SI Dimensions of Physical Quantities listed by Category
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/SL1Phys06.004
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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 
Pseudo-dimensional quantities: 
Plane angle  1  rad  radian 
Solid angle  1  sr  steradian 
Universal dimensionless quantities 
Count of events | Number of instances  1    This covers all kinds of enumerations 
Probability of an event  1    Real number in a dimensionless interval [0,1] 
Ratio of commensurable quantities  1    Q1/Q2, with Q1 and Q2 having the same dimension 
Relative variation  1    ΔQ/Q, for any quantity Q 
Logarithmic ratio logb(A/A') in any base b  1    Applicable to any ratio of commensurable quantities 
Logarithmic scale differential | Relative differential  1    d{ln(Q)} = dQ/Q, for any quantity Q 
Pseudo-dimensional quantities: 
Phase | Phase angle  1  rad  φ typically in exp(i(ωt+φ)) 
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 
Gain or Loss of a device  1  usually in dB  [Output]/[Input], provided they are commensurable quantities 
Attenuation | Amplification (generic)   1  usually in dB  [Quantity(p)]/[Quantity(p')], with p being some parameter 
Logarithmic ratio ln(A/A')  1  Np  Neper. Uses natural logarithm 
Logarithmic scale probability density  1  1/Np  [Probability]/[Natural-logarithmic ratio] 
Operators 
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 
Nabla ( ∇ ) | div | grad | rot | curl  m-1   Any derivative-like construct with respect to a distance 
Laplace operator | Laplacian m-2   2 = ∂2/∂x2 + ∂2/∂y2 + ∂2/∂z2 
D'Alembert operator | D'Alembertian  m-2   (1/c2)2/∂t2 - ∂2/∂x2 - ∂2/∂y2 - ∂2/∂z2 
Multiple derivatives with respect to time  s-p   dp/dtp, ∂p/∂tp; for p = 1,2,3,.. 
Multiple derivatives with respect to a length  m-p   dp/drp, ∂p/∂rp; for p = 1,2,3,..., r = x | y | z 
Quantities related only to time 
Time | Duration  s  s  second 
Half life  s    of a non-conservative / decaying quantity 
Settling time  s  typically dB/s  Used to describe transient phenomena 
Relaxation time  s    Used for returns to equilibria 
Activity | Frequency of events  s-1   [Counts]/[Time] 
Count rate | Expectation frequency  s-1   [Counts]/[Time] 
Relative growth rate  s-1   [Relative variation]/[Time] 
Relative evolution rate | Log-scale evolution rate  s-1   d{ln(Q)}/dt = (dQ/dt)/Q 
Settling rate  s-1 typically dB/s  [Ratio]/[ΔTime]. Used for transient phenomena 
Relaxation rate  s-1   1/[Relaxation time] 
Frequency of waves  s-1 Hz  hertz 
Phase drift rate  s-1 rad.s-1 [Phase angle]/[Time] 
Angular velocity / speed  s-1 rad.s-1 [Plane angle]/[Time] 
Frequency drift rate  s-2 Hz.s-1 [ΔFrequency]/[Time]. Applicable to waves 
Angular acceleration / deceleration  s-2 rad.s-2 [ΔAngularVelocity]/[Time] 
Quantities related only to space 
Position vector  m    in all Euclidean n-dimensional spaces 
Length | Distance  m  m  meter 
Perimeter | Circumference | Radius  m     
Thickness  m    usually referred to planar structures 
Wavelength  m    [Wave velocity]/[Frequency] 
Wavenumber  m-1   [Number of waves]/[Distance] 
K-space vector | Reciprocal space position  m-1    
Curvature radius  m    of a line in plane/space or surface in space 
Curvature  m-1   1/[Curvature radius] 
Convergence  m-1 dioptry  used in optics, but not only .. 
Attenuation / amplification over a distance  m-1 dB/m  [Attenuation]/[Distance]. Mostly in acoustic and electronics 
Extinction coefficient  m-1 dB/m  [Ratio]/m. Used mostly for radiation 
Propagation / transmission loss  m-1 dB/m  [Ratio]/m. Generic, usable for any quantity 
Area | Cross section  m2   [Distance]*[Distance] 
Surface element | Surface area  m2   [Distance]*[Distance]. Applicable to 3D bodies 
Volume element | Volume  m3   [Area]*[Distance] 
Propagation through space and time 
Velocity | Speed  m.s-1   [Distance]/[Time] 
Acceleration | Deceleration  m.s-2   [ΔVelocity]/[ΔTime] 
Drift speed  m.s-1   Steady-state speed of an object 
Surface / area growth rate  m2.s-1   [ΔArea]/[Time] 
Volume growth rate  m3.s-1   [ΔVolume]/[Time]. For example, of a crystal 
Volume flow  m3.s-1   [Volume]/[Time]. For example, through a device 
Matter distribution and transport 
Particle density  m-3   [Count]/[Volume]. Obsolete: number density 
Mass  kg  kg  kilogram 
Mass production rate  kg.s-1   [ΔMass]/[Time] 
Mass density | Specific density  kg.m-3   [Mass]/[Volume] 
Mass density gradient | Specific density gradient  kg.m-4   [Mass density]/[Distance] 
Specific volume  m3.kg-1   [Volume]/[Mass] 
Concentration ratio by volume  1  Dimensionless  [Partial volume]/[Total volume] 
Concentration ratio by mass  1  Dimensionless  [Partial mass]/[Total mass]. Not by weight: obsolete) 
Mass flow (total)  kg.s-1   [ΔMass]/[Time]. For example, through a device 
Diffusion coefficient  m2.s-1   [Distance2]/[Time] 
Molar distribution and transport quantities: 
Particle count, molar  mol-1   [Count]/[Mol]. For example, the Avogadro constant 
Molar production rate  mol.s-1   [ΔQuantity]/[Time] 
Molar mass  kg.mol-1   [Mass]/[Quantity] 
Molar volume  m3.mol-1   [Volume]/[Quantity] 
Molar density | Density of substance  m-3.mol   [Quantity]/[Volume] 
Molarity | Concentration  m-3.mol   [Quantity]/[Volume]. Same as molar density 
Molarity gradient | Concentration gradient  m-4.mol   [Molarity]/[Distance] 
Molar concentration ratio  1  Dimensionless  [Partial quantity]/[Total quantity] 
Molality (intended as concentration)  kg-1.mol mol/kg  [Quantity]/[Mass]. Obsolete 
Katalytic activity  mol.s-1 katal  [ΔQuantity]/[Time] 
Mechanics and hydrodynamics 
Force  kg.m.s-2 N  newton. [Mass]*[Acceleration] 
Moment of motion  kg.m.s-1   [Mass]*[Velocity], [Mass flow]*[Distance] 
Impulse  kg.m.s-1   [ΔMoment of motion], [Force]*[ΔTime], [Mass]*[ΔVelocity] 
Moment of force | Torque  kg.m2.s-2 N.m  [Force]*[Distance]. Like energy 
Couple  kg.m2.s-2 N.m  2*[Force]*[Distance] for two non-aligned opposing forces 
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] 
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] 
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 inertia  kg.m2   [Mass]*[Distance2] 
Angular moment of motion  kg.m2.s-1 J.s  [Moment of motion]*[Distance] 
Circulation  m2.s-1 J.s.kg-1 [Angular moment]/[Mass], [Velocity]*[Loop length] 
Spin  1  Dimensionless  of a quantum particle 
Stress | Tension | Compression  kg.m-1.s-2 N.m-2, Pa (pascal) [Force]/[Area]. ... same as pressure 
Compressive strength  kg.m-1.s-2 N.m-2, Pa [Force]/[Area]. Like pressure 
Strain (mechanical)  1  Dimensionless  [ΔLength]/[Length] Relative deformation 
Friction  kg.m.s-2 N  Tangential force between two moving surfaces 
Traction  kg.m.s-2 N  Maximum tangential force before slipping 
Velocity, superficial  m.s-1 m/s  In porous media; as if the space was filled only by the fluid 
Velocity, advection  m.s-1 m/s  In porous media; actual progress along pressure gradient 
Wave function for N particles (quantum)  m-3N/2 tentative  |ψ|2N is a dimensionless probability element.
Mechanical and hydrodynamic properties of matter 
Compressibility | Modulus of compression  kg-1.m.s2 Pa-1 [Pressure]/([ΔVolume]/[Volume]). Inverse of bulk modulus 
Bulk modulus  kg.m-1.s-2 N.m-2, Pa ([ΔVolume]/[Volume])/[Pressure]. Inverse of compressibility 
Young modulus  kg.m-1.s-2 N.m-2, Pa [Stress]/[Strain]. Like shear modulus 
Shear modulus | Modulus of rigidity  kg.m-1.s-2 N.m-2, Pa [Stress]/[Strain]. Same dimension aas Young modulus 
Poisson's ratio  1  Dimensionless  [Transversal striction]/[Londitudinal elongation] 
Impact | Notch resistance  kg.s-2 J.m-2 [Energy]/[Area] 
Hardness | Tensile strength  kg.m-1.s-2 N.m-2, Pa [Force]/[Area]. Like pressure 
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 
Friction coefficient  1  Dimensionless  [Tangential force]/[Normal force] 
Traction coefficient  1  Dimensionless  [Traction]/[Weight] 
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] 
Critical angle of repose  rad  or degree  Steepest angle of a slope before a slide 
Porosity, volume  1  Dimensionless  [Volume of pores]/[Total volume], in porous media 
Porosity, superficial  1  Dimensionless  [Void cross section]/[Total cross section], in porous media 
Permeability, hydraulic  m2 1 darcy = 10-12 m2 [Velocity]*[Viscosity]/[Pressure gradient], in porous media 
Conductivity, hydraulic  m.s-1 m/s  Used for porous media 
Specific acoustic impedance / resistance / reactance  kg.m-2.s-1 Pa.s/m , reyl [ΔPressure]*[Velocity], intensive property 
Specific acoustic conductance / susceptance  kg-1.m2.s reyl-1 Inverse of specific acoustic impedance 
Acoustic impedance / resistance / reactance  kg.m-4.s-1 Pa.s/m3, reyl/m2 [ΔPressure]/[Volume flow rate], extensive property 
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 
Specific heat | internal energy | enthalpy  m2.s-2 J.kg-1 [Heat]/[Mass] 
Heat capacity  kg.m2.s-2.K-1 J.K-1 [ΔHeat]/[ΔTemperature] 
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] 
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] 
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 thermodynamical quantities: 
Molar heat | internal energy | enthalpy  kg.m2.s-2.mol-1 J.mol-1 [Heat]/[Quantity] 
Molar energy  kg.m2.s-2.mol-1 J.mol-1 [Energy]/[Quantity] 
Molar entropy  kg.m2.s-2.K-1.mol-1 J.K-1.mol-1 [Entropy]/[Quantity] 
Molar free energy | free enthalpy  kg.m2.s-2.mol-1 J.mol-1 [Energy]/[Quantity]. Molar versions of the above 
Thermodynamic and thermal properties of matter 
Thermal expansion coefficient  K-1   ([ΔLength]/[Length])/[Temperature] 
Heat capacity, specific  m2.s-2.K-1 J.K-1.kg-1 [Heat capacity]/[Mass] 
Heat capacity, molar  kg.m2.s-2.K-1.mol-1 J.K-1.mol-1 [Heat capacity]/[Quantity] 
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] 
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] 
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]/[ΔQuantity] 
Softening point  K    Temperature at which hardness drops below a level 
Annealing point  K    Temperature at which viscosity drops below 1012 Pa.s 
Strain point  K    Temperature at which viscosity drops below 1013.5 Pa.s 
Flash point  K    Temperature at which vapour can be kept burning 
Fire point  K    Temperature at which ignited vapour keeps burning 
Thermal properties of devices 
Thermal resistance  kg-1.m-2.s3K K/W  [ΔT]/[Power].
Electromagnetism 
Charge, electric  s.A  C  coulomb. [Current]*[Time] 
Charge density  m-3.s.A  C.m-3 [Charge]/[Volume] 
Current, electric  A  A  ampere. [Charge]/[Time] 
Current density | Current intensity  m-2.A   [Current]/[Area] 
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] 
Electric dipole moment  m.s.A  C.m  [Charge]*[Distance] 
Electric quadrupole moment  m2.s.A  C.m2 [Electric dipole]*[Distance], [Electric charge]*[Distance2] 
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 | Electric displacement  m-2.s.A C.m-2 [Charge]/[Area]. Same as electric flux density 
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 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   [Magnetic moment]/[Volume]. Like magnetic field strength 
Magnetic charge (bound)  m-2.A   - ∇.[Magnetization] , -Divergence of magnetization 
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]. Same as magnetic moment 
Magnetic quadrupole moment  m3.A m.J.T-1 [Magnetic dipole]*[Distance] 
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] 
Relativistic four-current (Jα)  m-2.A   Like current density and [Charge]*[c] 
Relativistic four-potential (Aα)  kg.m.s-2.A-1 m-1.s.V, m.T Like magnetic vector potential and [El.potential]/[c] 
Relativistic electromagnetic field tensor (Fμν)  kg.s-2.A-1 T  Like magnetic flux density 
Relativistic displacement four-tensor (Dμν)  m-1.A   Like magnetic intensity 
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] 
Reluctance, magnetic  kg-1.m-1.s2.A2 m.H-1 1/[Permeability] 
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 | rigidity  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 
Thermoelectric power | Thermopower  kg.m2.s-3.A-1.K-1 V.K-1 [ΔPotential]/[ΔTemperature] 
Seeback coefficient  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]) 
Properties of electric/magnetic devices and circuit components 
Bandwidth  s-1 Hz  [ΔFrequency] 
Voltage | Electromotive force (emf)  kg.m2.s-3.A-1 V  [ΔPotential] 
Current, electric  A  A  ampere. [Charge]/[Time] 
Magnetomotive force (mmf)  A    [Current]*[Number of turns] 
Impedance, of a circuit  kg.m2.s-3.A-2 Ω  ohm 
Admittance, of a circuit  kg-1.m-2.s3.A2 S  siemens. 1/[Circuit impedance] 
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)  1/[Resistance] 
Capacitance  kg-1.m-2.s4.A2 C.V-1, F  farad. [Charge]/[ΔPotential] 
Reactance, capacitive  kg.m2.s-3.A-2 Ω (ohm)  1/(i[Angular frequency].[Capacitance]) 
Susceptance, capacitive  kg-1.m-2.s3.A2 S (siemens)  1/[Reactance] 
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] 
Impedance, inductive  kg.m2.s-3.A-2 Ω (ohm)  i[Angular frequency].[Inductance] 
Admittance, inductive  kg-1.m-2.s3.A2 S (siemens)  1/[Inductive impedance] 
Number of turns  1    Applicable to coils, transformers, etc 
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]
Chemistry, physical chemistry, atomic and molecular physics 
Concentration | Molar density | Molarity  m-3.mol   [Quantity]/[Volume]. Same as 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 elements 
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 
Mass number of an isotope  1  Dimensionless  Number of protons+neutrons in the isotope nuclide 
Electronegativity, Pauling χ  1  Dimensionless  Relative tendency of an atom to attract electrons; χ(H)=2.20.  
Electron affinity (always molar)  kg.m2.s-2.mol-1 J.mol-1 Energy released when binding an electron 
Chemico-physical properties of matter 
Ionization energy, molar  kg.m2.s-2.mol-1 J.mol-1 Energy to ionize a molecule/atom 
Volume, molar  m3.mol-1   [Volume]/[Quantity] 
Heat of fusion | evaporation, molar  kg.m2.s-2.mol-1 J.mol-1 [Energy]/[Quantity] 
Chemical potential, molar  kg.m2.s-2.mol-1 J.mol-1 [ΔInternalEnergy]/[ΔQuantity] 
Solubility, molar  m-3.mol   [Quantity]/[Volume] 
Reduction | Redox potential  kg.m2.s-3.A-1 V (volt)   
Conductivity, molar  kg-1.s3.A2.mol-1 S.m2.mol-1 [El.conductivity]/[Concentration] 
Relaxivity, molar  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] 
Compression factor of a real gas  1  Dimensionless  pV/(nRT). For ideal gas equals 1; temperature dependent 
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
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+...
Gravitation, Astronomy, Cosmology 
Gravitational field intensity | Gravity  m.s-2   [Force]/[Mass], Same as acceleration 
Gravitational field potential  m2.s-2   [Energy]/[Mass] 
Gravitational constant G  kg-1.m3.s-2   [Force]*[Distance]2/[Mass]2. Appears in Newton's equation 
Mean motion  s-1   Of a body on a Kepler orbit; sqrt(G(M1+M2)/r3) 
Mean anomaly  1  Dimensionless  Of a body on a Kepler orbit; t.sqrt(G(M1+M2)/r3) 
Star magnitude (astronomy)  1  Dimensionless  m-m'= -100.4(S/S'). S,S' are luminous fluxes of two stars 
Cosmological constant Λ  m-2   Appears in Einstein's equation 
Cosmological expansion rate  s-1 km/s/Mpc  [Velocity]/[Distance]. Mpc stands for Megaparsec 
Optics 
Albedo, of a surface  1  Dimensionless  [Reflected elmag power]/[Incident elmag power] 
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 
Constringence | Abbé number | V-number  1  Dimensionless  VD = (nD-1)/(nF-nC) 
Radiation and radioactivity 
Radioactivity | Activity  s-1 Bq  bequerel. [Counts]/[Time] 
Irradiance  kg.s-3 W.m-2 [Power]/[Area]. For all kinds of energy deposition 
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    Of a radioisotope 
Radiation power  m2.s-3 W/kg  [Power]/[Mass]. Heat generated by a radioisotope 
Radiation power, molar  kg.m2.s-3.mol-1 W/mol  [Power]/[Quantity]. Heat generated by a radioisotope 
Informatics 
Information  bit-1 bit  bit; the elementary information quantum 
Baud rate | Information flux  bit.s-1 Baud  baud. [Information]/[Time] 
Economy and finance 
Transactions count  1  Dimensionless  All kinds of counts 
Interest  1  %  [ΔWealth]/[Wealth]. Usually expressed as percentage 
Wealth | Asset  cur  currency  Currencies like $, EUR, Yuan, ... are different units 
Debt | Liability  cur  currency  Usually intended as negative wealth 
Value | Price  cur  currency  Prefixes: K..thousands, M..millions, B..billions 
Transaction value | Sale | Purchase  cur  currency  Often used: mean and total values 
Time period  s  year,quarter,month  Abbrevs: mrq.. most recent quarter, ttm.. trailing twelve months 
Fiscal year | Calendar year  s  year  Abbrevs: lfy.. last fiscal year, yoy.. year over year 
Transactions rate | Activity  s-1 1/year  [Transactions]/[Time period] 
Transactions volume | Sales flow  cur.s-1   [Value]/[Time period]. For example $/day or Eur/year 
Velocity / circulation of money  s-1 1/year  [Transactions]/[Time period] 
Interest rate  s-1 %/year  [Interest]/[Time period] 
Return on asset / equity  s-1 %/year  ([ΔValue]/[Value])/[Time period] 
Cash flow | Flow (generic)  cur.s-1 currency/year  [Value]/[ΔTime]. Mathematically, time derivative 
Earnings | Income rate  cur.s-1 currency/year  [Value]/[Time period] 
GDP Gross domestic product  cur.s-1 currency/year  [Earnings]. Usually refered to nations/states/admin.regions 
Debt/GDP ratio  s year  [Debt]/[Earnings]. Independent of currency / population size 
P/E Price/Earnings ratio  s year  [Value]/[Earnings]. Used to assess an asset/company 
Bond duration  s year  In general, the duration of a fixed cash flow 

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 >>.
  • Gibbins 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 >>.
  • Strothman J, Editor,
    ISA Handbook of Measurement Equations and Tables,
    2nd Edition, ISA (Instrumentation, Systems, and Automation) 2006.
    ISBN 978-1556179464. Paperback >>. 2015 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


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Copyright ©2005 Stanislav Sýkora. Stan's Library ISSN 2421-1230, DOI: 10.3247/SL1Phys06.004 Designed by Stan Sýkora