|Definition:|| derived unit that, for a given system of quantities and for a chosen set of base units, is a product of powers of base units with no other proportionality factor than one
NOTE 1 – A power of a base unit is the base unit raised to an exponent.
NOTE 2 – Coherence can be determined only with respect to a particular system of quantities and a given set of base units. If, for example, the metre, the second, and the mole are base units, the metre per second is the coherent derived unit of velocity when velocity is defined by the quantity equation ν = dr /dt, and the mole per cubic metre is the coherent derived unit of amount-of-substance concentration when amount-of-substance concentration is defined by the quantity equation c = n/V. The kilometre per hour and the knot are not coherent derived units in such a system.
NOTE 3 – A derived unit can be coherent with respect to one system of quantities, but not to another. For example, the centimetre per second is the coherent unit of speed in the CGS systems but is not a coherent unit of speed in the SI.
NOTE 4 – The coherent derived unit for every quantity of dimension one in any system of quantities is the number one, symbol 1. Both the name and the symbol of the unit one are generally omitted, unless there exists a special name for the unit one.