Coherent derived units

Derived units are products of powers of base units. Coherent derived units are products of powers of base units that include no numerical factor other than 1.

Examples of coherent derived units in the SI expressed in terms of base units:

Derived quantity SI coherent derived unit
Name

Symbol

Name

Symbol

area

A

square meter

m2

volume

V

cubic meter

m3

speed, velocity

υ

meter per second

m/s

acceleration

a

meter per second squared

m/s2

wavenumber

σ

reciprocal meter

m-1

density, mass density

ρ

kilogram per cubic meter

kg/m3

surface density

ρΑ

kilogram per meter squared

kg/m2

specific volume

v

cubic meter per kilogram

m3/kg

current density

j

amper per meter squared

A/m2

magnetic field strength

H

amper per meter

A/m

amount concetration (1), concetration

c

mole per cubic meter

mol/m3

mass concetration

ρ, γ

kilogram per cubic meter

kg/m3

luminance

Lv

candela per meter squared

cd/m2

refractive index (2)

n

one

1

relative permeability (2)

μr

one

1

(1) In the field of clinical chemistry this quantity is also called substance concentration.

(2) These are dimensionless quantities, or quantities of dimension one, and the symbol “1” for the unit (the number “one”) is generally omitted in specifying the values of dimensionless quantities