SI derived unit

The International System of Units (SI) specifies a set of seven base units from which all other SI units of measurement are derived. Each of these other units (SI derived units) is either dimensionless or can be expressed as a product of (positive or negative, but usually integral) powers of one or more of the base units.

For example, the SI derived unit of area is the square metre (m²), and the SI derived unit of density is the kilogram per cubic metre (kg/m³ or kg m⁻³). The degree Celsius (see the table below) has a somewhat unclear status, and is arguably an exception to this rule. The names of SI units are written in lowercase. The symbols for units named after persons, however, are always written with an uppercase initial letter (e.g. the symbol for the hertz is "Hz"; but the symbol for the metre is "m").^[1]

1 Derived units with special names
2 Examples of derived quantities and units
3 Other units used with SI
4 Supplementary units
5 See also
6 References
7 Bibliography

Derived units with special names

In addition to the two dimensionless derived units radian (rad) and steradian (sr), 20 other derived units have special names.

Named units derived from SI base units
Name	Symbol	Quantity	Equivalents	SI base unit Equivalents
hertz	Hz	frequency	1/s	s⁻¹
radian	rad	angle	m/m	dimensionless
steradian	sr	solid angle	m²/m²	dimensionless
newton	N	force, weight	kg⋅m/s²	kg⋅m⋅s⁻²
pascal	Pa	pressure, stress	N/m²	kg⋅m⁻¹⋅s⁻²
joule	J	energy, work, heat	N⋅m C⋅V W⋅s	kg⋅m²⋅s⁻²
watt	W	power, radiant flux	J/s V⋅A	kg⋅m²⋅s⁻³
coulomb	C	electric charge or quantity of electricity	s⋅A	s⋅A
volt	V	voltage, electrical potential difference, electromotive force	W/A J/C	kg⋅m²⋅s⁻³⋅A⁻¹
farad	F	electrical capacitance	C/V s/Ω	kg⁻¹⋅m⁻²⋅s⁴⋅A²
ohm	Ω	electrical resistance, impedance, reactance	V/A	kg⋅m²⋅s⁻³⋅A⁻²
siemens	S	electrical conductance	1/Ω A/V	kg⁻¹⋅m⁻²⋅s³⋅A²
weber	Wb	magnetic flux	J/A T⋅m²	kg⋅m²⋅s⁻²⋅A⁻¹
tesla	T	magnetic field strength, magnetic flux density	V⋅s/m² Wb/m² N/(A⋅m)	kg⋅s⁻²⋅A⁻¹
henry	H	inductance	V⋅s/A Ω⋅s Wb/A	kg⋅m²⋅s⁻²⋅A⁻²
degree Celsius	°C	temperature relative to 273.15 K	K − 273.15	K − 273.15
lumen	lm	luminous flux	cd⋅sr	cd
lux	lx	illuminance	lm/m²	m⁻²⋅cd
becquerel	Bq	radioactivity (decays per unit time)	1/s	s⁻¹
gray	Gy	absorbed dose (of ionizing radiation)	J/kg	m²⋅s⁻²
sievert	Sv	equivalent dose (of ionizing radiation)	J/kg	m²⋅s⁻²
katal	kat	catalytic activity	mol/s	s⁻¹⋅mol

Examples of derived quantities and units

Some SI derived units
Name	Symbol	Quantity	Expression in terms of SI base units
square metre	m²	area	m²
cubic metre	m³	volume	m³
metre per second	m/s	speed, velocity	m⋅s⁻¹
cubic metre per second	m³/s	volumetric flow	m³⋅s⁻¹
metre per second squared	m/s²	acceleration	m⋅s⁻²
metre per second cubed	m/s³	jerk, jolt	m⋅s⁻³
metre per quartic second	m/s⁴	snap, jounce	m⋅s⁻⁴
radian per second	rad/s	angular velocity	s⁻¹
newton second	N⋅s	momentum, impulse	m⋅kg⋅s⁻¹
newton metre second	N⋅m⋅s	angular momentum	m²⋅kg⋅s⁻¹
newton metre	N⋅m = J/rad	torque, moment of force	m²⋅kg⋅s⁻²
newton per second	N/s	yank	m⋅kg⋅s⁻³
reciprocal metre	m⁻¹	wavenumber	m⁻¹
kilogram per square metre	kg/m²	area density	m⁻²⋅kg
kilogram per cubic metre	kg/m³	density, mass density	m⁻³⋅kg
cubic metre per kilogram	m³/kg	specific volume	m³⋅kg⁻¹
mole per cubic metre	mol/m³	amount of substance concentration	m⁻³⋅mol
cubic metre per mole	m³/mol	molar volume	m³⋅mol⁻¹
joule second	J⋅s	action	m²⋅kg⋅s⁻¹
joule per kelvin	J/K	heat capacity, entropy	m²⋅kg⋅s⁻²⋅K⁻¹
joule per kelvin mole	J/(K⋅mol)	molar heat capacity, molar entropy	m²⋅kg⋅s⁻²⋅K⁻¹⋅mol⁻¹
joule per kilogram kelvin	J/(K⋅kg)	specific heat capacity, specific entropy	m²⋅s⁻²⋅K⁻¹
joule per mole	J/mol	molar energy	m²⋅kg⋅s⁻²⋅mol⁻¹
joule per kilogram	J/kg	specific energy	m²⋅s⁻²
joule per cubic metre	J/m³	energy density	m⁻¹⋅kg⋅s⁻²
newton per metre	N/m = J/m²	surface tension, stiffness	kg⋅s⁻²
watt per square metre	W/m²	heat flux density, irradiance	kg⋅s⁻³
watt per metre kelvin	W/(m⋅K)	thermal conductivity	m⋅kg⋅s⁻³⋅K⁻¹
square metre per second	m²/s	kinematic viscosity, diffusion coefficient	m²⋅s⁻¹
pascal second	Pa⋅s = N⋅s/m²	dynamic viscosity	m⁻¹⋅kg⋅s⁻¹
coulomb per square metre	C/m²	electric displacement field, polarization vector	m⁻²⋅s⋅A
coulomb per cubic metre	C/m³	electric charge density	m⁻³⋅s⋅A
ampere per square metre	A/m²	electric current density	A⋅m⁻²
siemens per metre	S/m	conductivity	m⁻³⋅kg⁻¹⋅s³⋅A²
siemens square metre per mole	S⋅m²/mol	molar conductivity	kg^-1⋅s³⋅mol⁻¹⋅A²
farad per metre	F/m	permittivity	m⁻³⋅kg⁻¹⋅s⁴⋅A²
henry per metre	H/m	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	magnetic field strength	A⋅m⁻¹
candela per square metre	cd/m²	luminance	cd⋅m⁻²
lumen second	lm⋅s	luminous energy	cd⋅sr⋅s
lux second	lx⋅s	luminous exposure	cd⋅sr⋅s⋅m⁻²
coulomb per kilogram	C/kg	exposure (X and gamma rays)	kg⁻¹⋅s⋅A
gray per second	Gy/s	absorbed dose rate	m²⋅s⁻³
ohm metre	Ω⋅m	resistivity	m³⋅kg⋅s⁻³⋅A⁻²

Other units used with SI

Some other units such as the hour, litre, tonne, and electron volt 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.^[2]

References

^ http://physics.nist.gov/Pubs/SP811/sec06.html
^ "Resolution 8 of the CGPM at its 20th Meeting (1995)".

Bibliography

I. Mills, Tomislav Cvitas, Klaus Homann, Nikola Kallay, IUPAC (June 1993). Quantities, Units and Symbols in Physical Chemistry (2nd ed.). Blackwell Science Inc. p. 72.

SI units

Base units	ampere candela kelvin kilogram metre mole second

Derived units with special names	becquerel coulomb degree Celsius farad gray henry hertz joule katal lumen lux newton ohm pascal radian siemens sievert steradian tesla volt watt weber

Other accepted units	astronomical unit dalton day decibel degree Celsius degree of arc electronvolt hectare hour litre minute minute of arc neper second of arc tonne atomic units natural units

See also	Conversion of units History of the metric system Metric prefixes Proposed redefinitions Systems of measurement

Book Category Outline

SI derived unit

SI derived unit

Contents

Derived units with special names

Examples of derived quantities and units

Other units used with SI

Supplementary units

See also

References

Bibliography

Categories

International System of Units

Encyclopedia Article

Lux

Encyclopedia Article

SI base unit

Encyclopedia Article

Energy

Encyclopedia Article

Watt

Encyclopedia Article

Suggestions

Watt

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Pascal (unit)

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International System of Units

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Joule

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Siemens (unit)

Encyclopedia Article