SI derived unit
SI derived units are units of measurement derived from the seven SI base units specified by the International System of Units (SI). They can be expressed as a product (or ratio) of one or more of the base units, possibly scaled by an appropriate power of exponentiation (see: Buckingham π theorem). Some are dimensionless, as when the units cancel out in ratios of like quantities. SI coherent derived units involve only a trivial proportionality factor, not requiring conversion factors.
The SI has special names for 22 of these coherent derived units (for example, hertz, the SI unit of measurement of frequency), but the rest merely reflect their derivation: for example, the square metre (m^{2}), the SI derived unit of area; and the kilogram per cubic metre (kg/m^{3} or kg⋅m^{−3}), the SI derived unit of density.
The names of SI coherent derived units, when written in full, are always in lowercase. However, the symbols for units named after persons are written with an uppercase initial letter. For example, the symbol for hertz is "Hz", while the symbol for metre is "m".^{[1]}
Special names
The International System of Units assigns special names to 22 derived units, which includes two dimensionless derived units, the radian (rad) and the steradian (sr).
Name | Symbol | Quantity | Equivalents | SI base unit Equivalents |
---|---|---|---|---|
hertz | Hz | frequency | 1/s | s^{−1} |
radian | rad | angle | m/m | 1 |
steradian | sr | solid angle | m^{2}/m^{2} | 1 |
newton | N | force, weight | kg⋅m/s^{2} | kg⋅m⋅s^{−2} |
pascal | Pa | pressure, stress | N/m^{2} | kg⋅m^{−1}⋅s^{−2} |
joule | J | energy, work, heat | m⋅N, C⋅V, W⋅s | kg⋅m^{2}⋅s^{−2} |
watt | W | power, radiant flux | J/s, V⋅A | kg⋅m^{2}⋅s^{−3} |
coulomb | C | electric charge or quantity of electricity | s⋅A, F⋅V | s⋅A |
volt | V | voltage, electrical potential difference, electromotive force | W/A, J/C | kg⋅m^{2}⋅s^{−3}⋅A^{−1} |
farad | F | electrical capacitance | C/V, s/Ω | kg^{−1}⋅m^{−2}⋅s^{4}⋅A^{2} |
ohm | Ω | electrical resistance, impedance, reactance | 1/S, V/A | kg⋅m^{2}⋅s^{−3}⋅A^{−2} |
siemens | S | electrical conductance | 1/Ω, A/V | kg^{−1}⋅m^{−2}⋅s^{3}⋅A^{2} |
weber | Wb | magnetic flux | J/A, T⋅m^{2},V⋅s | kg⋅m^{2}⋅s^{−2}⋅A^{−1} |
tesla | T | magnetic induction, magnetic flux density | V⋅s/m^{2}, Wb/m^{2}, N/(A⋅m) | kg⋅s^{−2}⋅A^{−1} |
henry | H | electrical inductance | V⋅s/A, Ω⋅s, Wb/A | kg⋅m^{2}⋅s^{−2}⋅A^{−2} |
degree Celsius | °C | temperature relative to 273.15 K | K | K |
lumen | lm | luminous flux | cd⋅sr | cd |
lux | lx | illuminance | lm/m^{2} | cd⋅m^{−2} |
becquerel | Bq | radioactivity (decays per unit time) | 1/s | s^{−1} |
gray | Gy | absorbed dose (of ionizing radiation) | J/kg | m^{2}⋅s^{−2} |
sievert | Sv | equivalent dose (of ionizing radiation) | J/kg | m^{2}⋅s^{−2} |
katal | kat | catalytic activity | mol/s | s^{−1}⋅mol. |
By field of application
Kinematics
Name | Symbol | Quantity | Expression in terms of SI base units |
---|---|---|---|
metre per second | m/s | speed, velocity | m⋅s^{−1} |
metre per second squared | m/s^{2} | acceleration | m⋅s^{−2} |
metre per second cubed | m/s^{3} | jerk, jolt | m⋅s^{−3} |
metre per second to the fourth | m/s^{4} | snap, jounce | m⋅s^{−4} |
radian per second | rad/s | angular velocity | s^{−1} |
radian per second squared | rad/s^{2} | angular acceleration | s^{−2} |
hertz per second | Hz/s | frequency drift | s^{−2} |
cubic metre per second | m^{3}/s | volumetric flow | m^{3}⋅s^{−1} |
Mechanics
Name | Symbol | Quantity | Expression in terms of SI base units |
---|---|---|---|
square metre | m^{2} | area | m^{2} |
cubic metre | m^{3} | volume | m^{3} |
newton-second | N⋅s | momentum, impulse | m⋅kg⋅s^{−1} |
newton metre second | N⋅m⋅s | angular momentum | m^{2}⋅kg⋅s^{−1} |
newton-metre | N⋅m = J/rad | torque, moment of force | m^{2}⋅kg⋅s^{−2} |
newton per second | N/s | yank | m⋅kg⋅s^{−3} |
reciprocal metre | m^{−1} | wavenumber, optical power, curvature, spatial frequency | m^{−1} |
kilogram per square metre | kg/m^{2} | area density | m^{−2}⋅kg |
kilogram per cubic metre | kg/m^{3} | density, mass density | m^{−3}⋅kg |
cubic metre per kilogram | m^{3}/kg | specific volume | m^{3}⋅kg^{−1} |
joule-second | J⋅s | action | m^{2}⋅kg⋅s^{−1} |
joule per kilogram | J/kg | specific energy | m^{2}⋅s^{−2} |
joule per cubic metre | J/m^{3} | energy density | m^{−1}⋅kg⋅s^{−2} |
newton per metre | N/m = J/m^{2} | surface tension, stiffness | kg⋅s^{−2} |
watt per square metre | W/m^{2} | heat flux density, irradiance | kg⋅s^{−3} |
square metre per second | m^{2}/s | kinematic viscosity, thermal diffusivity, diffusion coefficient | m^{2}⋅s^{−1} |
pascal-second | Pa⋅s = N⋅s/m^{2} | dynamic viscosity | m^{−1}⋅kg⋅s^{−1} |
kilogram per metre | kg/m | linear mass density | m^{−1}⋅kg |
kilogram per second | kg/s | mass flow rate | kg⋅s^{−1} |
watt per steradian square metre | W/(sr⋅m^{2}) | radiance | kg⋅s^{−3} |
watt per steradian cubic metre | W/(sr⋅m^{3}) | radiance | m^{−1}⋅kg⋅s^{−3} |
watt per metre | W/m | spectral power | m⋅kg⋅s^{−3} |
gray per second | Gy/s | absorbed dose rate | m^{2}⋅s^{−3} |
metre per cubic metre | m/m^{3} | fuel efficiency | m^{−2} |
watt per cubic metre | W/m^{3} | spectral irradiance, power density | m^{−1}⋅kg⋅s^{−3} |
joule per square metre second | J/(m^{2}⋅s) | energy flux density | kg⋅s^{−3} |
reciprocal pascal | Pa^{−1} | compressibility | m⋅kg^{−1}⋅s^{2} |
joule per square metre | J/m^{2} | radiant exposure | kg⋅s^{−2} |
kilogram square metre | kg⋅m^{2} | moment of inertia | m^{2}⋅kg |
newton metre second per kilogram | N⋅m⋅s/kg | specific angular momentum | m^{2}⋅s^{−1} |
watt per steradian | W/sr | radiant intensity | m^{2}⋅kg⋅s^{−3} |
watt per steradian metre | W/(sr⋅m) | spectral intensity | m⋅kg⋅s^{−3} |
Chemistry
Name | Symbol | Quantity | Expression in terms of SI base units |
---|---|---|---|
mole per cubic metre | mol/m^{3} | molarity, amount of substance concentration | m^{−3}⋅mol |
cubic metre per mole | m^{3}/mol | molar volume | m^{3}⋅mol^{−1} |
joule per kelvin mole | J/(K⋅mol) | molar heat capacity, molar entropy | m^{2}⋅kg⋅s^{−2}⋅K^{−1}⋅mol^{−1} |
joule per mole | J/mol | molar energy | m^{2}⋅kg⋅s^{−2}⋅mol^{−1} |
siemens square metre per mole | S⋅m^{2}/mol | molar conductivity | kg^{−1}⋅s^{3}⋅A^{2}⋅mol^{−1} |
mole per kilogram | mol/kg | molality | kg^{−1}⋅mol |
kilogram per mole | kg/mol | molar mass | kg⋅mol^{−1} |
cubic metre per mole second | m^{3}/(mol⋅s) | catalytic efficiency | m^{3}⋅s^{−1}⋅mol^{−1} |
Electromagnetics
Name | Symbol | Quantity | Expression in terms of SI base units |
---|---|---|---|
coulomb per square metre | C/m^{2} | electric displacement field, polarization density | m^{−2}⋅s⋅A |
coulomb per cubic metre | C/m^{3} | electric charge density | m^{−3}⋅s⋅A |
ampere per square metre | A/m^{2} | electric current density | m^{−2}⋅A |
siemens per metre | S/m | electrical conductivity | m^{−3}⋅kg^{−1}⋅s^{3}⋅A^{2} |
farad per metre | F/m | permittivity | m^{−3}⋅kg^{−1}⋅s^{4}⋅A^{2} |
henry per metre | H/m | magnetic permeability | m⋅kg⋅s^{−2}⋅A^{−2} |
volt per metre | V/m | electric field strength | m⋅kg⋅s^{−3}⋅A^{−1} |
ampere per metre | A/m | magnetization, magnetic field strength | m^{−1}⋅A |
coulomb per kilogram | C/kg | exposure (X and gamma rays) | kg^{−1}⋅s⋅A |
ohm metre | Ω⋅m | resistivity | m^{3}⋅kg⋅s^{−3}⋅A^{−2} |
coulomb per metre | C/m | linear charge density | m^{−1}⋅s⋅A |
joule per tesla | J/T | magnetic dipole moment | m^{2}⋅A |
square metre per volt second | m^{2}/(V⋅s) | electron mobility | kg^{−1}⋅s^{2}⋅A |
reciprocal henry | H^{−1} | magnetic reluctance | m^{−2}⋅kg^{−1}⋅s^{2}⋅A^{2} |
weber per metre | Wb/m | magnetic vector potential | m⋅kg⋅s^{−2}⋅A^{−1} |
weber metre | Wb⋅m | magnetic moment | m^{3}⋅kg⋅s^{−2}⋅A^{−1} |
tesla metre | T⋅m | magnetic rigidity | m⋅kg⋅s^{−2}⋅A^{−1} |
ampere radian | A⋅rad | magnetomotive force | A |
metre per henry | m/H | magnetic susceptibility | m^{−1}⋅kg^{−1}⋅s^{2}⋅A^{2} |
Photometry
Name | Symbol | Quantity | Expression in terms of SI base units |
---|---|---|---|
lumen second | lm⋅s | luminous energy | s⋅cd |
lux second | lx⋅s | luminous exposure | m^{−2}⋅s⋅cd |
candela per square metre | cd/m^{2} | luminance | m^{−2}⋅cd |
lumen per watt | lm/W | luminous efficacy | m^{−2}⋅kg^{−1}⋅s^{3}⋅cd |
Thermodynamics
Name | Symbol | Quantity | Expression in terms of SI base units |
---|---|---|---|
joule per kelvin | J/K | heat capacity, entropy | m^{2}⋅kg⋅s^{−2}⋅K^{−1} |
joule per kilogram kelvin | J/(K⋅kg) | specific heat capacity, specific entropy | m^{2}⋅s^{−2}⋅K^{−1} |
watt per metre kelvin | W/(m⋅K) | thermal conductivity | m⋅kg⋅s^{−3}⋅K^{−1} |
kelvin per watt | K/W | thermal resistance | m^{−2}⋅kg^{−1}⋅s^{3}⋅K |
reciprocal kelvin | K^{−1} | thermal expansion coefficient | K^{−1} |
kelvin per metre | K/m | temperature gradient | m^{−1}⋅K |
Other units used with SI
Some other units such as the hour, litre, tonne, bar, and electronvolt are not SI units, but are widely used in conjunction with SI units.
Supplementary units
Until 1995, the SI classified the radian and the steradian as supplementary units, but this designation was abandoned and the units were grouped as derived units.^{[3]}
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