SI coherent derived units

SI coherent derived units

Derived units are defined as products of powers of the base units. When the product of powers includes no numerical factor other than one, the derived units are called coherent derived units. The base and coherent derived units of the SI form a coherent set, designated the set of coherent SI units.

When coherent units are used, equations between the numerical values of quantities take exactly the same form as the equations between the quantities themselves. i.e. If only units from a coherent set are used, conversion factors between units are never required.

The expression for the coherent unit of a derived quantity may be obtained from the dimensional product of that quantity by replacing the symbol for each dimension by the symbol of the corresponding base unit.

Each physical quantity has only one coherent SI unit, even if this unit can be expressed in different forms by using some of the special names and symbols. The inverse, however, is not true: in some cases the same SI unit can be used to express the values of several different quantities.

Examples of SI coherent derived units expressed in terms of SI base units
Name Symbol Quantity
square metre m2 area
cubic metre m3 volume
metre per second m s‑1 speed,
metre per second squared m s−2 acceleration
cubic metre per second m3 s−1 volumetric flow rate
reciprocal metre m−1 wavenumber
kilogram per cubic metre kg m−3 density,
mass concentration
kilogram per
square metre
kg m−2 surface density
cubic metre per kilogram kg−1 m3 specific volume
kilogram metre per second kg m s−1 momentum
kilogram metre squared per second kg m2 s−1 angular momentum
ampere per
square metre
m−2 A current density
ampere per metre m−1 A magnetic field strength
coulomb per kilogram kg−1 s A exposure (x- and γ-rays)
mole per cubic metre m−3 mol amount concentration,
candela per
square metre
m−2 cd luminance