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SI derived unit#Derived units with special names

{{Short description|Measurement unit derived from basic metric value}}

{{Use dmy dates|date=August 2015}}

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 (m2), the SI derived unit of area; and the kilogram per cubic metre (kg/m3 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".{{cite journal|url=http://physics.nist.gov/Pubs/SP811/sec06.html|title=Special Publication 811|first=Curt|last=Suplee|journal=Nist |date=2 July 2009}}

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).

class="wikitable sortable"

|+ style="font-size:larger;font-weight:bold;"|Named units derived from SI base units{{SIbrochure8th}}

Name

! Symbol

! Quantity

! Equivalents

! SI base unit
Equivalents

hertz

| align = "center"| Hz

| frequency

| align = "center"| 1/s

| align = "center"| s−1

radian

| align = "center"| rad

| angle

| align = "center"| m/m

| align="center" | 1

steradian

| align = "center"| sr

| solid angle

| align = "center"| m2/m2

| align="center" | 1

newton

| align = "center"| N

| force, weight

| align = "center"| kg⋅m/s2

| align = "center"| kg⋅m⋅s−2

pascal

| align = "center"| Pa

| pressure, stress

| align = "center"| N/m2

| align = "center"| kg⋅m−1⋅s−2

joule

| align = "center"| J

| energy, work, heat

| align = "center"| m⋅N, C⋅V, W⋅s

| align = "center"| kg⋅m2⋅s−2

watt

| align = "center"| W

| power, radiant flux

| align = "center"| J/s, V⋅A

| align = "center"| kg⋅m2⋅s−3

coulomb

| align = "center"| C

| electric charge or quantity of electricity

| align = "center"| s⋅A, F⋅V

| align = "center"| s⋅A

volt

| align = "center"| V

| voltage, electrical potential difference, electromotive force

| align = "center"| W/A, J/C

| align = "center"| kg⋅m2⋅s−3⋅A−1

farad

| align = "center"| F

| electrical capacitance

| align = "center"| C/V, s/Ω

| align = "center"| kg−1⋅m−2⋅s4⋅A2

ohm

| align = "center"| Ω

| electrical resistance, impedance, reactance

| align = "center"| 1/S, V/A

| align = "center"| kg⋅m2⋅s−3⋅A−2

siemens

| align = "center"| S

| electrical conductance

| align = "center"| 1/Ω, A/V

| align = "center"| kg−1⋅m−2⋅s3⋅A2

weber

| align = "center"| Wb

| magnetic flux

| align = "center"| J/A, T⋅m2,V⋅s

| align = "center"| kg⋅m2⋅s−2⋅A−1

tesla

| align = "center"| T

| magnetic induction, magnetic flux density

| align = "center"| V⋅s/m2, Wb/m2, N/(A⋅m)

| align = "center"| kg⋅s−2⋅A−1

henry

| align = "center"| H

| electrical inductance

| align = "center"| V⋅s/A, Ω⋅s, Wb/A

| align = "center"| kg⋅m2⋅s−2⋅A−2

degree Celsius

| align = "center"| °C

| temperature relative to 273.15 K

| align = "center"| K

| align = "center"| K

lumen

| align = "center"| lm

| luminous flux

| align = "center"| cd⋅sr

| align = "center"| cd

lux

| align = "center"| lx

| illuminance

| align = "center"| lm/m2

| align = "center"| cd⋅m−2

becquerel

| align = "center"| Bq

| radioactivity (decays per unit time)

| align = "center"| 1/s

| align = "center"| s−1

gray

| align = "center"| Gy

| absorbed dose (of ionizing radiation)

| align = "center"| J/kg

| align = "center"| m2⋅s−2

sievert

| align = "center"| Sv

| equivalent dose (of ionizing radiation)

| align = "center"| J/kg

| align = "center"| m2⋅s−2

katal

| align = "center"| kat

| catalytic activity

| align = "center"| mol/s

| align = "center"| s−1⋅mol.

By field of application

=Kinematics=

class="wikitable sortable"
Name

! Symbol

! Quantity

! Expression in terms
of SI base units

metre per secondm/s

| speed, velocity

m⋅s−1
metre per second squaredm/s2

| acceleration

m⋅s−2
metre per second cubedm/s3

| jerk, jolt

m⋅s−3
metre per second to the fourthm/s4

| snap, jounce

m⋅s−4
kilogram metre per second to the thirdkg⋅m/s3

| yank

m⋅kg⋅s−3
radian per secondrad/s

| angular velocity

s−1
radian per second squaredrad/s2

| angular acceleration

s−2
hertz per secondHz/s

| frequency drift

s−2
cubic metre per secondm3/s

| volumetric flow

m3⋅s−1

=Mechanics=

class="wikitable sortable"
Name

! Symbol

! Quantity

! Expression in terms
of SI base units

square metrem2

| area

m2
cubic metrem3

| volume

m3
newton-secondN⋅s

| momentum, impulse

m⋅kg⋅s−1
newton metre secondN⋅m⋅s

| angular momentum

m2⋅kg⋅s−1
newton-metreN⋅m = J/rad

| torque, moment of force

m2⋅kg⋅s−2
newton per secondN/s

| yank

m⋅kg⋅s−3
reciprocal metrem−1

| wavenumber, optical power, curvature, spatial frequency

m−1
kilogram per square metrekg/m2

| area density

m−2⋅kg
kilogram per cubic metrekg/m3

| density, mass density

m−3⋅kg
cubic metre per kilogramm3/kg

| specific volume

m3⋅kg−1
joule-secondJ⋅s

| action

m2⋅kg⋅s−1
joule per kilogramJ/kg

| specific energy

m2⋅s−2
joule per cubic metreJ/m3

| energy density

m−1⋅kg⋅s−2
newton per metreN/m = J/m2

| surface tension, stiffness

kg⋅s−2
watt per square metreW/m2

| heat flux density, irradiance

kg⋅s−3
square metre per secondm2/s

| kinematic viscosity, thermal diffusivity, diffusion coefficient

| m2⋅s−1

pascal-secondPa⋅s = N⋅s/m2

| dynamic viscosity

m−1⋅kg⋅s−1
kilogram per metrekg/m

| linear mass density

m−1⋅kg
kilogram per secondkg/s

| mass flow rate

kg⋅s−1
watt per steradian square metreW/(sr⋅m2)

| radiance

kg⋅s−3
watt per steradian cubic metreW/(sr⋅m3)

| radiance

m−1⋅kg⋅s−3
watt per metreW/m

| spectral power

m⋅kg⋅s−3
gray per secondGy/s

| absorbed dose rate

m2⋅s−3
metre per cubic metrem/m3

| fuel efficiency

m−2
watt per cubic metreW/m3

| spectral irradiance, power density

m−1⋅kg⋅s−3
joule per square metre secondJ/(m2⋅s)

| energy flux density

kg⋅s−3
reciprocal pascalPa−1

| compressibility

m⋅kg−1⋅s2
joule per square metreJ/m2

| radiant exposure

kg⋅s−2
kilogram square metrekg⋅m2

| moment of inertia

m2⋅kg
newton metre second per kilogramN⋅m⋅s/kg

| specific angular momentum

m2⋅s−1
watt per steradianW/sr

| radiant intensity

m2⋅kg⋅s−3
watt per steradian metreW/(sr⋅m)

| spectral intensity

m⋅kg⋅s−3

=Chemistry=

class="wikitable sortable"
Name

! Symbol

! Quantity

! Expression in terms
of SI base units

mole per cubic metremol/m3

| molarity, amount of substance concentration

m−3⋅mol
cubic metre per molem3/mol

| molar volume

m3⋅mol−1
joule per kelvin moleJ/(K⋅mol)

| molar heat capacity, molar entropy

| m2⋅kg⋅s−2⋅K−1⋅mol−1

joule per moleJ/mol

| molar energy

m2⋅kg⋅s−2⋅mol−1
siemens square metre per moleS⋅m2/mol

| molar conductivity

kg−1⋅s3⋅A2⋅mol−1
mole per kilogrammol/kg

| molality

kg−1⋅mol
kilogram per molekg/mol

| molar mass

kg⋅mol−1
cubic metre per mole secondm3/(mol⋅s)

| catalytic efficiency

m3⋅s−1⋅mol−1

=Electromagnetics=

class="wikitable sortable"
Name

! Symbol

! Quantity

! Expression in terms
of SI base units

coulomb per square metreC/m2

| electric displacement field, polarization density

m−2⋅s⋅A
coulomb per cubic metreC/m3

| electric charge density

m−3⋅s⋅A
ampere per square metreA/m2

| electric current density

m−2⋅A
siemens per metreS/m

| electrical conductivity

| m−3⋅kg−1⋅s3⋅A2

farad per metreF/m

| permittivity

m−3⋅kg−1⋅s4⋅A2
henry per metreH/m

| magnetic permeability

m⋅kg⋅s−2⋅A−2
volt per metreV/m

| electric field strength

m⋅kg⋅s−3⋅A−1
ampere per metreA/m

| magnetization, magnetic field strength

m−1⋅A
coulomb per kilogramC/kg

| exposure (X and gamma rays)

kg−1⋅s⋅A
ohm metreΩ⋅m

| resistivity

m3⋅kg⋅s−3⋅A−2
coulomb per metreC/m

| linear charge density

m−1⋅s⋅A
joule per teslaJ/T

| magnetic dipole moment

m2⋅A
square metre per volt secondm2/(V⋅s)

| electron mobility

kg−1⋅s2⋅A
reciprocal henryH−1

| magnetic reluctance

m−2⋅kg−1⋅s2⋅A2
weber per metreWb/m

| magnetic vector potential

m⋅kg⋅s−2⋅A−1
weber metreWb⋅m

| magnetic moment

m3⋅kg⋅s−2⋅A−1
tesla metreT⋅m

| magnetic rigidity

m⋅kg⋅s−2⋅A−1
ampere radianA⋅rad

| magnetomotive force

A
metre per henrym/H

| magnetic susceptibility

m−1⋅kg−1⋅s2⋅A2

=Photometry=

class="wikitable sortable"
Name

! Symbol

! Quantity

! Expression in terms
of SI base units

lumen secondlm⋅s

| luminous energy

s⋅cd
lux secondlx⋅s

| luminous exposure

m−2⋅s⋅cd
candela per square metrecd/m2

| luminance

m−2⋅cd
lumen per wattlm/W

| luminous efficacy

m−2⋅kg−1⋅s3⋅cd

=Thermodynamics=

class="wikitable sortable"
Name

! Symbol

! Quantity

! Expression in terms
of SI base units

joule per kelvinJ/K

| heat capacity, entropy

m2⋅kg⋅s−2⋅K−1
joule per kilogram kelvinJ/(K⋅kg)

| specific heat capacity, specific entropy

| m2⋅s−2⋅K−1

watt per metre kelvinW/(m⋅K)

| thermal conductivity

| m⋅kg⋅s−3⋅K−1

kelvin per wattK/W

| thermal resistance

m−2⋅kg−1⋅s3⋅K
reciprocal kelvinK−1

| thermal expansion coefficient

K−1
kelvin per metreK/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{{anchor|SI supplementary unit}}

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.{{cite web | title = Resolution 8 of the CGPM at its 20th Meeting (1995) | url = http://www.bipm.org/en/CGPM/db/20/8/ | access-date = 2014-09-23 | publisher = Bureau International des Poids et Mesures}}

See also

References

{{reflist}}

Bibliography

  • {{cite book|author=I. Mills, Tomislav Cvitas, Klaus Homann, Nikola Kallay, IUPAC|title=Quantities, Units and Symbols in Physical Chemistry|edition= 2nd|date=June 1993|publisher= Blackwell Science Inc |page=72}}

External links

  • {{Commonscatinline}}

{{SI units}}

{{Portal bar|Physics}}

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