| Quantity |
Dimension |
Alternatives |
Root definition and Notes |
| Basic SI quantities |
| Length |
m |
m |
meter |
| Mass |
kg |
kg |
kilogram |
| Time |
s |
s |
second |
| Current, electric |
A |
A |
ampere |
| Temperature |
K |
K |
kelvin |
| Quantity of substance |
mol |
mol |
mole |
| Luminosity | Luminous intensity |
cd |
cd |
candle |
| Universal dimensionless quantities |
| Ratio of like quantities |
1 |
|
|
| Relative variation |
1 |
|
ΔQ/Q, for any quantity Q. |
| Logarithmic scale differential | Relative differential |
1 |
|
d{ln(Q)} = dQ/Q, for any quantity Q |
| Probability of an event |
1 |
|
Real number lying in the interval [0,1]. |
| Plane angle |
1 |
rad |
radian |
| Phase angle |
1 |
rad |
φ in exp(i(ωt+φ)) |
| Solid angle |
1 |
sr |
steradian |
| Logarithmic ratio logb(A/A') |
1 |
log in any base b |
Applicable to any ratio of like quantities. |
| Logarithmic ratio ln(A/A') |
1 |
Np |
neper. Uses natural logarithm. |
| Ln-scale probability density |
1 |
Np-1 |
[Probability]/[Natural-logarithmic ratio] |
| Logarithmic ratio Log(P/P')/10 |
1 |
dB |
decibel. Uses base-10 logarithm. Applies to power P |
| Logarithmic ratio Log(X/X')/20 |
1 |
dB |
decibel. Uses base-10 logarithm. Applies to amplitudes X |
| Quantities related only to time |
| Time | Duration |
s |
s |
second |
| Log-scale evolution rate | Relative evolution rate |
s-1 |
|
d{ln(Q)}/dt = (dQ/dt)/Q. |
| Count rate |
s-1 |
|
[Events]/[Time]. |
| Activity | Radioactivity |
s-1 |
Bq |
bequerel. [Events]/[Time]. |
| Frequency of waves or events |
s-1 |
Hz |
hertz . |
| Frequency drift rate |
s-2 |
Hz.s-1 |
[ΔFrequency]/[Time]. |
| Phase drift rate |
s-1 |
rad.s-1 |
[Phase angle]/[Time]. |
| Angular velocity |
s-1 |
rad.s-1 |
[Plane angle]/[Time]. |
| Angular acceleration |
s-2 |
rad.s-2 |
[ΔAngularVelocity]/[Time]. |
| Relaxation time |
s |
|
Used in all branches of Science. |
| Relaxation rate |
s-1 |
|
1/[Relaxation time]. |
| Quantities related only to space |
| Length |
m |
m |
meter |
| Distance | Position vector |
m |
|
in all Euclidean n-dimensional spaces. |
| Area | Cross section |
m2 |
|
[Distance]*[Distance]. |
| Volume |
m3 |
|
[Area]*[Distance] |
| Curvature radius |
m |
|
of a line in plane/space or surface in space |
| K-space vector |
m-1 |
|
same as reciprocal space position. |
| Convergence |
m-1 |
dioptry |
in optics, but not only ... |
| Extinction coefficient |
m-1 |
|
In transmition of a radiation through space. |
| Wavenumber |
m-1 |
|
[Number of waves]/[Distance]. |
| Wavelength |
m |
|
[Wave velocity]/[Frequency]. |
| Kinematics |
| Velocity | Speed |
m.s-1 |
|
[Distance]/[Time] |
| Drift speed |
m.s-1 |
|
Steady-state speed of an object . |
| Acceleration, linear |
m.s-2 |
|
[ΔVelocity]/[Time] |
| Matter distribution and transport |
| Mass |
kg |
kg |
kilogram |
| Specific density | Density of mass |
kg.m-3 |
|
[Mass]/[Volume]. |
| Specific volume |
m3.kg-1 |
|
[Volume]/[Mass]. |
| Number density |
m-3 |
|
[Particles]/[Volume]. |
| Number density, molar |
mol-1 |
|
[Particles]/[Mol]. The Avogadro constant. |
| Concentration | Molar concentration |
m-3.mol |
|
[Quantity]/[Volume]. Also density of substance |
| Volume concentration |
1 |
Dimensionless |
[Volume of substance]/[Total volume] |
| Mass | Weight concentration |
1 |
Dimensionless |
[Mass of substance]/[Total mass]. |
| Molar mass |
kg.mol-1 |
|
[Mass]/[Quantity] |
| Molar density | Molarity | Molar concentration |
m-3.mol |
|
[Quantity]/[Volume]. |
| Molality |
kg-1.mol |
mol/kg |
[Quantity]/[Mass]. |
| Molar volume |
m3.mol-1 |
|
[Volume]/[Quantity]. |
| Mass flow | Mass production rate |
kg.s-1 |
|
[ΔMass]/[Time]. |
| Diffusion coefficient |
m2.s-1 |
|
[Distance2]/[Time]. |
| Katalytic activity | Molar production rate |
mol.s-1 |
katal |
[ΔQuantityOfSubstance]/[Time]. |
| Mechanics |
| Moment of motion |
kg.m.s-1 |
|
[Mass]*[Velocity], [Mass flow]*[Distance]. |
| Force |
kg.m.s-2 |
N |
newton. [Mass]*[Acceleration]. |
| Moment of force | Torque |
kg.m2.s-2 |
N.m |
[Force]*[Distance]. Same as energy. |
| Pressure | Stress | Tension |
kg.m-1.s-2 |
N.m-2, Pa |
pascal. [Force]/[Area]. |
| Energy | Lagrangian | Hamiltonian |
kg.m2.s-2 |
N.m, J |
joule. [Force]*[Distance], [Power]*[Time]. |
| Specific energy |
m2.s-2 |
J.kg-1 |
[Energy]/[Mass]. |
| Molar energy |
kg.m2.s-2.mol-1 |
J.mol-1 |
[Energy]/[Quantity]. |
| Energy density |
kg.m-1.s-2 |
J.m-3 |
[Energy]/[Volume]. |
| Power | Energy flux |
kg.m2.s-3 |
J.s-1, W |
watt. [ΔEnergy]/[ΔTime]. |
| Action |
kg.m2.s-1 |
J.s |
[Energy]*[Time], [Moment of motion]*[Distance] |
| Angular moment of motion |
kg.m2.s-1 |
J.s |
[Moment of motion]*[Distance]. |
| Angular moment of inertia |
kg.m2 |
|
[Mass]*[Distance2]. |
| Circulation |
m2.s-1 |
J.s.kg-1 |
[Angular moment of motion]/[Mass] |
| Spin |
1 |
Dimensionless |
of a quantum particle |
| Gravity |
| Gravitational field intensity | Gravity |
m.s-2 |
|
[Force]/[Mass], [Acceleration]. |
| Gravitational field potential |
m2.s-2 |
|
[Energy]/[Mass]. |
| Mechanical properties of matter |
| Compressibility | Bulk modulus | Compression modulus |
kg-1.m.s2 |
Pa-1 |
[Pressure]/([ΔVolume]/[Volume]). |
| Young modulus |
kg.m-1.s-2 |
N.m-2, Pa |
[Stress]/([ΔLength]/[Length]). |
| Shear modulus | Modulus of rigidity |
kg.m.s-2 |
N, N.rad-1 |
[Force]/[ΔAngle]. |
| Impact | Notch resistance |
kg.s-2 |
J.m-2 |
[Energy]/[Area] |
| Hardness |
kg.m-1.s-2 |
N.m-2 |
[Force]/[Area] |
| Friction coefficient |
1 |
Dimensionless |
[Tangential force]/[Normal force]. |
| Self-diffusion coefficient |
m2.s-1 |
|
[Distance2]/[Time]. |
| Surface tension |
kg.s-2 |
N/m |
[Force]/[Length]. Same as surface energy. |
| Surface energy |
kg.s-2 |
J/m2 |
[Energy]/[Area]. Same as surface tension. |
| Viscosity, dynamic |
kg.m-1.s-1 |
Pa.s |
([Force]/[Area])/[ΔVelocity] |
| Viscosity, kinematic |
m2.s-1 |
|
[Dynamic viscosity]/[Density] |
| Reynolds number |
1 |
Dimensionless |
[Velocity]*[length]/[Kinematic viscosity] |
| Thermodynamics |
| Temperature |
K |
K |
kelvin |
| Temperature gradient | Thermal gradient |
K.m-1 |
|
[ΔTemperature]/[Distance]. |
| Heat | Internal energy | Enthalpy |
kg.m2.s-2 |
J |
Same as energy. |
| Heat flux |
kg.m2.s-3 |
J.s, W |
[ΔHeat]/[ΔTime]. Same as power. |
| Heat flux density | Irradiance |
kg.s-3 |
W.m-2 |
[Heat flux]/[Area]. |
| Specific heat | internal energy | enthalpy |
m2.s-2 |
J.kg-1 |
[Heat]/[Mass]. |
| Molar heat | internal energy | enthalpy |
kg.m2.s-2.mol-1 |
J.mol-1 |
[Heat]/[Quantity]. |
| Free energy | Free enthalpy |
kg.m2.s-2 |
J |
Helmholtz | Gibbs functions, respectively. |
| Specific free energy | free enthalpy |
m2.s-2 |
J.kg-1 |
[Energy]/[Mass]. Also specific Helmholtz | Gibbs functions |
| Molar free energy | free enthalpy |
kg.m2.s-2.mol-1 |
J.mol-1 |
[Energy]/[Quantity]. Molar versions of the above |
| Heat capacity |
kg.m2.s-2.K-1 |
J.K-1 |
[ΔHeat]/[ΔTemperature]. |
| Entropy |
kg.m2.s-2.K-1 |
J.K-1 |
[ΔHeat]/[Temperature]. |
| Specific entropy |
m2.s-2.K-1 |
J.K-1.kg-1 |
[Entropy]/[Mass]. |
| Molar entropy |
kg.m2.s-2.K-1.mol-1 |
J.K-1.mol-1 |
[Entropy]/[Quantity]. |
| Thermodynamic properties of matter |
| Thermal expansion coefficient |
K-1 |
|
([ΔLength]/[Length])/[Temperature]. |
| Thermal | Heat conductivity |
kg.m.s-3.K-1 |
W.m-1.K-1 |
[Heat flux]/([Distance]*[ΔTemperature]). |
| Thermal diffusivity |
m2.s-1 |
|
([∂Temp]/[∂Time])/[∇2Temp]. |
| Prandtl number |
1 |
Dimensionless |
[Kinematic viscosity]/[Thermal diffusivity]. |
| Specific heat capacity |
m2.s-2.K-1 |
J.K-1.kg-1 |
[Heat capacity]/[Mass]. |
| Molar heat capacity |
kg.m2.s-2.K-1.mol-1 |
J.K-1.mol-1 |
[Heat capacity]/[Quantity]. |
| Joule-Thomson coefficient |
kg-1.m.s2.K |
K.Pa-1 |
[ΔTemperature]/[ΔPressure]. |
| Pi coefficient, molar |
kg.m-1.s-2.mol-1 |
J.m-3 |
[ΔInternalEnergy]/[ΔVolume]. |
| Chemical potential, molar |
kg.m2.s-2.mol-1 |
J.mol-1 |
[ΔInternalEnergy]/[ΔQuantityOfSubstance]. |
| Electromagnetism |
| Current, electric |
A |
A |
ampere |
| Current density | Current intensity |
m-2.A |
|
[Current]/[Area] |
| Charge, electric |
s.A |
C |
coulomb. [Current]*[Time] |
| Charge density |
m-3.s.A |
C.m-3 |
[Charge]/[Volume] |
| Specific charge | Charge/mass ratio |
kg-1.s.A |
C.kg-1 |
[Charge]/[Mass] |
| Molar charge |
s.A.mol-1 |
C.mol-1 |
[Charge]/[Quantity] |
| Quantum charge |
1 |
Dimensionless |
[Charge]/[Elementary charge quantum] |
| Surface density of charge |
m-2.s.A |
C.m-2 |
[Charge]/[Area] |
| Potential, electric |
kg.m2.s-3.A-1 |
W.A-1, J.C-1, C.F-1, V |
volt. [Power]/[Current], [Energy]/[Charge] |
| Electromotive force (emf) |
kg.m2.s-3.A-1 |
V |
[ΔPotential] |
| Electric dipole moment |
m.s.A |
C.m |
[Charge]*[Distance] |
| Electric quadrupole moment |
m2.s.A |
C.m2 |
[El.dipole]*[Distance] |
| Resistance |
kg.m2.s-3.A-2 |
V.A-1, Ω |
ohm. [ΔPotential]/[Current] |
| Conductance |
kg-1.m-2.s3.A2 |
A.V-1, S |
siemens. [Current]/[ΔPotential]. Inverse of resistance |
| Capacitance |
kg-1.m-2.s4.A2 |
C.V-1, F |
farad. [Charge]/[ΔPotential] |
| 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 polarization |
m-2.s.A |
C.m-2 |
[Charge]/[Area]. Same as electric flux density |
| Magnetic field strength | Magnetic intensity |
m-1.A |
|
[Current]/[Distance]. |
| Magnetization |
m-1.A |
|
[Magnetic moment]/[Volume]. As magnetic field strength |
| Magnetomotive force (mmf) |
A |
|
[Current]*[Number fo turms] |
| 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]. |
| Vector potential |
kg.m.s-2.A-1 |
V.s.m-1, T.m |
[Electric field strength]*[Time], [Mag.flux density]*[Distance] |
| Poynting vector |
kg.s-3 |
W.m-2 |
[El.field strength]/[Mag.field strength]. Same as irradiance |
| Magnetic field gradient |
kg.m-1.s-2.A-1 |
T.m-1 |
[ΔMagnetic flux density]/[Distance]. |
| Magnetic dipole moment |
m2.A |
J.T-1 |
[Current]*[Area] |
| Magnetic quadrupole moment |
m3.A |
m.J.T-1 |
[Magnetic dipole]*[Distance] |
| Inductance | Mutual inductance |
kg.m2.s-2.A-2 |
V.s.A-1, Wb.A-1, H |
henry. [ΔPotential]/[dCurrent/dt] or [Magnetic flux]/[Current] |
| Gyromagnetic ratio |
kg-1.s.A |
Hz.T-1 |
[Mag.moment]/[Angular moment of motion]. |
| Magnetogyric ratio |
kg.s-1.A-1 |
T.Hz-1 |
[Angular moment of motion]/[Mag.moment]. |
| Current noise, variance nJ2 |
s.A2 |
A2/Hz |
[Current]2/[Bandwidth] |
| Voltage noise, variance nV2 |
kg2.m4.s-5.A-2 |
V2/Hz |
[Voltage]2/[Bandwidth] |
| Electromagnetic properties of matter |
| Resistivity |
kg.m3.s-3.A-2 |
Ω.m |
[Resistance]*[Length])/[Area]. |
| Conductivity |
kg-1.m-3.s3.A2 |
S.m-1 |
1/[Resistivity]. |
| Permittivity, electric |
kg-1.m-3.s4.A2 |
F.m-1 |
[El.flux density]/[El.field strength]. |
| Dielectric constant | Relative permittivity |
1 |
Dimensionless |
[Permittivity]/[Permittivity of vacuum]. |
| Permeability, magnetic |
kg.m.s-2.A-2 |
N.A-2, H.m-1 |
[Mag.flux density]/[Mag.field strength]. |
| Relative permeability, magnetic |
1 |
Dimensionless |
[Permeability]/[Permeability of vacuum]. |
| Susceptibility, magnetic |
1 |
Dimensionless |
[Relative permeability] - 1. |
| Characteristic impedance |
kg.m2.s-3.A-2 |
V.A-1, Ω, ohm |
√([Mag.Permeability]/[El.Permittivity]). |
| Electric|Dielectric strength |
kg.m.s-3.A-1 |
V.m-1 |
[ΔPotential]/[Distance]. |
| Verdet constant |
kg-1.m-1.s2.A1 |
rad.m-1.T-1 |
([Angle]/[Length])/[Magnetic flux density] |
| Work function |
kg.m2.s-2 |
J, eV |
[Energy] needed to remove an electron. |
| Seeback coef. | Thermopower | Thermoelectric power |
kg.m2.s-3.A-1.K-1 |
V.K-1 |
[ΔPotential]/[ΔTemperature]. |
| Thomson coefficient |
kg.m2.s-3.A-1.K-1 |
W.K-1.A-1 |
[Heat flux]/([ΔTemperature]*[Current]). |
| Peltier coefficient |
kg.m2.s-3.A-1 |
W.A-1, V |
[Heat flux]/[Current]. |
| Piezzoelectric coefficient |
kg.m.s-3.A-1 |
V.m-1 |
[El.field strength]/([ΔLength]/[Length]). |
| Electrostriction coefficient |
kg-2.m-2.s6.A2 |
m2.V-2 |
([ΔVolume]/[Volume])/[El.field strength]2. |
| g-factor of a particle |
1 |
Dimensionless |
[Mag.moment]/([Spin].[Bohr magneton]) |
| Optics |
| Convergence |
m-1 |
dioptry |
dioptry |
| Luminosity | Luminous intensity |
cd |
cd |
candle or lumen/sr |
| Luminous flux | Luminous power |
cd.sr |
lm |
lumen. [Luminosity]*[Solid angle]. |
| Luminance |
cd.m-2 |
|
[Luminosity]/[Area] |
| Luminous energy |
cd.sr.s |
lm.s |
[Luminous flux]*[Time]. Also known as talbot |
| Illuminance |
cd.sr.m-2 |
lm.m-2, lx |
lux. [Luminous flux]/[Area]. |
| Luminous emittance |
cd.sr.m-2 |
lm.m-2, lx |
lux. Same as illuminance, but for sources |
| Luminous efficacy |
cd.sr.kg-1.m-1.s3 |
lm/W |
[Luminous flux]/[Power] |
| Luminous efficiency | Luminous coefficient |
1 |
Dimensionless |
[Luminous efficacy]/[683 lm/W]. |
| Irradiance |
kg.s-3 |
W.m-2 |
[Power]/[Area]. For all kinds of energy deposition |
| Radiance |
kg.s-3.sr-1 |
W.m-2.sr-1 |
([Power]/[Area])/[Solid angle] |
| Optical properties of matter |
| Extinction coefficient |
m-1 |
|
|
| Refractive index |
1 |
Dimensionless |
Light speeds ratio (in medium)/(in vacuum) |
| Specific refractivity |
m3.kg-1 |
|
[(r2-1)/(r2+2)]/[Specific density], where r is refractive index |
| Molar refractivity |
m3.mol-1 |
|
[(r2-1)/(r2+2)]/[Concentration] |
| Dispersivity quotient |
m-1 |
|
[ΔRefractive index]/[ΔWavelength] |
| Dispersive power |
1 |
Dimensionless |
Ratio of differences of refractive indices. |
| Abbé number |
1 |
Dimensionless |
Inverse of refractive index. |
| Star magnitude (astronomy) |
1 |
Dimensionless |
m-m'= -100.4(S/S'). S,S' are luminous fluxes of two stars |
| Chemistry and physical chemistry. |
| Concentration | Molar density | Molarity |
m-3.mol |
|
[Quantity]/[Volume]. Also called Density of substance |
| Molality |
kg-1.mol |
mol/kg |
[Quantity]/[Mass]. |
| Katalytic activity | Molar production rate |
mol.s-1 |
katal |
[Quantity]/[Time]. |
| Molar mass |
kg.mol-1 |
|
[Mass]/[Quantity] |
| Molar charge |
s.A.mol-1 |
C.mol-1 |
[Charge]/[Quantity] |
| Molecular | ionic quantum charge |
1 |
Dimensionless |
[Charge of a molecule or ion]/[Elementary charge quantum] |
| Ionic strength | Ionic force |
m-3.mol |
|
Sum([Conc.]*[Ionic quantum charge]2) |
| Ion mobility |
kg-1.m-1.s2.A |
m2.s-1.V-1 |
[Velocity]/[Electric field strength] . |
| Drift speed |
m.s-1 |
|
Steady-state speed of ions in electric field . |
| Fugacity |
kg.m-1.s-2 |
Pa |
Effective pressure in real gases. |
| Osmotic pressure |
kg.m-1.s-2 |
Pa |
|
| Thermodynamic force |
kg.m.s-2.mol-1 |
N/mol |
[ΔChemical potential]/[Distance] |
| Chemico-physical properties of matter |
| Molar volume |
m3.mol-1 |
|
[Volume]/[Quantity]. |
| Chemical potential, molar |
kg.m2.s-2.mol-1 |
J.mol-1 |
[ΔInternalEnergy]/[ΔQuantityOfSubstance]. |
| Solubility, molar |
m-3.mol |
|
[Quantity]/[Volume]. |
| Reduction | Redox potential |
kg.m2.s-3.A-1 |
V |
|
| Molar conductivity |
kg-1.s3.A2.mol-1 |
S.m2.mol-1 |
[El.conductivity]/[Concentration]. |
| Molar relaxivity |
m3.s-1.mol-1 |
|
[Relaxation rate]/[Concentration]. |
| Ebullioscopic constant |
kg.mol-1.K |
K/(mol/kg) |
[ΔTemperature]/[Molality]. |
| Cryoscopic constant |
kg.mol-1.K |
K/(mol/kg) |
[ΔTemperature]/[Molality]. |
| van der Waals constant: a |
kg.m5.s-2 |
Pa.m6 |
a in (p+a/V2)(V-b)=RT. |
| van der Waals constant: b |
m3 |
|
b in (p+a/V2)(V-b)=RT. |
| van der Waals virial constant: A |
kg-1.m5.s-2.mol-2 |
|
A in p=(n/V)RT+(n/V)2(RTB-A). |
| van der Waals virial constant: B |
kg-1.m3.mol-1 |
|
B in p=(n/V)RT+(n/V)2(RTB-A). |
| Virial coefficient: second |
kg.m5.s-2.mol-2 |
Pa.(mol.m-3)-2 |
A in p=(n/V)RT+A(n/V)2+B(n/V)3+C(n/V)4. |
| Virial coefficient: third |
kg.m8.s-2.mol-3 |
Pa.(mol.m-3)-3 |
B in p=(n/V)RT+A(n/V)2+B(n/V)3+C(n/V)4. |
| Virial coefficient: fourth |
kg.m11.s-2.mol-4 |
Pa.(mol.m-3)-4 |
C in p=(n/V)RT+A(n/V)2+B(n/V)3+C(n/V)4. |
| Radiation and radioactivity. |
| Irradiance |
kg.s-3 |
W.m-2 |
[Power]/[Area]. For all kinds of energy deposition. |
| Activity | Radioactivity |
s-1 |
Bq |
bequerel. [Events]/[Time]. |
| Absorbed dose |
m2.s-2 |
J.kg-1, Gy |
gray. [Energy]/[Mass]. |
| Absorbed dose rate |
m2.s-3 |
Gy.s-1 |
[Absorbed dose]/[Time]. |
| Absorbed dose equivalent |
m2.s-2 |
J.kg-1, Sv |
sievert. [const].[Energy]/[Mass]. |
| Exposure |
kg-1.s.A |
C.kg-1 |
[Charge]/[Mass]. For ionising radiations. |
| Radiation properties of matter |
| Half life |
s |
|
typically of a radioactive substance |
| Informatics |
| Information |
bit-1 |
bit |
bit; the elementary information quantum. |
| Baud rate | Information flux |
bit.s-1 |
Baud |
baud. [Information]/[Time]. |
| Operators |
| d/dt |
s-1 |
|
|
| dp/dtp |
s-p |
|
For p = 1,2,3,... |
| ∇ | div | grad | rot | curl |
m-1 |
|
Any derivative with respect to a distance. |
| ∇2 | Laplacian | D'Allembertian |
m-2 |
|
|
| dp/drp |
m-p |
|
For p = 1,2,3,... [r] is a Length. |