SI derived units

SI derived units

Derived units are products of powers of base units.

SI coherent derived units with special names

Coherent derived units are products of powers of base units that include no numerical factor other than 1. The base units and coherent derived units of the SI form a coherent set, designated the set of coherent SI units.

Name Symbol Quantity Expressed in terms of SI base units Expressed in terms of other SI units
hertz Hz frequency s−1 1/s
radian rad angle 1 m/m
steradian sr solid angle 1 m2/m2
newton N force kg m s−2
pascal Pa pressure, stress kg m−1 s−2 N/m2
joule J energy, work, heat kg m2 s−2 N m
W s
watt W power, radiant flux kg m2 s−3 J/s
coulomb C electric charge s A F V
volt V electric potential difference, electromotive force kg m2 s−3 A−1 W/A
farad F electric capacitance kg−1 m−2 s4 A2 C/V
ohm Ω electric resistance, impedance, reactance kg m2 s−3 A−2 1/S
siemens S electric conductance kg−1 m−2 s3 A2 1/Ω
weber Wb magnetic flux kg m2 s−2 A−1 V s
tesla T magnetic flux density, magnetic field strength kg s−2 A−1 Wb/m2
henry H inductance kg m2 s−2 A−2 Wb/A
degree Celsius °C Celsius temperature K
lumen lm luminous flux cd cd sr
lux lx illuminance m−2 cd lm/m2
becquerel Bq activity referred
to a radionuclide
s−1 1/s
gray Gy absorbed dose (of ionizing radiation), specific energy (imparted), kerma m2 s−2 J/kg
sievert Sv dose equivalent (of ionizing radiation) m2 s−2 J/kg
katal kat catalytic activity s−1 mol

Examples of SI coherent derived units without special names and symbols

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
reciprocal metre m−1 wavenumber
kilogram per cubic metre kg m-3 density,
mass density
kilogram per square metre kg m-2 surface density
cubic metre per kilogram m3 kg-1 specific volume
ampere per square metre m2 A current density
ampere per metre m-1 A magnetic field strength
mole per cubic metre m-3 mol amount concentration,
kilogram per cubic metre kg m-3 mass concentration
candela per square metre m-2 cd luminance

Examples of SI coherent derived units whose names and symbols include SI coherent derived units with special names and symbols

Name Symbol Quantity Expressed in terms of SI base units
pascal second Pa s dynamic viscosity kg m-1 s-1
newton metre N m moment of force kg m2 s-2
newton per metre N/m surface tension kg s-2
radian per second rad/s angular velocity s-1
radian per second squared rad/s2 angular acceleration s-2
watt per square metre W/m2 heat flux density,
kg s-3
joule per kelvin J/K heat capacity,
kg m2 s-2 K-1
joule per kilogram kelvin J/(kg K) specific heat capacity,
specific entropy
m2 s-2 K-1
joule per kilogram J/kg specific energy m2 s-2
watt per metre kelvin W/(m K) thermal conductivity kg m s-3 K-1
joule per cubic metre J/m3 energy density kg m-1 s-2
volt per metre V/m electric field strength kg m s-3 A-1
coulomb per cubic metre C/m3 electric charge density m-3 s A
coulomb per square metre C/m2 surface charge density,
electric flux density,
electric displacement
m-2 s A
farad per metre F/m permittivity kg-1 m-3 s4 A2
henry per metre H/m permeability kg m s-2 A-2
joule per mole J/mol molar energy kg m2 s-2 mol-1
joule per mole kelvin J/(mol K) molar entropy,
molar heat capacity
kg m2 s-2 K-1 mol-1
coulomb per kilogram C/kg exposure (x- and γ-rays) kg-1 s A
gray per second Gy/s absorbed dose rate m2 s-3
watt per steradian W/sr radiant intensity kg m2 s-3
watt per square metre steradian W/(m2 sr) radiance kg s-3
katal per cubic metre kat/m3 catalytic activity m-3 s-1 mol