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
|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|
|kilogram per cubic metre||kg m−3||density,
|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|
|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,