Dimensional Formulae

7/29/2019 Dimensional Formulae

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Quantity Dimension Alternatives Definition/Notes

A:

Acceleration,

angulars-2 rad.s-2 [AngularVelocity]/[Time]

Abb number 1 Dimensionless Inverse ofrefractive index.

Absorbed radiationdose

m2.s-2 J.kg-1, Gy (gray) [Energy]/[Mass]

Absorbed dose rate m2.s-3 Gy.s-1 [Absorbed dose]/[Time]

Acceleration, linear m.s-2 [Velocity]/[Time]

Action kg.m2.s-1 J.s [Energy]*[Time], [Moment ofmotion]*[Distance]

Activity of

radioactive sources-1 Bq (becquerel) [Events]/[Time]

Admittance,

inductivekg-1.m-2.s3.A2 S (siemens) 1/[Inductive impedance].

Admittance, of acircuit kg-1

.m-2

.s3

.A2

S (siemens)

1/[Circuit impedance].

Angular

acceleration s-2 rad.s-2 [AngularVelocity]/[Time]

Angular moment of

inertiakg.m2 [Mass]*[Distance2]

Angular moment of

motionkg.m2.s-1 J.s [Moment of

motion]*[Distance]. Like[action].

Angular velocity s-1 rad.s-1 [Plane angle]/[Time]

Annealing point K Temperature at which

viscosity drops below 1012Pa.s

Area m2 [Distance]*[Distance]

Attenuation m-1 dB/m [Ratio]/m. Applies topropagation.

B:

Bandwidth s-1 Hz [Frequency]

Baud rate bit.s-1 baud [Information]/[Time]. Also:information flux.

Bulk modulus kg-1.m.s2 Pa-1 [Pressure]/([Volume]/[Volume]). Same ascompressibility.

C:

Capacitance,

electrickg-1.m-2.s4.A2 C.V-1, F (farad) [Charge]/[Potential]

Capacitive

reactancekg.m2.s-3.A-2 (ohm) 1/(i[Angular frequency].

[Capacitance])

Capacitive

susceptancekg-1.m-2.s3.A2 S (siemens) 1/[Capacitive reactance].

Circulation m2.s-1 J.s.kg-1 [Angular moment]/[Mass],[Velocity]*[Loop length]

Characteristicimpedance

kg.m2.s-3.A-2 V.A-1, , ohm ([Mag.Permeability]/[El.Permittivity])


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Charge, electric s.A C (coulomb) [Current]*[Time]

Charge, quantum 1 Dimensionless [Charge]/[Elementary chargequantum]

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 kg-1.s.A C.kg-1 [Charge]/[Mass]. Same asspecific charge

Charge, molar s.A.mol-1 C.mol-1 [Charge]/[Quantity]

Chemical potential,

molarkg.m2.s-2.mol-1

J.mol-1 [InternalEnergy]/[QuantityOfSubstance]

Circuit admittance kg-1.m-2.s3.A2 S (siemens) 1/[Circuit impedance].

Circuit impedance kg.m2.s-3.A-2 (ohm)

Collision cross

section

m2 [Distance]*[Distance]. Same

as cross section

Compressibility kg-1.m.s2 Pa-1 [Pressure]/([Volume]/[Volume]). Same as bulkmodulus.

Compression kg.m-1.s-2 N.m-2, Pa (pascal) [Force]/[Area]. ... same aspressure

Compression

moduluskg-1.m.s2 Pa-1 [Pressure]/([Volume]/

[Volume]). Same ascompressibility.

Compressive

strengthkg.m-1.s-2 N.m-2, Pa [Force]/[Area]. Same

dimension as pressure.

Concentration,molar

m-3.mol [Quantity]/[Volume]. Same asmolar density.

Concentration, by

mass1 Dimensionless [Mass of substance]/[Total

mass]. Same as massconcentration

Concentration, by

volume1 Dimensionless [Volume of substance]/[Total

volume]. Same as volumeconcentration.

Concentration, by

weight1 Dimensionless [Mass of substance]/[Total

mass]. Same as massconcentration

Conductance,

electrickg-1.m-2.s3.A2 A.V-1, S (siemens) 1/[Resistance].

Conductivity,

electrickg-1.m-3.s3.A2 S.m-1 1/[Resistivity]

Conductivity, molar kg-1.s3.A2.mol-1

S.m2.mol-1 [El.conductivity]/[Concentration]

Conductivity,

thermalkg.m.s-3.K-1 W.m-1.K-1 [Heat flux]/

([Distance]*[Temperature])

Constringence 1 Dimensionless [Transversal striction]/[Londitudinal elongation].

Convergence

m-1

dioptry

in optics, but not only ...

Count of 1 This covers all kinds of


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events/instances enumerations.

Count rate s-1 [Events]/[Time]

Couple kg.m2.s-2 N.m 2*[Force]*[Distance] for twonon-aligned opposing forces.

Critical angle of

repose

rad or degree Steepest angle of a slope

before a slideCross section m2 [Distance]*[Distance]

Cryoscopic constant kg.mol-1.K K/(mol/kg) [Temperature]/[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 nJ2

s.A2 A2/Hz [Current]2/[Bandwidth]

Curvature radius

m

of a line in plane/space orsurface in space

D:

Density of electric

chargem-3.s.A C.m-3 [Charge]/[Volume]

Density of electric

currentm-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 asspecific density.

Density of

substance

m-3.mol [Quantity]/[Volume]. Same asconcentration.

Dielectric constant 1 Dimensionless [Permittivity]/[Permittivity ofvacuum]. Same as relativepermittivity

Dielectric

strength/rigiditykg.m.s-3.A-1 V.m-1 [Potential]/[Distance]. Same

as electric strength

Diffusion coefficient m2.s-1 [Distance2]/[Time].

Diffusivity, thermal m2.s-1 ([Temperatute]/[Time])/[2Temperature].

Dipole moment,

electric

m.s.A C.m [Charge]*[Distance]

Dipole moment,

magneticm2.A J.T-1 [Current]*[Area]

Dispersive power 1 Dimensionless Ratio of differences ofrefractive indices.

Dispersivity

quotientm-1 [Refractive index]/

[Wavelength]

Distance m in all Euclidean n-dimensional spaces.

Dose of absorbed

radiationm2.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


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object..Duration s s (second)

Dynamic viscosity kg.m-1.s-1 Pa.s ([Force]/[Area])/[Velocity]

E:

Ebullioscopic

constantkg.mol-1.K K/(mol/kg) [Temperature]/[Molality].

Electric capacitance kg-1.m-2.s4.A2 C.V-1, F (farad) [Charge]/[Potential]

Electric charge s.A C (coulomb) [Current]*[Time]

Electric

conductancekg-1.m-2.s3.A2 A.V-1, S (siemens) [Current]/[Potential].

Inverse ofresistance.

Electric

conductivitykg-1.m-3.s3.A2 S.m-1 1/[Resistivity].

Electric

conductivity, molarkg-1.s3.A2.mol-1

S.m2.mol-1 [El.conductivity]/[Concentration].

Electric current A A (ampere)

Electric dipolemoment m.s.A

C.m

[Charge]*[Distance]

Electric field

strengthkg.m.s-3.A-1 V.m-1 [Potential]/[Distance]. Also

called electric intensity

Electric field

gradientkg.s-3.A-1 V.m-2 [El.field strength]/

[Distance].

Electric flux density m-2.s.A C.m-2 [Charge]/[Area]. Also calledelectric induction

Electric inductance kg.m2.s-2.A-2 V.s.A-1, H (henry) [Potential]/[dCurrent/dt]

Electric induction m-2.s.A C.m-2 [Charge]/[Area]. Moreproperly electric flux density

Electric intensity kg.m.s-3.A-1 V.m-1 [Potential]/[Distance]. Moreproperly electric fieldstrength

Electric

permittivitykg-1.m-3.s4.A2 F.m-1 [El.flux density]/[El.field

strength].

Electric

permittivity,

relative

1 Dimensionless [Permittivity]/[Permittivity ofvacuum]. Same as dielectricconstant

Electric

polarizationm-2.s.A C.m-2 [Charge]/[Area]. Like electric

flux density

Electric potential

kg.m

2

.s

-3

.A

-1

W.A

-1

, J.C

-1

, V(volt) [Power]/[Current], [Energy]/[Charge]

Electric quadrupole

momentm2.s.A C.m2 [Electric dipole]*[Distance],

[Electric charge]*[Distance2]

Electric resistance kg.m2.s-3.A-2 V.A-1, (ohm) [Potential]/[Current]

Electric resistivity kg.m3.s-3.A-2 .m ([Resistance]*[Length])/[Area].

Electric strength kg.m.s-3.A-1 V.m-1 [Potential]/[Distance]. Alsocalled dielectric strength.

Electromagnetic

vector potentialkg.m.s-2.A-1 V.s.m-1, T.m [El.field strength]*[Time] or

[Mag.flux

density]*[Distance]Electromotive force kg.m2.s-3.A-1 V [Potential]


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(emf)

Electrostriction

coefficientkg-2.m-2.s6.A2 m2.V-2 ([Volume]/[Volume])/

[Electric field strength]2.

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 kg.m2.s-3 J.s-1, W (watt) [Energy]/[Time]. Same aspower.

Enthalpy kg.m2.s-2 J Like energy and heat.

Enthalpy, molar kg.m2.s-2.mol-1

J.mol-1 [Enthalpy]/[Quantity]. Likemolar heat.

Enthalpy, specific m2.s-2 J.kg-1 [Enthalpy]/[Mass]. Like

specific heat.

Entropy kg.m2.s-2.K-1 J.K-1 [Heat]/[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 on

log-scales-1 d{ln(Q)}/dt = (dQ/dt)/Q. Also

relative evolution rate

Expansion

coefficient, thermalK-1 ([Length]/[Length])/

[Temperature].

Exposure kg-1.s.A C.kg-1 [Charge]/[Mass]. Used forionising radiations.

Extinctioncoefficient

m-1 dB/m Used for propagation ofradiation.

F:

Fire point K Temperature at which ignitedvapour keeps burning

Flash point K Temperature at which vapourcan be kept burning

Force kg.m.s-2 N (newton) [Mass]*[Acceleration].

Force,

thermodynamickg.m.s-2.mol-1

N/mol [Chemical potential]/[Distance].

Free energy

kg.m

2

.s

-2

J

Also Helmholtz function.Like energy.

Free energy, molar kg.m2.s-2.mol-1

J.mol-1 [Free energy]/[Quantity].Also molarHelmholtzfunction

Free energy,

specificm2.s-2 J.kg-1 [Free energy]/[Mass]. Also

specific Helmholtz function

Free enthalpy kg.m2.s-2 J Also Gibbs function. Likeenergy.

Free enthalpy,


J.mol-1 [Free enthalpy]/[Quantity].Also molarGibbs function

Free enthalpy,specific

m2.s-2 J.kg-1 [Free enthalpy]/[Mass]. Alsospecific Gibbs function


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Frequency of waves

or eventss-1 Hz (hertz)

Frequency drift

rates-2 Hz.s-1 [Frequency]/[Time].

Friction kg.m.s-2 N (newton) Tangential force between two

moving surfaces.Friction coefficient 1 Dimensionless [Tangential force]/[Normal

force].

Fugacity kg.m-1.s-2 Pa Effective pressure in realgases.

G:

Gain of a device 1 Dimensionless [Output]/[Input], like-quantities ratio. Often in dB.

g-factor of a

particle1 Dimensionless [Magnetic moment]/([Spin].

[Bohr magneton])

Gradient, of electricfield kg.s

-3

.A

-1

V.m

-2

[El.field strength]/[Distance].

Gradient, of

magnetic fieldkg.m-1.s-2.A-1 T.m-1 [Mag.flux density]/

[Distance].

Gradient, thermal K.m-1 [Temperature]/[Distance].Same as temperaturegradient

Gravitational field

intensitym.s-2 [Force]/[Mass],

[Acceleration]. Same asgravity

Gravitational field

potential

m2.s-2 [Energy]/[Mass].

Gravity m.s-2 [Force]/[Mass],[Acceleration]. Same as grav.field intensity

Gyromagnetic ratio kg-1.s.A Hz.T-1 [Mag.moment]/[Angularmoment of motion].

H:

Half life s typically of a radioactivesubstance

Hamiltonian kg.m2.s-2 J [Force]*[Distance],[Power]*[Time]. Like energy

Hardness kg.m-1.s-2 N.m-2 [Force]/[Area]. Same aspressure.

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 [Heat]/[Temperature].

Heat capacity,

molarkg.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 | Thermal kg.m.s-3.K-1 W.m-1.K-1 [Heat flux]/


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conductivity ([Distance]*[Temperature]).

Heat flux kg.m2.s-3 J.s, W [Heat]/[Time]. Likepower.

Heat flux density kg.s-3 W.m-2 [Heat flux]/[Area]. Same asirradiance.

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,

characteristickg.m2.s-3.A-2 V.A-1, , ohm ([Mag.Permeability]/

[El.Permittivity]).

Impedance,

inductivekg.m2.s-3.A-2 (ohm) i[Angular frequency].

[Inductance]

Impedance, of a

circuitkg.m2.s-3.A-2 (ohm)

Impulse kg.m.s-1 [Moment of motion],

[Force]*[Time],[Mass]*[Velocity].

Inductance kg.m2.s-2.A-2 V.s.A-1, Wb.A-1, H(henry)

[Potential]/[dCurrent/dt],[Mag.flux]/[Current]

Induction, electric m-2.s.A C.m-2 [Charge]/[Area]. Same aselectric flux density

Inductive

admittancekg-1.m-2.s3.A2 S (siemens) 1/[Inductive impedance].

Inductive

impedancekg.m2.s-3.A-2 (ohm) i[Angular frequency].

[Inductance]

Information bit-1 bit One bit is the elementary

information quantum.Information flux bit.s-1 baud [Information]/[Time]. Also

called baud rate.

Intensity of electric

currentm-2.A [Current]/[Area]. Same as

current density.

Internal energy kg.m2.s-2 J Like energy and heat.

Internal energy,


J.mol-1 [Internal energy]/[Quantity].Like molar heat.

Internal energy,

specificm2.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 fieldstrength].

Ionic force

(strength)m-3.mol Sum([Concentration]*[Ionic

quantum charge]2).Ionic quantum

charge1 Dimensionless [Ion charge]/[Elementary

charge quantum]

Ionic strength

(force)m-3.mol Sum([Concentration]*[Ionic

quantum charge]2).Irradiance kg.s-3 W.m-2 [Heat flux]/[Area]. Same as

heat flux density

J:

Joule-Thomsoncoefficient

kg-1.m.s2.K K.Pa-1 [Temperature]/[Pressure].


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K:

Katalytic activity mol.s-1 katal [Quantity]/[Time]. Same asmolar production rate

Kinematic viscosity m2.s-1 [Dynamic viscosity]/[Density]

K-space vector m-1 same as reciprocal spaceposition.

L:

Lagrangian kg.m2.s-2 J [Force]*[Distance],[Power]*[Time]. Like energy

Length m m (meter)

Linear stiffness kg.s-2 N.m-1 [Force]/[Displacement]. ... ofa structure

Logarithmic ratio

logb(A/A')

1 log in any base b Applicable to any ratio of likequantities.

Logarithmic ratioln(A/A') 1

Np (neper)

Uses natural logarithm.

Logarithmic ratio

Log(P/P')/101 dB (decibel) Uses base-10

logarithm.Aplies only topower P.

Logarithmic ratio

Log(X/X')/201 dB (decibel) Aplies to voltages (X=V) and

currents (X=I).

Logarithmic scale

differential1 Dimensionless dQ/Q, d{ln(Q)}, for any

quantity Q. Also relativedifferential

Luminance cd.m-2 [Luminosity]/[Area]

Luminosity cd cd (candle) Same as luminous intensityLuminous

coefficient1 Dimensionless [Luminous efficacy]/[683

lm/W]. Same as luminousefficiency

Luminous efficacy cd.sr.kg-1.m-1.s3

lm/W [Luminous flux]/[Power]

Luminous efficiency 1 Dimensionless [Luminous efficacy]/[683lm/W]. Same as luminouscoefficient

Luminous

emittancecd.sr.m-2 lm.m-2, lx (lux) Same as illuminance, but for

sources

Luminous energy cd.sr.s lm.s [Luminous flux]*[Time].Also 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 dipole

momentm2.A J.T-1 [Current]*[Area]. Like

magnetic moment.

Magnetic fieldgradient

kg.m-1

.s-2

.A-1

T.m-1

[Mag.flux density]/[Distance].


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Magnetic field

strengthm-1.A [Current]/[Distance]. Also

called magnetic intensity

Magnetic flux kg.m2.s-2.A-1 V.s, W.s.A-1, Wb(weber)

[Potential]*[Time], [Power]/[dCurrent/dt]

Magnetic flux

density

kg.s-2.A-1 Wb.m-2, T (tesla) [Mag.flux]/[Area]. Also

called magnetic inductionMagnetic induction kg.s-2.A-1 Wb.m-2, T (tesla) [Mag.flux]/[Area]. More

properly magnetic fluxdensity

Magnetic intensity m-1.A [Current]/[Distance]. Moreproperly magnetic fieldstrength

Magnetic moment m2.A J.T-1 [Current]*[Area]

Magnetic

permeabilitykg.m.s-2.A-2 H.m-1 [Mag.flux density]/[Mag.field

strength].

Magneticpermeability,

relative1

Dimensionless

[Permeability]/[Permeabilityof vacuum].

Magnetic

quadrupole

moment

m3.A m.J.T-1 [Mag.dipole]*[Distance]

Magnetic

susceptibility1 Dimensionless [Relative permeability]-1.

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'=-100.4(S/S'), where S,S'are the luminous fluxes of twostars

Mass kg kg (kilogram)

Mass density kg.m-3 [Mass]/[Volume]. Same asspecific density.

Mass concentration 1 Dimensionless [Mass of substance]/[Totalmass]. Also concentration byweight

Mass flow kg.s-1 kg [Mass]/[Time]. Same asmass production rate

Mass production

ratekg.s-1 [Mass]/[Time]. Same as

mass flow.

Mass, molar kg.mol-1 [Mass]/[Quantity]

Modulus of

compressionkg-1.m.s2 Pa-1 [Pressure]/([Volume]/

[Volume]). Same ascompressibility3

Modulus of rigidity kg.m.s-2 N, N.rad-1 [Force]/[Angle]. Same as

shear modulus.

Mobility, ionic kg-1.m-1.s2.A m2.s-1.V-1 [Velocity]/[Electric field


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strength].Molality kg-1.mol mol/kg [Quantity]/[Mass]. A way to

specify concentration of asolution.

Molar charge s.A.mol-1 C.mol-1 [Charge]/[Quantity]

Molarconcentration

m-3.mol [Quantity]/[Volume]. Same asconcentration

Molar conductivity,

electrickg-1.m-3.s3.A2.mol-1

S.m-1.mol-1 [El.conductivity]/[Concentration].

Molar density m-3.mol [Quantity]/[Volume]. Same asconcentration.

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]. Likemolar heat.

Molar entropy

kg.m

2

.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 molarHelmholtzfunction

Molar free enthalpy kg.m2.s-2.mol-1

J.mol-1 [Free enthalpy]/[Quantity].Also molarGibbs 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 internalenergy

kg.m2.s-2.mol-1J.mol-1 [Internal energy]/[Quantity].

Like molar heat.

Molar mass kg.mol-1 [Mass]/[Quantity]

Molar production

ratemol.s-1 katal [Quantity]/[Time]. Like

katalytic activity.

Molar refractivity m3.mol-1 [(r2-1)/(r2+2)]/[Concentration], where r isthe refractive index

Molar relaxivity m3.s-1.mol-1 [Relaxation rate]/[Concentration].

Molar solubility m-3.mol [Quantity]/[Volume]. Same asconcentration

Molar volume m3.mol-1 [Volume]/[Quantity].

Molarity m-3.mol [Quantity]/[Volume]. Same asconcentration ormolardensity

Molecular quantum

charge1 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], [Massflow]*[Distance].

Mutual inductance

kg.m2

.s-2

.A-2

V.s.A-1

, Wb.A-1

, H(henry) [Potential]/[dCurrent/dt],[Mag.flux]/[Current]


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N:

Notch resistance kg.s-2 J.m-2 [Energy]/[Area]

Number density m-3 [Particles]/[Volume].

Number density,

molarmol-1 [Particles]/[Mol]. The

Avogadro constant.

Number ofevents/instances

1 This covers all kinds ofenumerations.

Number of turns 1 Often used in electricengineering.

O:

Osmotic pressure kg.m-1.s-2 Pa

P:

Peltier coefficient kg.m2.s-3.A-1 W.A-1, V [Heat flux]/[Current].

Permeability,

magnetickg.m.s-2.A-2 H.m-1 [Mag.flux density]/[Mag.field

strength].

Permittivity,electric kg

-1

.m-3

.s4

.A2

F.m-1

[El.flux density]/[El.fieldstrength].

Permittivity,

relative1 Dimensionless [Permittivity]/[Permittivity of

vacuum]. Dielectricconstant.

Phase angle 1 rad in exp(i(t+))

Phase drift rate s-1 rad.s-1 [Phase angle]/[Time].

Pi coefficient, molar kg.m-1.s-2.mol-1

J.m-3 [InternalEnergy]/[Volume].

Piezzoelectric

coefficientkg.m.s-3.A-1 V.m-1 [Electric field strength]/

([Length]/[Length]).

Plane angle 1 radPolarization,

electricm-2.s.A C.m-2 [Charge]/[Area]. Like electric

flux density.

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) [Energy]/[Time].Equivalent to energy flux.

Prandtl number 1 Dimensionless [Kinematic viscosity]/

[Thermal diffusivity].

Propagation loss m-1 dB/m [Ratio]/m. Used for any otherquantity.

Poynting vector kg.s-3 W.m-2 [El.field strength]/[Mag.fieldstrength]. Like irradiance

Pressure kg.m-1.s-2 N.m-2, Pa (pascal) [Force]/[Area].

Probability of an

event1 Real number lying in the

interval [0,1].

Probability density

on ln-scale1 Np-1 [Probability]/[Natural-

logarithmic ratio]

Q:

Quadrupolemoment, electric

m2.s.A C.m2 [Electric dipole]*[Distance],[Electric charge]*[Distance2]


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Quadrupole

moment, magneticm3.A m.J.T-1 [Mag.dipole]*[Distance]

Quantity of

substancemol mol

Quantum charge 1 Dimensionless [Charge]/[Elementary charge

quantum] Quantum charge,

molecular or ionic1 Dimensionless [Molecule/ion charge]/

[Charge quantum]

Quotient of

dispersivitym-1 [Refractive index]/

[Wavelength]

R:

Radiance kg.s-3.sr-1 W.m-2.sr-1 ([Power]/[Area])/[Solidangle].

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)

[Events]/[Time].

Radius of curvature m of a line in plane/space orsurface in space

Rotational stiffness kg.m2.s-2.rad-1

N.m.rad-1 [Moment of force]/[Angle]. ...of a structure.

Ratio of like

quantities1 Dimensionless Q1/Q2, with Q1 and Q2

having the same dimension

Reactance,

capacitivekg.m2.s-3.A-2 (ohm) 1/(i[Angular frequency].

[Capacitance])

Reciprocal space

positionm-1 same as k-space vector.

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 amedium)/(in vacuum).

Refractivity, molar m3.mol-1 [(r2-1)/(r2+2)]/[Concentration]

Refractivity,

specificm3.kg-1 [(r2-1)/(r2+2)]/[Specific

density],

Relative differential 1 Dimensionless dQ/Q, d{ln(Q)}, for anyquantity Q. Also log-scaledifferential

Relative evolutionrate s

-1

d{ln(Q)}/dt = (dQ/dt)/Q. Alsoevolution rate on log-scale

Relative

permeability,

magnetic

1 Dimensionless [Permeability]/[Permeabilityof vacuum].

Relative

permittivity,

electric

1 Dimensionless [Permittivity]/[Permittivity ofvacuum]. Dielectricconstant.

Relative variation 1 Dimensionless Q/Q, for any quantity Q.

Relaxation rate s-1 1/[Relaxation time]. Used inall branches of Science.

Relaxation time s Used in all branches ofScience.


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Relaxivity, molar m3.s-1.mol-1 [Relaxation rate]/[Concentration].

Reluctance,

magnetickg-1.m-1.s2.A2 m.H-1 1/[Permeability].

Resistance, electric kg.m2.s-3.A-2 V.A-1, (ohm) [Potential]/[Current]

Resistance, thermal kg-1.m-2.s3K K/W of a device. [T]/[Power].Resistance to

impactkg.s-2 J.m-2 [Energy]/[Area]. Same

dimension as notchresistance

Resistivity, electric kg.m3.s-3.A-2 .m ([Resistance]*[Length])/[Area].

Reynolds number 1 Dimensionless [Velocity]*[length]/[Kinematic viscosity]

RF attenuation m-1 dB/m [Ratio]/m. Applies topropagation.

S:Seeback coefficient kg.m2.s-3.A-1.K-1

V.K-1 [Potential]/[Temperature].Same as thermoelectricpower

Self-diffusion

coefficientm2.s-1 [Distance2]/[Time].

Settling rate s-1 typically dB/s [Ratio]/[Time].

Shear modulus kg.m.s-2 N, N.rad-1 [Force]/[Angle]. Same asmodulus of rigidity

Softening point K Temperature at whichhardness 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. Applies topropagation.

Specific charge kg-1.s.A C.kg-1 [Charge]/[Mass].Charge/mass ratio.

Specific density kg.m-3 [Mass]/[Volume]. Same asdensity of mass

Specific energy m2.s-2 J.kg-1 [Energy]/[Mass].

Specific enthalpy m2.s-2 J.kg-1 [Enthalpy]/[Mass]. Likespecific 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]. Alsospecific Helmholtz function

Specific free

enthalpym2.s-2 J.kg-1 [Free enthalpy]/[Mass]. Also

specific Gibbs function

Specific heat m2.s-2 J.kg-1 [Heat]/[Mass].

Specific heat

capacitym2.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


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density]

Specific volume m3.kg-1 [Volume]/[Mass].

Speed m.s-1 [Distance]/[Time]. Same asvelocity.

Spin 1 Dimensionless of a quantum particle

Star magnitude 1 Dimensionless m-m' = -100.4(S/S'), where S,S'are luminous fluxes of twostars

Stiffness, linear kg.s-2 N.m-1 [Force]/[Displacement]. ... ofa structure.

Stiffness, rotational kg.m2.s-2.rad-1

N.m.rad-1 [Moment of force]/[Angle]. ...of a structure.

Strain point K Temperature at whichviscosity drops below 1013.5

Pa.s

Strength,compressive kg.m

-1

.s

-2

N.m

-2

, Pa [Force]/[Area]. Samedimension as pressure.

Strength, dielectric kg.m.s-3.A-1 V.m-1 [Potential]/[Distance]. Sameas electric strength

Strength, electric

fieldkg.m.s-3.A-1 V.m-1 [Potential]/[Distance]. Also

called electric intensity

Strength, ionic m-3.mol Sum([Concentration]*[Ionicquantum charge]2).

Strength, magnetic

fieldm-1.A [Current]/[Distance]. Also

called magnetic intensity

Strength, tensile kg.m-1.s-2 N.m-2, Pa [Force]/[Area]. Same as

pressure.Surface density of

chargem-2.s.A C.m-2 [Charge]/[Area]

Surface element m2 [Distance]*[Distance]. Sameas area

Surface energy kg.s-2 J/m2 [Energy]/[Area]. Same assurface tension.

Surface tension kg.s-2 N/m [Force]/[Length]. Same assurface energy.

Susceptance,

capacitivekg-1.m-2.s3.A2 S (siemens) 1/[Reactance].

Susceptibility,

magnetic1 Dimensionless [Relative permeability]-1.

Stress kg.m-1.s-2 Pa, N.m-2 [Force]/[Area]. Same aspressure.

T:

Temperature K K(kelvin)

Temperature

gradientK.m-1 [Temperature]/[Distance].

Same as thermal gradient

Tensile strength kg.m-1.s-2 N.m-2, Pa [Force]/[Area]. Same aspressure.

Tension

kg.m-1

.s-2

Pa, N.m-2

[Force]/[Area]. Likepressure.


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Thermal

conductivitykg.m.s-3.K-1 W.m-1.K-1 [Heat flux]/

([Distance]*[Temperature]).Same as heat conductivity

Thermal diffusivity m2.s-1 ([Temperatute]/[Time])/[2Temperature].

Thermal expansioncoefficient

K-1 ([Length]/[Length])/[Temperature].

Thermal gradient K.m-1 [Temperature]/[Distance].Same as temperaturegradient

Thermal resistance kg-1.m-2.s3K K/W of a device. [T]/[Power].Thermodynamic

forcekg.m.s-2.mol-1

N/mol [Chemical potential]/[Distance].

Thermoelectric

power |

Thermopower

kg.m2.s-3.A-1.K-1

V.K-1 [Potential]/[Temperature].Same as Seeback coefficient

Thomson coefficient kg.m2.s-3.A-1.K-1

W.K-1.A-1 [Heat flux]/([Temperature]*[Current]).

Time s s (second)

Torque kg.m2.s-2 N.m [Force]*[Distance]. Same asmoment of force

Traction kg.m.s-2 N (newton) Maximum tangential forcebefore slipping.

Traction coefficient 1 Dimensionless [Traction]/[Weight].

Transmission loss m-1 dB/m [Ratio]/m. Used for any otherquantity.

U:V:

van der Waals

constant: akg.m5.s-2 Pa.m6 a in (p+a/V2)(V-b)=RT.

van der Waals

constant: bm3 b in (p+a/V2)(V-b)=RT.

van der Waals virial

constant: Akg-1.m5.s-2.mol-2

A in p=(n/V)RT+(n/V)2(RTB-A).

van der Waals virial

constant: Bkg-1.m3.mol-1 B in p=(n/V)RT+(n/V)2(RTB-

A).Variance of current

noise nJ2

s.A2 A2/Hz [Current]2/[Bandwidth]

Variance of voltage

noise nV2

kg2.m4.s-5.A-2 V2/Hz [Voltage]2/[Bandwidth]

Vector potential,

electromagnetickg.m.s-2.A-1 V.s.m-1, T.m [El.field strength]*[Time],

[Mag.fluxdensity]*[Distance]

Velocity m.s-1 [Distance]/[Time]. Same asspeed.

Verdet constant kg-1.m-1.s2.A1 rad.m-1.T-1 ([Angle]/[Length])/[Magneticflux density]

Virial coefficient:second kg.m

5

.s-

2.mol-2 Pa.(mol.m-3

)-2

A inp=(n/V)RT+A(n/V)2+B(n/V)3


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+C(n/V)4.Virial coefficient:

thirdkg.m8.s-2.mol-3

Pa.(mol.m-3)-3 B inp=(n/V)RT+A(n/V)2+B(n/V)3

+C(n/V)4.Virial coefficient:

fourth

kg.m11.s-

2.mol-4Pa.(mol.m-3)-4 C in

p=(n/V)RT+A(n/V)2+B(n/V)3+C(n/V)4.

Viscosity, dynamic kg.m-1.s-1 Pa.s ([Force]/[Area])/[Velocity]

Viscosity, kinematic m2.s-1 [Dynamic viscosity]/[Density]

Voltage kg.m2.s-3.A-1 V [Potential], same aselectromotive force

Voltage noise,

variance nV2

kg2.m4.s-5.A-2 V2/Hz [Voltage]2/[Bandwidth]

Volume m3 [Area]*[Distance]

Volumeconcentration 1

Dimensionless

[Volume of substance]/[Totalvolume]

W:

Wavelength m [Wave velocity]/[Frequency].

Wavenumber m-1 [Number of waves]/[Distance].

Work function kg.m2.s-2 J, eV [Energy] needed to remove anelectron.

X:

Y:

Young modulus kg.m-1.s-2 N.m-2, Pa [Stress]/([Length]/[Length]).

Z:

Dimensional Formulae

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