unit syntax to specify a quantity with any applicable unit. To do so, append the unit to any constant or variable in a model using a syntax where you enclose the unit in brackets, for example, 200[ft] and 3e6[kg/m^3].

Both the name and the symbol can be used for a unit (but only names that form a single word without spaces or hyphens are possible to use). For example, 2.4[ampere] and 2.4[A] are both valid to indicate an electric current in SI units. The SI units can also contain standard prefixes. Appending a unit means that you multiply the constant or variable to the left of the unit declaration with this unit. This multiplication takes precedence over other operators so, for example, 1/2[m] evaluates to 0.5 m−1 (0.5[1/m]) whereas both (1/2)[m] and 1/2*1[m] evaluate to 50 cm (0.5[m] or 50[cm]). Also, if L is a variable defined as 2[m], L[1/s] evaluates to 2[m/s].

The following examples show how to apply the unit syntax:

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Adding two quantities of the same kind that use different units: 0.5[ft]+33[mm]. The COMSOL Multiphysics software converts the result to the base unit system’s length unit (0.1854 m for SI units, for example). A quantity without a unit is treated as given in the base unit’s systems unit, so, for example, 0.5+33[mm] evaluates to 0.533 m when using SI units.

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Using multiplication with a unit to get consistent units for two quantities that you want to add, for example, 14[kg]+ht.rho[m^3], which works if ht.rho represents the density for a heat transfer model. You can also concatenate several units, for example, 3.6[N][m], which is equivalent to typing 3.6[N*m] and evaluates to 3.6 N·m.


	For unit names with spaces and hyphens, such as British thermal unit and pound-force, only use the symbols when declaring units.

It is possible to add constants (without units) to any quantity. The COMSOL Multiphysics software then assumes that this value has the same unit as that quantity (as indicated in the window).

All data in the material databases and Material Library product use SI units and this unit syntax.

Declaring Units for Parameters, Variables, and Functions


	It is important to be aware of the following aspects of unit handling.

When using parameters, variables, and functions in expressions:

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If user-defined parameters or variables are used in the physics, it is good practice to use the unit syntax to define them. The windows for parameters and variables display the resulting unit, in the models base unit system, of user-defined parameters and variables. It is important to verify that the variables have the expected unit before using them in the physics settings. The unit of parameters and variables is otherwise undefined.

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Most user-defined and built-in functions expect dimensionless inputs and outputs, so it is good practice to use make inputs, such as time, dimensionless using unit syntax. If the input is not dimensionless, the COMSOL Multiphysics software marks the expression in an orange color and reports an unexpected unit of input. For example, to use the time t as input to a Rectangle function rect1, use [1/s] to make the input dimensionless: rect1(t[1/s]).

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Using properties with undefined units in a model does not affect the numerical results during the analysis, but undefined units are required in the results and visualization stages — expressions involving such parameters and variables are also unitless.

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If other units than the base unit system’s units are used or if SI prefixes are included, the conversion to base units also affects the value (quantity) using a scaling factor (and an offset for temperature units). The column in a window for displays the quantity and unit in the base unit system so that you can see the result of the unit conversion. For example, a parameter is defined as 3[ft], the result in the column is if the base unit system is SI.