SI Dimensions of Physical Quantities

SI Dimensions of Physical Quantities: Alphabetic List

compiled by Stanislav Sýkora, Extra Byte, Castano Primo, Italy 20022.
Stan's Library, ISSN 2421-1230, Vol.I. First release February 28, 2005. Permalink via DOI: 10.3247/SL1Phys06.003

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Quantity	Dimension	Alternatives	Definition/Notes
A:
Abbé number \| Constringence \| V-number	1	Dimensionless	V_D = (n_D-1)/(n_F-n_C)
Absorbed radiation dose	m².s^-2	J.kg^-1, Gy (gray)	[Energy]/[Mass]
Absorbed dose rate	m².s^-3	Gy.s^-1	[Absorbed dose]/[Time]
Acceleration, angular	s^-2	rad.s^-2	[ΔAngular velocity]/[ΔTime]
Acceleration \| Deceleration	m.s^-2		[ΔVelocity]/[ΔTime]
Acoustic impedance / resistance / reactance	kg.m^-4.s^-1	Pa.s/m³, reyl/m²	[Pressure]/[Volume flow rate]
Acoustic impedance, specific	kg.m^-2.s^-1	Pa.s/m, reyl	[ΔPressure][Velocity]. Also s.acu. resistance / reactance*
Acoustic conductance, specific	kg^-1.m².s	reyl^-1	Inverse of s.acu. impedance. Also s.acu. susceptance
Action	kg.m².s^-1	J.s	[Energy][Time], [Moment of motion][Distance]
Activity of a radioactive source	s^-1	Bq (becquerel)	[Counts]/[Time]
Activity, katalytic	mol.s^-1	katal	[ΔQuantity]/[Time]. Same as molar production rate
Activity, transactions rate	s^-1	1/year	[Transactions]/[Time period]. Economy and finance
Admittance, inductive	kg^-1.m^-2.s³.A²	S (siemens)	1/[Inductive impedance]
Admittance, of a circuit	kg^-1.m^-2.s³.A²	S (siemens)	1/[Circuit impedance]
Advection velocity	m.s^-1	m/s	In porous media; actual progress along pressure gradient
Albedo, of a surface	1	Dimensionless	[Reflected elmag power]/[Incident elmag power]
Amplification \| Attenuation (generic)	1	usually in dB	[Quantity(p)]/[Quantity(p')], with p being some parameter
Angular acceleration	s^-2	rad.s^-2	[ΔAngular velocity]/[ΔTime]
Angular moment of inertia	kg.m²		[Mass]*[Distance²]
Angular moment of motion	kg.m².s^-1	J.s	[Moment of motion][Distance]. Like [action*]
Angular velocity	s^-1	rad.s^-1	[ΔPlane angle]/[ΔTime]
Annealing point	K		Temperature at which viscosity drops below 10¹² Pa.s
Area	m²		[Distance]*[Distance]
Area growth rate	m².s^-1		[ΔArea]/[Time]
Asset \| Wealth	cur	currency	Economy and finance
Atomic number	1	Dimensionless	Number of protons in an atomic nucleus
Atomic weight \| Relative atomic mass	au	atomic units	Average over a typical isotopic composition
Attenuation \| Amplification (generic)	1	usually in dB	[Quantity(p)]/[Quantity(p')], with p being some parameter
Attenuation / amplification over a distance	m^-1	dB/m	[Attenuation]/[Distance]. Mostly in acoustic and electronics
Attenuation / amplification over a period	s^-1	dB/s	[Attenuation]/[Time]. Mostly in acoustic and electronics
B:
Bandwidth	s^-1	Hz	[ΔFrequency]
Baud rate \| Information flux	bit.s^-1	baud	[Information]/[Time]
Bond duration	s	year	Economy and finance
Bulk modulus	kg.m^-1.s^-2	N.m^-2, Pa	([ΔVolume]/[Volume])/[Pressure]. Inverse of compressibility
C:
Capacitance, electric	kg^-1.m^-2.s⁴.A²	C.V^-1, F (farad)	[Charge]/[ΔPotential]
Capacitive reactance	kg.m².s^-3.A^-2	Ω (ohm)	1/(i[Angular frequency].[Capacitance])
Capacitive susceptance	kg^-1.m^-2.s³.A²	S (siemens)	1/[Capacitive reactance]
Cash flow	cur.s^-1	currency/year	[Value]/[ΔTime]. Economy and finance
Circulation	m².s^-1	J.s.kg^-1	[Angular moment]/[Mass], [Velocity]*[Loop length]
Characteristic impedance	kg.m².s^-3.A^-2	V.A^-1, Ω, ohm	√([Mag.Permeability]/[El.Permittivity])
Charge, electric	s.A	C (coulomb)	[Current]*[Time]
Charge, magnetic (bound)	m^-2.A		- ∇.[Magnetization] , -Divergence of magnetization
Charge, quantum	1	Dimensionless	[Charge]/[Elementary charge quantum]
Charge, molecular/ionic, quantum	1	Dimensionless	[Charge of a molecule or ion]/[Elementary charge quantum]
Charge density	m^-3.s^.A	C.m^-3	[Charge]/[Volume]
Charge/mass ratio \| Specific charge	kg^-1.s.A	C.kg^-1	[Charge]/[Mass]
Charge, molar	s.A.mol^-1	C.mol^-1	[Charge]/[Quantity]
Chemical potential, molar	kg.m².s^-2.mol^-1	J.mol^-1	[ΔInternalEnergy]/[ΔQuantity]
Circuit admittance	kg^-1.m^-2.s³.A²	S (siemens)	1/[Circuit impedance]
Circuit impedance	kg.m².s^-3.A^-2	Ω (ohm)
Circulation / velocity of money	s^-1	1/year	[Transactions]/[Time period]. Economy and finance
Circumference \| Perimeter	m
Collision cross section \| Cross section	m²		[Distance]*[Distance]
Compressibility	kg^-1.m.s²	Pa^-1	[Pressure]/([ΔVolume]/[Volume]). Inverse of bulk modulus
Compression	kg.m^-1.s^-2	N.m^-2, Pa (pascal)	[Force]/[Area]. Same as pressure
Compression factor of a real gas	1	Dimensionless	pV/(nRT). For ideal gas equals 1; temperature dependent
Compressive strength	kg.m^-1.s^-2	N.m^-2, Pa	[Force]/[Area]. Like pressure
Concentration, molar	m^-3.mol		[Quantity]/[Volume]. Same as molar density
Concentration gradient, molar	m^-4.mol		[Molarity]/[Distance]. Same as molarity gradient
Concentration ratio, molar	1	Dimensionless	[Partial quantity]/[Total quantity]
Concentration ratio, by mass	1	Dimensionless	[Partial mass]/[Total mass]
Concentration ratio, by volume	1	Dimensionless	[Partial volume]/[Total volume]..
Concentration, by weight (obsolete)	1	Dimensionless	[Partial mass]/[Total mass]. Obsolete: use by mass
Conductance, electric	kg^-1.m^-2.s³.A²	A.V^-1, S (siemens)	1/[Resistance]
Conductivity, electric	kg^-1.m^-3.s³.A²	S.m^-1	1/[Resistivity]
Conductivity, hydraulic	m.s^-1	m/s	Used for porous media
Conductivity, molar	kg^-1.s³.A².mol^-1	S.m².mol^-1	[El.conductivity]/[Concentration]
Conductivity, thermal	kg.m.s^-3.K^-1	W.m^-1.K^-1	[Heat flux]/([Distance]*[ΔTemperature])
Constringence \| Abbé number \| V-number	1	Dimensionless	V_D = (n_D-1)/(n_F-n_C)
Convergence	m^-1	dioptry	in optics, but not only
Cosmological constant Λ	m^-2		Present in Einstein's equation
Cosmological expansion rate	s^-1	km/s/Mpc	[Velocity]/[Distance]. Mpc stands for Megaparsec
Count of events/instances	1		This covers all kinds of enumerations
Count rate	s^-1		[Counts]/[Time]
Couple	kg.m².s^-2	N.m	2[Force][Distance] for two non-aligned opposing forces
Critical angle of repose	rad	or degree	Steepest angle of a slope before a slide
Cross section	m²		[Distance]*[Distance]
Cryoscopic constant	kg.mol^-1.K	K/(mol/kg)	[ΔTemperature]/[Molality]
Current, electric	A	A (ampere)
Current density, electric	m^-2.A		[Current]/[Area]. Same as current intensity
Current intensity, electric	m^-2.A		[Current]/[Area]. Same as current density
Current noise, variance n_J²	s.A²	A²/Hz	[Current]²/[Bandwidth]
Curvature	m^-1		1/[Curvature radius]
Curvature radius	m		of a line in plane/space or surface in space
D:
D'Alembert operator \| D'Alembertian	m^-2		(1/c²⁾∂²/∂t² - ∂²/∂x² - ∂²/∂y² - ∂²/∂z²
Debt \| Liability	cur	currency	Economy and finance
Debt/GDP ratio	s	year	[Debt]/[Earnings]. Economy and finance
Deceleration \| Acceleration	m.s^-2		[ΔVelocity]/[ΔTime]
Deceleration, angular	s^-2	rad.s^-2	[ΔAngular velocity]/[ΔTime]
Density of electric charge	m^-3.s.A	C.m^-3	[Charge]/[Volume]
Density of electric current	m^-2.A		[Current]/[Area]. Same as current intensity
Density of energy	kg.m^-1.s^-2	J.m^-3	[Energy]/[Volume]
Density of mass	kg.m^-3		[Mass]/[Volume]. Same as specific density
Density of mass, gradient of	kg.m^-4		[Mass density]/[Distance]. Same as specific density gradient
Density of particles	m^-3		[Count]/[Volume]. Obsolete: number density
Density of substance	m^-3.mol		[Quantity]/[Volume]. Same as molar concentration
Derivative with respect to time	s^-1		d/dt, ∂/∂t
Derivative with respect to a length	m^-1		d/dr, ∂/∂r, r = x \| y \| z
Dielectric constant \| Relative permittivity	1	Dimensionless	[Permittivity]/[Permittivity of vacuum]
Dielectric strength/rigidity \| Electric strength	kg.m.s^-3.A^-1	V.m^-1	[ΔPotential]/[Distance]
Diffusion coefficient	m².s^-1		[Distance]²/[Time]
Diffusivity, thermal	m².s^-1		([∂Temperatute]/[∂Time])/[∇²Temperature].
Dipole moment, electric	m.s.A	C.m	[Charge]*[Distance]
Dipole moment, magnetic	m².A	J.T^-1	[Current]*[Area]
Dispersive power	1	Dimensionless	Ratio of differences of refractive indices
Dispersivity quotient	m^-1		[ΔRefractive index]/[ΔWavelength]
Displacement, electric	m^-2.s.A	C.m^-2	[Charge]/[Area]. Same as electric flux density
Displacement four-tensor (relativistic D^μν)	m^-1.A		Like magnetic intensity
Distance	m		in all Euclidean n-dimensional spaces
Dose of absorbed radiation	m².s^-2	J.kg^-1, Gy (gray)	[Energy]/[Mass]
Dose rate	m².s^-3	Gy.s^-1	[Absorbed dose]/[Time]
Drift speed	m.s^-1		Steady-state speed of an object..
Duration	s	s (second)
Dynamic viscosity	kg.m^-1.s^-1	Pa.s	([Force]/[Area])/[ΔVelocity]
E:
Earnings \| Income rate	cur.s^-1	currency/year	[Value]/[Time period]. Economy and finance
Ebullioscopic constant	kg.mol^-1.K	K/(mol/kg)	[ΔTemperature]/[Molality]
Electric capacitance	kg^-1.m^-2.s⁴.A²	C.V^-1, F (farad)	[Charge]/[ΔPotential]
Electric charge	s.A	C (coulomb)	[Current]*[Time]
Electric conductance	kg^-1.m^-2.s³.A²	A.V^-1, S (siemens)	[Current]/[ΔPotential]. Inverse of resistance
Electric conductivity	kg^-1.m^-3.s³.A²	S.m^-1	1/[Resistivity]
Electric conductivity, molar	kg^-1.s³.A².mol^-1	S.m².mol^-1	[El.conductivity]/[Concentration]
Electric current	A	A (ampere)
Electric dipole moment	m.s.A	C.m	[Charge]*[Distance]
Electric displacement	m^-2.s.A	C.m^-2	[Charge]/[Area]. Same as electric flux density
Electric field strength \| Electric intensity	kg.m.s^-3.A^-1	V.m^-1	[ΔPotential]/[Distance]
Electric field gradient	kg.s^-3.A^-1	V.m^-2	[ΔEl.field strength]/[Distance]
Electric flux density \| Electric induction	m^-2.s.A	C.m^-2	[Charge]/[Area]
Electric inductance	kg.m².s^-2.A^-2	V.s.A^-1, H (henry)	[ΔPotential]/[dCurrent/dt]
Electric induction	m^-2.s.A	C.m^-2	[Charge]/[Area]. More properly electric flux density
Electric intensity	kg.m.s^-3.A^-1	V.m^-1	[ΔPotential]/[Distance]. More properly electric field strength
Electric permittivity	kg^-1.m^-3.s⁴.A²	F.m^-1	[El.flux density]/[El.field strength]
Electric permittivity, relative	1	Dimensionless	[Permittivity]/[Permittivity of vacuum]. Same as dielectric constant
Electric polarization	m^-2.s.A	C.m^-2	[Charge]/[Area]. Like electric flux density
Electric potential	kg.m².s^-3.A^-1	W.A^-1, J.C^-1, V (volt)	[Power]/[Current], [Energy]/[Charge]
Electric quadrupole moment	m².s.A	C.m²	[Electric dipole][Distance], [Electric charge][Distance²]
Electric resistance	kg.m².s^-3.A^-2	V.A^-1, Ω (ohm)	[ΔPotential]/[Current]
Electric resistivity	kg.m³.s^-3.A^-2	Ω.m	([Resistance]*[Length])/[Area]
Electric strength \| Dielectric strength	kg.m.s^-3.A^-1	V.m^-1	[ΔPotential]/[Distance]..
Electromagnetic field tensor (relativistic F^μν)	kg.s^-2.A^-1	T	Like magnetic flux density
Electromagnetic displacement (relat. D^μν)	m^-1.A		Like magnetic intensity
Electromagnetic four-current (relativistic J^α)	m^-2.A		Like current density and [Charge]*[c]
Electromagnetic four-potential (relativistic A^α)	kg.m.s^-2.A^-1	m^-1.s.V, m.T	Like magnetic vector potential and [El.potential]/[c]
Electromotive force (emf)	kg.m².s^-3.A^-1	V	[ΔPotential]
Electron affinity (always molar)	kg.m².s^-2.mol^-1	J.mol^-1	Energy released binding an electron
Electronegativity, Pauling χ	1	Dimensionless	Relative tendency of an atom to attract electrons; χ(H)=2.20.
Electrostriction coefficient	kg^-2.m^-2.s⁶.A²	m².V^-2	([ΔVolume]/[Volume])/[Electric field strength]²
Emittance, luminous	cd.sr.m^-2	lm.m^-2, lx (lux)	[Luminous flux]/[Area]. Same as luminous exitance
Energy	kg.m².s^-2	N.m, J (joule)	[Force][Distance], [Power][Time]
Energy, molar	kg.m².s^-2.mol^-1	J.mol^-1	[Energy]/[Quantity]
Energy, specific	m².s^-2	J.kg^-1	[Energy]/[Mass]
Energy density	kg.m^-1.s^-2	J.m^-3	[Energy]/[Volume]
Energy flux \| Power	kg.m².s^-3	J.s^-1, W (watt)	[ΔEnergy]/[ΔTime]
Enthalpy	kg.m².s^-2	J	Like energy and heat
Enthalpy, molar	kg.m².s^-2.mol^-1	J.mol^-1	[Enthalpy]/[Quantity]. Like molar heat
Enthalpy, specific	m².s^-2	J.kg^-1	[Enthalpy]/[Mass]. Like specific heat
Entropy	kg.m².s^-2.K^-1	J.K^-1	[ΔHeat]/[Temperature]
Entropy, molar	kg.m².s^-2.K^-1.mol^-1	J.K^-1.mol^-1	[Entropy]/[Quantity]
Entropy, specific	m².s^-2.K^-1	J.K^-1.kg^-1	[Entropy]/[Mass]
Evolution rate, log-scale	s^-1		d{ln(Q)}/dt = (dQ/dt)/Q. Same as relative evolution rate
Expansion coefficient, thermal	K^-1		([ΔLength]/[Length])/[Temperature]
Expansion rate, cosmological	s^-1	km/s/Mpc	[Velocity]/[Distance]. Mpc stands for Megaparsec
Expectation frequency	s^-1		[Counts]/[Time]. Like count rate
Exposure	kg^-1.s.A	C.kg^-1	[Charge]/[Mass]. Used for ionising radiations
Extinction coefficient	m^-1	dB/m	[Ratio]/m. Used mostly for radiation
F:
Field tensor, electromagnetic (relativistic F^μν)	kg.s^-2.A^-1	T	Like magnetic flux density
Fire point	K		Temperature at which ignited vapour keeps burning
Flash point	K		Temperature at which vapour can be kept burning
Flow	cur.s^-1	currency/year	[ΔValue]/[ΔTime]. Economy and finance: time derivative
Flow rate, of mass \| Mass production rate	kg.s^-1		[ΔMass]/[Time]. For example, through a pipe
Flow rate, of volume	m³.s^-1		[ΔVolume]/[Time]. For example, through a pipe
Force	kg.m.s^-2	N (newton)	[Mass]*[Acceleration]
Force, thermodynamic	kg.m.s^-2.mol^-1	N/mol	[ΔChemical potential]/[Distance]
Four-current (relativistic J^α)	m^-2.A		Like current density and [Charge]*[c]
Four-potential (relativistic A^α)	kg.m.s^-2.A^-1	m^-1.s.V, m.T	Like magnetic vector potential and [El.potential]/[c]
Four-tensor elmag displacement (relat. D^μν)	m^-1.A		Like magnetic intensity
Four-tensor elmag field (relativistic F^μν)	kg.s^-2.A^-1	T	Like magnetic flux density
Free energy	kg.m².s^-2	J	Also Helmholtz function. Like energy
Free energy, molar	kg.m².s^-2.mol^-1	J.mol^-1	[Free energy]/[Quantity]. Like Helmholtz function
Free energy, specific	m².s^-2	J.kg^-1	[Free energy]/[Mass]. Like specific Helmholtz function
Free enthalpy	kg.m².s^-2	J	Also Gibbs function. Like energy
Free enthalpy, molar	kg.m².s^-2.mol^-1	J.mol^-1	[Free enthalpy]/[Quantity]. Like molar Gibbs function
Free enthalpy, specific	m².s^-2	J.kg^-1	[Free enthalpy]/[Mass]. Like specific Gibbs function
Frequency of events	s^-1		[Counts]/[Time]
Frequency of waves	s^-1	Hz	hertz
Frequency drift rate	s^-2	Hz.s^-1	[ΔFrequency]/[Time]
Friction	kg.m.s^-2	N	Tangential force between two moving surfaces
Friction coefficient	1	Dimensionless	[Tangential force]/[Normal force]
Fugacity	kg.m^-1.s^-2	Pa	Effective pressure in real gases
G:
Gain of a device	1	Dimensionless	[Output]/[Input], like-quantities ratio. Often in dB
GDP Gross domestic product	cur.s^-1	currency/year	[Earnings]. Economy and financee: of an administrative region
g-factor of a particle	1	Dimensionless	[Magnetic moment]/([Spin].[Bohr magneton])
Gradient, of electric field	kg.s^-3.A^-1	V.m^-2	[ΔEl.field strength]/[Distance]
Gradient, of magnetic field	kg.m^-1.s^-2.A^-1	T.m^-1	[ΔMag.flux density]/[Distance]
Gradient, of mass density	kg.m^-4		[Mass density]/[Distance]. Same as specific density gradient
Gradient, of pressure	kg.m^-2.s^-2	N.m^-3, Pa/m	[Pressure]/[Distance]
Gradient, thermal	K.m^-1		[ΔTemperature]/[Distance]. Same as temperature gradient
Gravitational constant G	kg^-1.m³.s^-2		[Force]*[Distance]²/[Mass]². Appears in Newton's equation
Gravitational field intensity \| Gravity	m.s^-2		[Force]/[Mass], [Acceleration]
Gravitational field potential	m².s^-2		[Energy]/[Mass].
Gravity \| Gravitational field intensity	m.s^-2		[Force]/[Mass], [Acceleration]
Growth rate, relative	s^-1		[Relative variation]/[Time]
Growth rate, linear	m.s^-1		[ΔLength]/[Time]
Growth rate, of area/surface	m².s^-1		[ΔArea]/[Time]
Growth rate, of volume	m³.s^-1		[ΔVolume]/[Time]
Gyromagnetic ratio	kg^-1.s.A	Hz.T^-1	[Mag.moment]/[Angular moment of motion]
H:
Half life	s		of a non-conservative / decaying quantity
Hamiltonian	kg.m².s^-2	J	[Force][Distance], [Power][Time]. Like energy
Hardness	kg.m^-1.s^-2	N.m^-2	[Force]/[Area]. Same as pressure
Heat	kg.m².s^-2	J	Like energy
Heat, molar	kg.m².s^-2.mol^-1	J.mol^-1	[Heat]/[Quantity]
Heat, specific	m².s^-2	J.kg^-1	[Heat]/[Mass]
Heat capacity	kg.m².s^-2.K^-1	J.K^-1	[ΔHeat]/[ΔTemperature]
Heat capacity, molar	kg.m².s^-2.K^-1.mol^-1	J.K^-1.mol^-1	[Heat capacity]/[Quantity]
Heat capacity, specific	m².s^-2.K^-1	J.K^-1.kg^-1	[Heat capacity]/[Mass]
Heat conductivity \| Thermal conductivity	kg.m.s^-3.K^-1	W.m^-1.K^-1	[Heat flux]/([Distance]*[ΔTemperature])
Heat flux	kg.m².s^-3	J.s, W	[ΔHeat]/[ΔTime]. Like power
Heat flux density	kg.s^-3	W.m^-2	[Heat flux]/[Area]. Same as irradiance
Heat of fusion/evaporation, specific	m².s^-2	J.kg^-1	[Energy]/[Mass]
Heat of fusion \| evaporation, molar	kg.m².s^-2.mol^-1	J.mol^-1	[Energy]/[Quantity]
Hydraulic conductivity	m.s^-1	m/s	Used for porous media
Hydraulic permeability	m²	1 darcy = 10^-12 m²	[Velocity][Viscosity]/[Pressure gradient], in porous media*
I:
Illuminance	cd.sr.m^-2	lm.m^-2, lx (lux)	[Luminous flux]/[Area]
Impact resistance	kg.s^-2	J.m^-2	[Energy]/[Area]
Impedance, acoustic	kg.m^-4.s^-1	Pa.s/m³, reyl/m²	[ΔPressure]/[Volume flow rate]. Also acu. resistance / reactance
Impedance, acoustic, specific	kg.m^-2.s^-1	Pa.s/m, reyl	[ΔPressure][Velocity]. Also s.acu. resistance / reactance*
Impedance, characteristic, electric	kg.m².s^-3.A^-2	V.A^-1, Ω, ohm	√([Mag.Permeability]/[El.Permittivity])
Impedance, inductive	kg.m².s^-3.A^-2	Ω (ohm)	i[Angular frequency].[Inductance]
Impedance, of a circuit	kg.m².s^-3.A^-2	Ω (ohm)
Impulse	kg.m.s^-1		[ΔMoment of motion], [Force][ΔTime], [Mass][ΔVelocity]
Income rate \| Earnings	cur.s^-1	currency/year	[Value]/[Time period]. Economy and finance
Inductance	kg.m².s^-2.A^-2	V.s.A^-1, Wb.A^-1, H (henry)	[ΔPotential]/[dCurrent/dt], [Mag.flux]/[Current]
Induction, electric	m^-2.s.A	C.m^-2	[Charge]/[Area]. Same as electric flux density
Inductive admittance	kg^-1.m^-2.s³.A²	S (siemens)	1/[Inductive impedance]
Inductive impedance	kg.m².s^-3.A^-2	Ω (ohm)	i[Angular frequency].[Inductance]
Information	bit^-1	bit	One bit is the elementary information quantum
Information flux \| Baud rate	bit.s^-1	baud	[Information]/[Time]
Intensity of electric current	m^-2.A		[Current]/[Area]. Same as current density
Interest	1	%	[ΔWealth]/[Wealth]. Economy and finance
Interest rate	s^-1	%/year	[Interest]/[Time period]. Economy and finance
Internal energy	kg.m².s^-2	J	Like energy and heat
Internal energy, molar	kg.m².s^-2.mol^-1	J.mol^-1	[Internal energy]/[Quantity]. Like molar heat
Internal energy, specific	m².s^-2	J.kg^-1	[Internal energy]/[Mass]. Like specific heat
Ion mobility	kg^-1.m^-1.s².A	m².s^-1.V^-1	[Velocity]/[Electric field strength].
Ionic force (strength)	m^-3.mol		Sum([Concentration]*[Ionic quantum charge]²).
Ionic quantum charge	1	Dimensionless	[Ion charge]/[Elementary charge quantum]
Ionic strength (force)	m^-3.mol		Sum([Concentration]*[Ionic quantum charge]²).
Ionization energy, molar	kg.m².s^-2.mol^-1	J.mol^-1	Energy to ionize a molecule/atom
Irradiance	kg.s^-3	W.m^-2	[Heat flux]/[Area]. Same as heat flux density
J:
Joule-Thomson coefficient	kg^-1.m.s².K	K.Pa^-1	[ΔTemperature]/[ΔPressure]
K:
Katalytic activity	mol.s^-1	katal	[ΔQuantity]/[Time]. Same as molar production rate
Kinematic viscosity	m².s^-1		[Dynamic viscosity]/[Density]
K-space vector \| Reciprocal space position	m^-1
L:
Lagrangian	kg.m².s^-2	J	[Force][Distance], [Power][Time]. Like energy
Laplace operator \| Laplacian	m^-2		∇² = ∂²/∂x² + ∂²/∂y² + ∂²/∂z²
Length	m	m (meter)
Liability \| Debt	cur	currency	Economy and finance
Linear stiffness	kg.s^-2	N.m^-1	[Force]/[Displacement]. ... of a structure
Logarithmic ratio log_b(A/A') in any base b	1		Applicable to any ratio of commensurable quantities
Logarithmic ratio ln(A/A')	1	Np	Neper. Uses natural logarithm
Logarithmic ratio Log(P/P')/10	1	dB (decibel)	Uses base-10 logarithm.Aplies only to power P
Logarithmic ratio Log(X/X')/20	1	dB (decibel)	Aplies to voltages (X=V) and currents (X=I)
Logarithmic scale differential	1	Dimensionless	dQ/Q, d{ln(Q)}, for any quantity Q. Also relative differential
Logarithmic scale probability density	1	1/Np	[Probability]/[Natural-logarithmic ratio]
Loss of a device	1	Dimensionless	[Output]/[Input], like-quantities ratio. Often in dB
Luminance	cd.m^-2		[Luminosity]/[Area]
Luminosity	cd	cd (candle)	Same as luminous intensity
Luminous coefficient	1	Dimensionless	[Luminous efficacy]/[683 lm/W]. Same as luminous efficiency
Luminous efficacy	cd.sr.kg^-1.m^-1.s³	lm/W	[Luminous flux]/[Power]
Luminous efficiency	1	Dimensionless	[Luminous efficacy]/[683 lm/W]. Same as luminous coefficient
Luminous emittance	cd.sr.m^-2	lm.m^-2, lx (lux)	[Luminous flux]/[Area]. Same as luminous exitance
Luminous energy	cd.sr.s	lm.s	[Luminous flux][Time]. Known as talbot*
Luminous flux	cd.sr	lm (lumen)	[Luminosity][Solid angle]. Same as luminous power*
Luminous intensity	cd	cd (candle)	Same as luminosity
Luminous power	cd.sr	lm (lumen)	[Luminosity][Solid angle]. Same as luminous flux*
M:
Magnetic charge (bound)	m^-2.A		- ∇.[Magnetization] , -Divergence of magnetization
Magnetic dipole moment	m².A	J.T^-1	[Current][Area]. Same as magnetic moment*
Magnetic field gradient	kg.m^-1.s^-2.A^-1	T.m^-1	[ΔMag.flux density]/[Distance]
Magnetic field strength \| Magnetic intensity	m^-1.A		[Current]/[Distance]
Magnetic flux	kg.m².s^-2.A^-1	V.s, W.s.A^-1, Wb (weber)	[ΔPotential]*[Time], [Power]/[dCurrent/dt]
Magnetic flux density \| Magnetic induction	kg.s^-2.A^-1	Wb.m^-2, T (tesla)	[Mag.flux]/[Area]
Magnetic induction	kg.s^-2.A^-1	Wb.m^-2, T (tesla)	[Mag.flux]/[Area]. More properly magnetic flux density
Magnetic intensity	m^-1.A		[Current]/[Distance]. More properly magnetic field strength
Magnetic moment	m².A	J.T^-1	[Current]*[Area]
Magnetic permeability	kg.m.s^-2.A^-2	H.m^-1	[Mag.flux density]/[Mag.field strength]
Magnetic permeability, relative	1	Dimensionless	[Permeability]/[Permeability of vacuum]
Magnetic quadrupole moment	m³.A	m.J.T^-1	[Mag.dipole]*[Distance]
Magnetic susceptibility	1	Dimensionless	[Relative permeability]-1
Magnetic vector potential	kg.m.s^-2.A^-1	m^-1.s.V, m.T	[Mag.flux density][Distance], [El.field strength][Time]
Magnetization	m^-1.A		[Mag.moment]/[Volume]. Like magnetic field strength
Magnetogyric ratio	kg.s^-1.A^-1	T.Hz^-1	[Angular moment of motion]/[Mag.moment]
Magnetomotive force (mmf)	A		[Current]*[Number of turns]
Magnitude of a star	1	Dimensionless	m-m'=-10^0.4(S/S'), where S,S' are the luminous fluxes of two stars
Mass	kg	kg (kilogram)
Mass density	kg.m^-3		[Mass]/[Volume]. Same as specific density
Mass density gradient \| Specific density gradient	kg.m^-4		[Mass density]/[Distance]
Mass concentration	1	Dimensionless	[Partial mass]/[Total mass]
Mass flow (total)	kg.s^-1	kg	[ΔMass]/[Time]. For example, through a device
Mass production rate	kg.s^-1		[ΔMass]/[Time]. Same as mass flow
Mass, molar	kg.mol^-1		[Mass]/[Quantity]
Mass number of an isotope	1	Dimensionless	Number of protons+neutrons in the isotope nuclide
Mean anomaly	1	Dimensionless	Of a body on a Kepler orbit; t.sqrt(G(M₁+M₂)/r³)
Mean motion	s^-1		Of a body on a Kepler orbit; sqrt(G(M₁+M₂)/r³)
Modulus of compression	kg^-1.m.s²	Pa^-1	[Pressure]/([ΔVolume]/[Volume]). Same as compressibility
Modulus of rigidity	kg.m^-1.s^-2	N.m^-2, Pa	[Stress]/[Strain]. Same as shear modulus
Mobility, ionic	kg^-1.m^-1.s².A	m².s^-1.V^-1	[Velocity]/[Electric field strength].
Molality (intended as concentration)	kg^-1.mol	mol/kg	[Quantity]/[Mass]
Molar charge	s.A.mol^-1	C.mol^-1	[Charge]/[Quantity]
Molar concentration	m^-3.mol		[Quantity]/[Volume]. Same as concentration or molarity
Molar concentration gradient	m^-4.mol		[Molarity]/[Distance]. Same as molarity gradient
Molar concentration ratio	1	Dimensionless	[Partial quantity]/[Total quantity]
Molar conductivity, electric	kg^-1.m^-3.s³.A².mol^-1	S.m^-1.mol^-1	[El.conductivity]/[Concentration]
Molar density	m^-3.mol		[Quantity]/[Volume]. Same as concentration
Molar energy	kg.m².s^-2.mol^-1	J.mol^-1	[Energy]/[Quantity]
Molar enthalpy	kg.m².s^-2.mol^-1	J.mol^-1	[Enthalpy]/[Quantity]. Like molar heat
Molar entropy	kg.m².s^-2.K^-1.mol^-1	J.K^-1.mol^-1	[Entropy]/[Quantity]
Molar free energy	kg.m².s^-2.mol^-1	J.mol^-1	[Free energy]/[Quantity]. Also molar Helmholtz function
Molar free enthalpy	kg.m².s^-2.mol^-1	J.mol^-1	[Free enthalpy]/[Quantity]. Also molar Gibbs function
Molar heat	kg.m².s^-2.mol^-1	J.mol^-1	[Heat]/[Quantity]
Molar heat capacity	kg.m².s^-2.K^-1.mol^-1	J.K^-1.mol^-1	[Heat capacity]/[Quantity]
Molar internal energy	kg.m².s^-2.mol^-1	J.mol^-1	[Internal energy]/[Quantity]. Like molar heat
Molar mass	kg.mol^-1		[Mass]/[Quantity]
Molar particle count	mol^-1		[Count]/[Mol]. For example, the Avogadro constant
Molar production rate	mol.s^-1		[ΔQuantity]/[Time].
Molar refractivity	m³.mol^-1		[(r²-1)/(r²+2)]/[Concentration], where r is the refractive index
Molar relaxivity	s^-1.mol^-1		[Relaxation rate]/[Concentration]
Molar solubility	m^-3.mol		[Quantity]/[Volume]. Same as concentration
Molar volume	m³.mol^-1		[Volume]/[Quantity]
Molarity	m^-3.mol		[Quantity]/[Volume]. Same as concentration or molar density
Molarity gradient	m^-4.mol		[Molarity]/[Distance]. Same as concentration gradient
Molecular quantum charge	1	Dimensionless	[Charge of a molecule]/[Elementary charge quantum]
Moment of force	kg.m².s^-2	N.m	[Force]*[Distance]
Moment of motion	kg.m.s^-1		[Mass][Velocity], [Mass flow][Distance]
Multiple derivatives with respect to time	s^-p		d^p/dt^p, ∂^p/∂t^p; for p = 1,2,3,..
Multiple derivatives with respect to a length	m^-p		d^p/dr^p, ∂^p/∂r^p; for p = 1,2,3,..., r = x \| y \| z
Mutual inductance	kg.m².s^-2.A^-2	V.s.A^-1, Wb.A^-1, H (henry)	[ΔPotential]/[dCurrent/dt], [Mag.flux]/[Current]
N:
Nabla ( ∇ ) \| div \| grad \| rot \| curl	m^-1		Any derivative-like construct with respect to a distance
Notch resistance	kg.s^-2	J.m^-2	[Energy]/[Area]
Number of instances / events	1		This covers all kinds of enumerations
Number density	m^-3		[Particles]/[Volume]. Obsolete; see particle density
Number of turns	1		Often used in electric engineering
O:
Osmotic pressure	kg.m^-1.s^-2	Pa
P:
Particle count, molar	mol^-1		[Count]/[Mol]. For example, the Avogadro constant
Particle density	m^-3		[Count]/[Volume]. Obsolete: number density
P/E Price/Earnings ratio	s	year	[Value]/[Earnings]. Economy and finance
Peltier coefficient	kg.m².s^-3.A^-1	W.A^-1, V	[Heat flux]/[Current]
Perimeter \| Circumference	m
Permeability, magnetic	kg.m.s^-2.A^-2	H.m^-1	[Mag.flux density]/[Mag.field strength]
Permeability, hydraulic	m²	1 darcy = 10^-12 m²	[Velocity][Viscosity]/[Pressure gradient], in porous media*
Permittivity, electric	kg^-1.m^-3.s⁴.A²	F.m^-1	[El.flux density]/[El.field strength]
Permittivity, relative	1	Dimensionless	[Permittivity]/[Permittivity of vacuum]. Dielectric constant
Phase \| Phase angle	1	rad	φ typically in exp(i(ωt+φ))
Phase drift rate	s^-1	rad.s^-1	[Phase angle]/[Time]
Pi coefficient, molar	kg.m^-1.s^-2.mol^-1	J.m^-3	[ΔInternalEnergy]/[ΔVolume]
Piezzoelectric coefficient	kg.m.s^-3.A^-1	V.m^-1	[Electric field strength]/([ΔLength]/[Length])
Plane angle	1	rad
Poisson's ratio	1	Dimensionless	[Transversal striction]/[Londitudinal elongation]
Polarization, electric	m^-2.s.A	C.m^-2	[Charge]/[Area]. Like electric flux density
Porosity, superficial	1	Dimensionless	[Void cross section]/[Total cross section], in porous media
Porosity, volume	1	Dimensionless	[Pores volume]/[Total volume], in porous media
Position vector	m		in all Euclidean n-dimensional spaces
Potential, electric	kg.m².s^-3.A^-1	W.A^-1, J.C^-1, V (volt)	[Power]/[Current], [Energy]/[Charge]
Power	kg.m².s^-3	J.s^-1, W (watt)	[ΔEnergy]/[ΔTime]. Equivalent to energy flux
Prandtl number	1	Dimensionless	[Kinematic viscosity]/[Thermal diffusivity]
Propagation loss	m^-1	dB/m	[Ratio]/m. Generic, usable for any quantity
Poynting vector	kg.s^-3	W.m^-2	[El.field strength]/[Mag.field strength]. Like irradiance
Pressure	kg.m^-1.s^-2	N.m^-2, Pa (pascal)	[Force]/[Area]
Pressure gradient	kg.m^-2.s^-2	N.m^-3, Pa/m	[Pressure]/[Distance]
Price \| Value	cur	currency	Economy and finance
Probability of an event	1		Real number in a dimensionless interval [0,1]
Probability density on log-scale	1	Np^-1	[Probability]/[Natural-logarithmic ratio]
Purchase \| Transaction value	cur	currency	Economy and finance
Q:
Quadrupole moment, electric	m².s.A	C.m²	[Electric dipole][Distance], [Electric charge][Distance²]
Quadrupole moment, magnetic	m³.A	m.J.T^-1	[Mag.dipole]*[Distance]
Quantity of substance	mol	mol
Quantum charge	1	Dimensionless	[Charge]/[Elementary charge quantum]
Quantum charge, molecular or ionic	1	Dimensionless	[Molecule/ion charge]/[Charge quantum]
Quotient of dispersivity	m^-1		[ΔRefractive index]/[ΔWavelength]
R:
Radiance	kg.s^-3.sr^-1	W.m^-2.sr^-1	([Power]/[Area])/[Solid angle]
Radiation dose	m².s^-2	J.kg^-1, Gy (gray)	[Energy]/[Mass]
Radiation dose rate	m².s^-3	Gy.s^-1	[Absorbed dose]/[Time]
Radioactivity	s^-1	Bq (becquerel)	[Counts]/[Time]
Radius of curvature	m		of a line in plane/space or surface in space
Rotational stiffness	kg.m².s^-2.rad^-1	N.m.rad^-1	[Moment of force]/[Angle]. ... of a structure
Ratio of commensurable quantities	1	Dimensionless	Q1/Q2, with Q1 and Q2 having the same dimension
Reactance, acoustic	kg.m^-4.s^-1	Pa.s/m³, reyl/m²	[ΔPressure]/[Volume flow rate]. Also acu. impedance / resistance
Reactance, acoustic, specific	kg.m^-2.s^-1	Pa.s/m, reyl	[ΔPressure][Velocity]. Also s.acu. impedance / resistance*
Reactance, capacitive	kg.m².s^-3.A^-2	Ω (ohm)	1/(i[Angular frequency].[Capacitance])
Reciprocal space position \| K-space vector	m^-1
Redox potential	kg.m².s^-3.A^-1	V (volt)	Same as reduction potential
Reduction potential	kg.m².s^-3.A^-1	V (volt)	Same as redox potential
Refractive index	1	Dimensionless	Light speeds ration (in a medium)/(in vacuum)
Refractivity, molar	m³.mol^-1		[(r²-1)/(r²+2)]/[Concentration]
Refractivity, specific	m³.kg^-1		[(r²-1)/(r²+2)]/[Specific density],
Relative atomic mass \| Atomic weight	au	atomic units	Average over a typical isotopic composition
Relative differential	1	Dimensionless	dQ/Q, d{ln(Q)}, for any quantity Q. Also log-scale differential
Relative evolution rate	s^-1		d{ln(Q)}/dt = (dQ/dt)/Q. Also log-scale evolution rate
Relative permeability, magnetic	1	Dimensionless	[Permeability]/[Permeability of vacuum]
Relative permittivity, electric	1	Dimensionless	[Permittivity]/[Permittivity of vacuum]. Dielectric constant
Relative variation	1	Dimensionless	ΔQ/Q, for any quantity Q
Relativistic displacement four-tensor (D^μν)	m^-1.A		Like magnetic intensity
Relativistic electromagnetic field tensor (F^μν)	kg.s^-2.A^-1	T	Like magnetic flux density
Relativistic four-current (J^α)	m^-2.A		Like current density and [Charge]*[c]
Relativistic four-potential (A^α)	kg.m.s^-2.A^-1	m^-1.s.V, m.T	Like magnetic vector potential and [El.potential]/[c]
Relaxation rate	s^-1		1/[Relaxation time]. Used for returns to equilibria
Relaxation time	s		Used for returns to equilibria
Relaxivity, molar	s^-1.mol^-1		[Relaxation rate]/[Concentration]
Reluctance, magnetic	kg^-1.m^-1.s².A²	m.H^-1	1/[Permeability]
Resistance, acoustic	kg.m^-4.s^-1	Pa.s/m³, reyl/m²	[ΔPressure]/[Volume flow rate]. Also acu. impedance / reactance
Resistance, acoustic, specific	kg.m^-2.s^-1	Pa.s/m, reyl	[ΔPressure][Velocity]. Also s.acu. impedance / reactance*
Resistance, electric	kg.m².s^-3.A^-2	V.A^-1, Ω (ohm)	[ΔPotential]/[Current]
Resistance, thermal	kg^-1.m^-2.s³K	K/W	of a device. [ΔT]/[Power].
Resistance to impact	kg.s^-2	J.m^-2	[Energy]/[Area]. Like notch resistance
Resistivity, electric	kg.m³.s^-3.A^-2	Ω.m	([Resistance]*[Length])/[Area]
Return on asset / equity	s^-1	%/year	([ΔValue]/[Value])/[Time period]. Economy and finance
Reynolds number	1	Dimensionless	[Velocity]*[length]/[Kinematic viscosity]
RF attenuation	m^-1	dB/m	[Ratio]/m. Used mostly for radiation
S:
Sale \| Transaction value	cur	currency	Economy and finance
Sales flow \| Transactions volume	cur.s^-1		[Value]/[Time period]. Economy and Finance
Seeback coefficient	kg.m².s^-3.A^-1.K^-1	V.K^-1	[ΔPotential]/[ΔTemperature]. Same as thermoelectric power
Self-diffusion coefficient	m².s^-1		[Distance²]/[Time]
Settling rate	s^-1	typically dB/s	[Ratio]/[ΔTime]
Settling time	s	typically dB/s	Used to describe transient phenomena
Shear modulus	kg.m^-1.s^-2	N.m^-2, Pa	[Stress]/[Strain]. Like Young modulus
Softening point	K		Temperature at which hardness drops below a level
Solid angle	1	sr (steradian)
Solubility, molar	m^-3.mol		[Quantity]/[Volume]. Same as concentration
Sonic attenuation	m^-1	dB/m	[Power ratio]/m. Used in acoustics
Specific acoustic impedance	kg.m^-2.s^-1	Pa.s/m, reyl	[ΔPressure][Velocity]. Also s.acu. resistance / reactance*
Specific acoustic conductance	kg^-1.m².s	reyl^-1	Also specific acoustic susceptance
Specific charge	kg^-1.s.A	C.kg^-1	[Charge]/[Mass]. Charge/mass ratio
Specific density	kg.m^-3		[Mass]/[Volume]. Same as density of mass
Specific density gradient	kg.m^-4		[Mass density]/[Distance]. Same as mass density gradient
Specific energy	m².s^-2	J.kg^-1	[Energy]/[Mass]
Specific enthalpy	m².s^-2	J.kg^-1	[Enthalpy]/[Mass]. Like specific heat
Specific entropy	m².s^-2.K^-1	J.K^-1.kg^-1	[Entropy]/[Mass]
Specific free energy	m².s^-2	J.kg^-1	[Free energy]/[Mass]. Also specific Helmholtz function
Specific free enthalpy	m².s^-2	J.kg^-1	[Free enthalpy]/[Mass]. Also specific Gibbs function
Specific heat	m².s^-2	J.kg^-1	[Heat]/[Mass]
Specific heat capacity	m².s^-2.K^-1	J.K^-1.kg^-1	[Heat capacity]/[Mass]
Specific internal energy	m².s^-2	J.kg^-1	[Internal energy]/[Mass]. Like specific heat
Specific refractivity	m³.kg^-1		[(r²-1)/(r²+2)]/[Specific density]
Specific volume	m³.kg^-1		[Volume]/[Mass]
Speed	m.s^-1		[Distance]/[Time]. Same as velocity
Spin	1	Dimensionless	of a quantum particle
Star magnitude	1	Dimensionless	m-m' = -10^0.4(S/S'), where S,S' are luminous fluxes of two stars
Stiffness, linear	kg.s^-2	N.m^-1	[Force]/[Displacement]. ... of a structure
Stiffness, rotational	kg.m².s^-2.rad^-1	N.m.rad^-1	[Moment of force]/[Angle]. ... of a structure
Strain (mechanical)	1	Dimensionless	[ΔLength]/[Length] Relative deformation
Strain point	K		Temperature at which viscosity drops below 10^13.5 Pa.s
Strength, compressive	kg.m^-1.s^-2	N.m^-2, Pa	[Force]/[Area]. Like pressure
Strength, dielectric	kg.m.s^-3.A^-1	V.m^-1	[ΔPotential]/[Distance]. Same as electric strength
Strength, electric field \| Electric intensity	kg.m.s^-3.A^-1	V.m^-1	[ΔPotential]/[Distance]
Strength, ionic	m^-3.mol		Sum([Concentration]*[Ionic quantum charge]²).
Strength, magnetic field \| Magnetic intensity	m^-1.A		[Current]/[Distance]
Strength, tensile	kg.m^-1.s^-2	N.m^-2, Pa	[Force]/[Area]. Same as pressure
Superficial porosity	1	Dimensionless	[Void cross section]/[Total cross section], in porous media
Superficial velocity	m.s^-1	m/s	In porous media; as if the space was filled only by the fluid
Surface area	m²		[Distance]*[Distance]. Applicable to 3D bodies
Surface density of charge	m^-2.s.A	C.m^-2	[Charge]/[Area]
Surface element	m²		[Distance][Distance]. Same as area*
Surface energy	kg.s^-2	J/m²	[Energy]/[Area]. Same as surface tension
Surface growth rate	m².s^-1		[ΔArea]/[Time]
Surface tension	kg.s^-2	N/m	[Force]/[Length]. Same as surface energy
Susceptance, acoustic, specific	kg^-1.m².s	reyl^-1	Also specific acoustic conductance
Susceptance, capacitive	kg^-1.m^-2.s³.A²	S (siemens)	1/[Reactance]
Susceptibility, magnetic	1	Dimensionless	[Relative permeability]-1
Stress	kg.m^-1.s^-2	Pa, N.m^-2	[Force]/[Area]. Same as pressure
T:
Temperature	K	K (kelvin)
Temperature gradient	K.m^-1		[ΔTemperature]/[Distance]. Same as thermal gradient
Tensile strength	kg.m^-1.s^-2	N.m^-2, Pa	[Force]/[Area]. Same as pressure
Tension	kg.m^-1.s^-2	Pa, N.m^-2	[Force]/[Area]. Like pressure
Thermal conductivity	kg.m.s^-3.K^-1	W.m^-1.K^-1	[Heat flux]/([Distance][ΔTemperature]). Same as heat conductivity*
Thermal diffusivity	m².s^-1		([∂Temperatute]/[∂Time])/[∇²Temperature].
Thermal expansion coefficient	K^-1		([ΔLength]/[Length])/[Temperature]
Thermal gradient	K.m^-1		[ΔTemperature]/[Distance]. Same as temperature gradient
Thermal resistance	kg^-1.m^-2.s³K	K/W	of a device. [ΔT]/[Power].
Thermodynamic force	kg.m.s^-2.mol^-1	N/mol	[ΔChemical potential]/[Distance]
Thermoelectric power \| Thermopower	kg.m².s^-3.A^-1.K^-1	V.K^-1	[ΔPotential]/[ΔTemperature]. Same as Seeback coefficient
Thickness	m		usually referred to planar structures
Thomson coefficient	kg.m².s^-3.A^-1.K^-1	W.K^-1.A^-1	[Heat flux]/([ΔTemperature]*[Current])
Time	s	s (second)
Torque \| Moment of force	kg.m².s^-2	N.m	[Force]*[Distance]
Traction	kg.m.s^-2	N (newton)	Maximum tangential force before slipping
Traction coefficient	1	Dimensionless	[Traction]/[Weight]
Transaction value \| Sale \| Purchase	cur	currency	Economy and finance
Transactions count	1	Dimensionless	Economy and finance
Transactions rate \| Activity	s^-1	1/year	[Transactions]/[Time period]. Economy and finance
Transactions volume \| Sales flow	cur.s^-1		[Value]/[Time period]. Economy and Finance
Transmission loss	m^-1	dB/m	[Ratio]/m. Generic, usable for any quantity
U:
V:
V-number \| Abbé number \| Constringence	1	Dimensionless	V_D = (n_D-1)/(n_F-n_C)
Value \| Price	cur	currency	Economy and finance
van der Waals constant: a	kg.m⁵.s^-2.mol^-2	Pa.m⁶	a in (p+a/V²)(V-b)=RT, where V is molar volume
van der Waals constant: b	m³.mol^-1		b in (p+a/V²)(V-b)=RT, where V is molar volume
Variance of current noise n_J²	s.A²	A²/Hz	[Current]²/[Bandwidth]
Variance of voltage noise n_V²	kg².m⁴.s^-5.A^-2	V²/Hz	[Voltage]²/[Bandwidth]
Vector potential, magnetic	kg.m.s^-2.A^-1	m^-1.s.V, m.T	[Mag.flux density][Distance], [El.field strength][Time]
Velocity	m.s^-1	m/s	[Distance]/[Time]. Same as speed
Velocity, advection	m.s^-1	m/s	In porous media; actual progress along pressure gradient
Velocity, of money (circulation)	s^-1	1/year	[Transactions]/[Time period]. Economy and finance
Velocity, superficial	m.s^-1	m/s	In porous media; as if the space was filled only by the fluid
Verdet constant	kg^-1.m^-1.s².A¹	rad.m^-1.T^-1	([Angle]/[Length])/[Magnetic flux density]
Virial coefficient: second	m³.mol^-1		B in pV/(nRT)=1+B(n/V)+C(n/V)²+D(n/V)³+...
Virial coefficient: third	m⁶.mol^-2		C in pV/(nRT)=1+B(n/V)+C(n/V)²+D(n/V)³+...
Virial coefficient: fourth	m⁹.mol^-3		C in pV/(nRT)=1+B(n/V)+C(n/V)²+D(n/V)³+...
Viscosity, dynamic	kg.m^-1.s^-1	Pa.s	([Force]/[Area])/[ΔVelocity]
Viscosity, kinematic	m².s^-1		[Dynamic viscosity]/[Density]
Voltage \| Electromotive force	kg.m².s^-3.A^-1	V	[ΔPotential]
Voltage noise, variance n_V²	kg².m⁴.s^-5.A^-2	V²/Hz	[Voltage]²/[Bandwidth]
Volume	m³		[Area]*[Distance]
Volume concentration	1	Dimensionless	[Partial volume]/[Total volume]
Volume flow	m³.s^-1		[Volume]/[Time]. For example, through a device
Volume growth rate	m³.s^-1		[Volume]/[Time]. For example, of a crystal
Volume porosity	1	Dimensionless	[Pores volume]/[Total volume], in porous media
W:
Wave function for N particles (quantum)	m^-3N/2	tentative	\|ψ\|²dτ^N is a dimensionless probability element.
Wavelength	m		[Wave velocity]/[Frequency]
Wavenumber	m^-1		[Number of waves]/[Distance]
Wealth \| Asset	cur	currency	Economy and finance
Work function	kg.m².s^-2	J, eV	[Energy] needed to remove an electron
X:
Y:
Young modulus	kg.m^-1.s^-2	N.m^-2, Pa	[Stress]/[Strain]. Like shear modulus
Z:

Notes

Purpose: Physical (or rather metrological) dimensions are often bewildering, even though the international SI system of units has simplified things a lot, compared to early 20th century and before. The main purpose of this page is to provide a fast, handy reference to the dimension you might need at the spur of a moment. Another, less evident, purpose is to stimulate curiosity and the desire to study Metrology and Dimensional Analysis.
Formats and editorial comments: - Bold magenta symbols in the Alternatives column indicate commonly used quantities, mostly defined by the SI system.
- Square brackets convert the quantity they enclose into its dimension.
- Abbreviations El. and Mag. stand for Electric and Magnetic, respectively.
- [Quantity] stands for [Quantity of substance] and its dimension is mol.
- Names of units are always written with small first letter, even when derived from names of persons (for example 1 newton).
Many links, other than those appearing below,: will be soon scattered through the text, accompanying the particular quantities. This feature will be intensified.
Feedback:: If you think a link, or a quantity, are missing, please, let me know. Such suggestions are most appreciated.
Disclaimer:: Since errors do happen, and also because not all metrological conventions are agreed upon and shared by everybody, the Editor of this page declines any responsibility for any damages that might result from its content, directly or indirectly. In other words, if you crash a spacecraft because some of your engineers used meters and others used feet, do not pretend that I should pay for it :-)

References

Beaman Jr. Joseph J., Longoria Raul G.,
Modeling of Physical Systems,
Wiley 2016. ISBN 978-1119945048. Hardcover >>.
Zohuri Bahman,
Dimensional Analysis and Self-Similarity Methods for Engineers and Scientists,
Springer 2015. ISBN 978-3319134758. Hardcover >>.
Isakov Edmund,
International System of Units (SI):
How the world measures almost everything, and the people who made it possible,
Industrial Press 2014. ISBN 978-0831102319. Paperback >>. Also available as Multimedia CD.
Bridgman Percy W.,
Dimensional Analysis,
Reprint of the 1922 clasic. TheClassics.us 2013. ISBN 978-1230226214. Paperback >>. Kindle >>.
Crease Robert P.,
World in the Balance: The Historic Quest for an Absolute System of Measurement,
W.W.Norton & Company 2012. ISBN 978-0393343540. Paperback >>. Kindle >>.
Gibbings J.C.,
Dimensional Analysis,
Springer 2011. ISBN 978-1849963169. Paperback >>. Kindle >>.
Klein Herbert A.,
The Science of Measurement: A Historical Survey,
Dover Publications 2011. ISBN 978-0486258393. Paperback >>. Kindle >>.
Gupta S.V.,
Units of Measurement: Past, Present and Future. International System of Units,
Springer 2009. ISBN 978-3642007378. Hardcover >>. Kindle >>.
Palmer Andrew C.,
Dimensional Analysis and Intelligent Experimentation,
World Scientific Publishing 2008. ISBN 978-9812708199. Paperback >>.
Charalambos D. Aliprantis, Border Kim,
Infinite Dimensional Analysis: A Hitchhiker's Guide,
3rd Edition, Springer 2007. ISBN 978-3540326960. Paperback >>.
Strothman J, Editor,
ISA Handbook of Measurement Equations and Tables,
2nd Edition, ISA (Instrumentation, Systems, and Automation) 2006.
ISBN 978-1556179464. Paperback >>. 2015 Kindle >>.
Szirtes Thomas,
Applied Dimensional Analysis and Modeling,
2nd Edition, Butterworth-Heinemann 2006. ISBN 978-0123706201. Paperback >>. Kindle >>.
Jerrard H.G.,
Dictionary of Scientific Units Including Dimensionless Numbers and Scales,
Springer 1992. ISBN 978-0412467202. Paperback >>.
Sena L.A.,
Units of physical quantities and their dimensions,
Mir Publishers 1973. Hardcover >>.
For more, see References on Systems of Units of Measurements

Links

Dimensional analysis on Wikipedia.
BIPM. The home page of the SI System of Units.
NIST Units of Measurements page.
NIST Units Bibliography to official on-line publications about the SI system.
Unit Converters list.
SI Units. A related resource on this website.
Constants of physics and mathematics. A related resource on this website.
Math Constants. A related resource on this website.
SI Dimensions of Physical Quantities. A related resource on this website (sorted alphabetically).
Dimensions of Physical Quantities by Category. Link to this resource. You can also cite its DOI link: 10.3247/SL1Phys06.004.
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