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