Units and equations of physical quantities

Definitions[edit]

Gravitational mass and inertia[edit]

A common misconception occurs between centre of mass and centre of gravity. They are defined in similar ways but are not exactly the same quantity. Centre of mass is the mathematical description of placing all the mass in the region considered to one position, centre of gravity is a real physical quantity, the point of a body where the gravitational force acts. They are equal if and only if the external gravitational field is uniform.

Quantity (common name/s)	(Common) symbol/s	Defining equation	SI units	Dimension
Centre of gravity	rcog (symbols vary)	ith moment of mass ${\displaystyle \mathbf {m} _{i}=\mathbf {r} _{i}m_{i}\,\!}$ Centre of gravity for a set of discrete masses: ${\displaystyle {\begin{aligned}\mathbf {r} _{\mathrm {cog} }&={\frac {1}{M\left|\mathbf {g} \left(\mathbf {r} _{i}\right)\right|}}\sum _{i}\mathbf {m} _{i}\left|\mathbf {g} \left(\mathbf {r} _{i}\right)\right|\\&={\frac {1}{M\left|\mathbf {g} \left(\mathbf {r} _{\mathrm {cog} }\right)\right|}}\sum _{i}\mathbf {r} _{i}m_{i}\left|\mathbf {g} \left(\mathbf {r} _{i}\right)\right|\end{aligned}}\,\!}$ Centre of gravity for a continuum of mass: ${\displaystyle {\begin{aligned}\mathbf {r} _{\mathrm {cog} }&={\frac {1}{M\left|\mathbf {g} \left(\mathbf {r} _{\mathrm {cog} }\right)\right|}}\int \left|\mathbf {g} \left(\mathbf {r} \right)\right|\mathrm {d} \mathbf {m} \\&={\frac {1}{M\left|\mathbf {g} \left(\mathbf {r} _{\mathrm {cog} }\right)\right|}}\int \mathbf {r} \left|\mathbf {g} \left(\mathbf {r} \right)\right|\mathrm {d} ^{n}m\\&={\frac {1}{M\left|\mathbf {g} \left(\mathbf {r} _{\mathrm {cog} }\right)\right|}}\int \mathbf {r} \rho _{n}\left|\mathbf {g} \left(\mathbf {r} \right)\right|\mathrm {d} ^{n}x\end{aligned}}\,\!}$	m	[L]
Standard gravitational parameterof a mass	μ	${\displaystyle \mu =Gm\,\!}$	N m2 kg−1	[L]3 [T]−2

Named units derived from SI base units^[2]

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 F⋅V	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	1/S 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	electrical inductance	V⋅s/A Ω⋅s Wb/A	kg⋅m2⋅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/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

Named units derived from SI base units^[2]

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 F⋅V	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	1/S 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	electrical inductance	V⋅s/A Ω⋅s Wb/A	kg⋅m2⋅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/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[edit]

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
radian per second squared	rad/s2	angular acceleration	s−2
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, optical power, curvature, spatial frequency	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	molarity, 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, thermal diffusivity, 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 density	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	electrical 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	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	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
kilogram per metre	kg/m	linear mass density	m−1⋅kg
coulomb per metre	C/m	linear charge density	m−1⋅s⋅A
mole per kilogram	mol/kg	molality	kg−1⋅mol
kilogram per mole	kg/mol	molar mass	kg⋅mol−1
metre per cubic metre	m/m3	fuel efficiency	m−2
kilogram per second	kg/s	mass flow rate	kg⋅s−1
joule per tesla	J/T	magnetic dipole moment	m2⋅A
watt per cubic metre	W/m3	spectral irradiance, power density	m−1⋅kg⋅s−3
kelvin per watt	K/W	thermal resistance	m−2⋅kg−1⋅s3⋅K
reciprocal kelvin	K−1	thermal expansion coefficient	K−1
kelvin per metre	K/m	temperature gradient	m−1⋅K
square metre per volt second	m2/(V⋅s)	electron mobility	kg−1⋅s2⋅A
joule per square metre second	J/(m2⋅s)	energy flux density	kg⋅s−3
reciprocal pascal	Pa−1	compressibility	m⋅kg−1⋅s2
reciprocal henry	H−1	magnetic reluctance	m−2⋅kg−1s2⋅A2
weber per metre	Wb/m	magnetic vector potential	m⋅kg⋅s−2⋅A−1
weber metre	Wb⋅m	magnetic moment	m3⋅kg⋅s−2⋅A−1
tesla metre	T⋅m	magnetic rigidity	m⋅kg⋅s−2⋅A−1
joule per square metre	J/m2	radiant exposure	kg⋅s−2
cubic metre per mole second	m3/(mol⋅s)	catalytic efficiency	m3⋅s−1⋅mol−1
kilogram square metre	kg⋅m2	moment of inertia	m2⋅kg
newton metre second per kilogram	N⋅m⋅s/kg	specific angular momentum	m2⋅s−1
hertz per second	Hz/s	frequency drift	s−2
lumen per watt	lm/W	luminous efficacy	m−2⋅kg−1⋅s3⋅lm
ampere radian	A⋅rad	magnetomotive force	A
metre per henry	m/H	magnetic susceptibility	m−1⋅kg−1⋅s2⋅A2
watt per steradian	W/sr	radiant intensity	m2⋅kg⋅s−3
watt per steradian metre	W/(sr⋅m)	spectral intensity	m⋅kg⋅s−3
watt per steradian square metre	W/(sr⋅m2)	radiance	kg⋅s−3
watt per steradian cubic metre	W/(sr⋅m3)	spectral radiance	m−1⋅kg⋅s−3
watt per metre	W/m	spectral power	m⋅kg⋅s−3