## SI Derived Units

#### Some Examples Expressed in Terms of SI Base Units

Derived quantityQuantity
symbol
NameExpression in SI base units
areaAsquare metrem2
volumeVcubic metrem3
speed, velocityu, v, cmetre per secondm s-1
accelerationa, g (free fall)metre per second squaredm s-2
moment of inertiaIkilogram square metrekg m2
kinematic viscosityvsquare metre per secondm2 s-1
wave numberσ, φreciprocal metrem-1
mass densityρkilogram per cubic metrekg m-3
specific volumevcubic metre per kilogramm3 kg-1
current densityj, iampere per square metreA m-2
magnetic field strengthHampere per metreA m-1
concentration of substance B:cB, [B]mole per cubic metre mol/m-3
molar massMkilogram per molekg mol-1
molar volumeVmcubic metre per molem3mol-1
luminanceLcandela per square metrecd m-2
mass fractionwkilogram per kilogramdimensionless
Table 4. SI derived units expressed in terms of SI base units.

The table above shows some examples of derived quantities and units expressed in terms of SI base units.

#### Dimensionless Quantities

Some quantities are defined as the ratios of two quantities of the same kind, and thus have a dimension expressed by the number one. Examples of such quantities are refractive index, relative permeability, and mass fraction. Other quantities having the unit 1 include "characteristic numbers" like the quantum number and numbers which represent a count, such as a number of molecules and partition function in statistical thermodynamics. All of these quantities are described as being dimensionless, or of dimension one, and have the coherent SI unit 1. Their values are simply expressed as numbers and, in general, the unit 1 is not shown. In a few cases, a special name is given to this unit, mainly to avoid confusion between some compound derived units. This is the case for the radian, steradian and neper.

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