The List of Dimensional Formula. A Useful Handout.

Dimensional Formulae of Physical Quantities S.No

Physical Quantity

1. 2. 3. 4. 5. 6. 7. 8. 9. 10 . 11 . 12 . 13 .

Area Volume Mass density Frequency Velocity, speed Acceleration Force Impulse Work, Energy Power

Relationship with other physical quantities Length × breadth Length × breadth × height Mass/volume 1/time period Displacement/time Velocity/time Mass × Acceleration Force × Time Force × Distance Work/Time

Remark

Dimensional Formula 0 2 0 [M L T ] [M L3 T0] [M L–3 T0] [M0 L0 T–1] [M0 L T–1] [M0 L T–2] [M L T–2] [M L T–1] [M L2 T–2] [M L2 T–3]

Momentum

Mass × Velocity

[M L T–1]

Pressure, stress

Force/Area

[M L–1 T2]

Strain

[M0 L0 T0]

14 . 15 . 16 . 17 . 18 . 19 . 20 . 21 . 22 . 23 . 24 . 25 . 26 .

Modulus of elasticity

change in dimension Original dimension Stress/Strain

Surface tension

Force/Length

[M L0 T–2]

Surface energy

Energy/Area

[M L0 T–2]

Velocity gradient

Velocity/distance

[M0 L0 T–1]

Pressure gradient

Pressure/distance

[M L–2 T–2]

Pressure energy

Pressure × volume

[M L2 T–2]

Coefficient of viscosity Angle, Angular displacement Trigonometric ratio (sinθ, cosθ, tanθ, etc). Angular velocity

Force/area × velocity gradient Arc/radius

[M L–1 T–1]

Length/length

[M0 L0 T0]

Angle/time

[M0 L0 T–1]

Angular acceleration

Angular velocity/time

[M0 L0 T–2]

Radius of gyration

Distance

[M0 L T0]

Moment of inertia

Mass × (radius of gyration)2

[M L2 T0]

[M L–1 T–2]

[M0 L0 T0]

Moment of inertial × angular velocity Force × distance

[M L2 T–1]

[M L2 T–2]

Angular frequency

Angular momentum/time Or Force × distance 2π × Frequency

Wavelength

Distance

[M0 L T0]

Hubble constant

Recession speed/distance

[M0 L0 T–1]

Intensity of wave

(Energy/time)/area

[M L0 T–3]

Radiation pressure

Intensity of wave Speed of light Energy/volume

[M L–1 T–2]

27 . 28 . 29 .

Angular momentum

30 . 31 . 32 . 33 . 34 . 35 . 36 . 37 . 38 . 39 . 40 . 41 . 42 .

Energy density

43 . 44 .

Angular impulse

45 . 46 . 47 .

Planck constant

Force × ( distance ) mass × mass Energy/frequency

Heat capacity, entropy

Heat energy/temperature

[M L2 T–2 K–1]

Specific heat capacity

[M0 L2 T–2 K–1]

48 . 49 .

Latent heat

Heat Energy Mass × temperature Heat energy/mass change in dimension Original dimension × temperature

[M0 L0 K–1]

Moment of force, moment of couple Torque

Critical velocity Escape velocity Heat energy, internal energy Kinetic energy Potential energy Rotational kinetic energy Efficiency

Gravitational constant

Thermal expansion coefficient or thermal expansivity

[M L2 T–2]

[M0 L0 T–1]

[M L–1 T–2]

Reynold's number × coefficient of viscocity Mass density × radius

[M0 L T–1]

(2 × acceleration due to gravity × earth’s radius)1/2 Work (= Force × distance)

[M0 L T–1]

(1/2) mass × (velocity)2

[M L2 T–2]

Mass × acceleration due to gravity × height ½ × moment of inertia × (angular velocity)2 output work or energy Input work or energy Torque × time 2

[M L2 T–2]

[M L2 T–2] [M0 L0 T0] [M L2 T–1] [M–1 L3 T–2] [M L2 T–1]

[M0 L2 T–2]

2

Heat energy × thickness Area × temperature × time

[M L T–3 K–1]

50 .

Thermal conductivity

51 .

Bulk modulus or (compressibility)–1

volume × ( change in pressure) ( change in volume)

[M L–1 T–2]

52 . 53 .

Centripetal acceleration Stefan constant

(Velocity)2 / radius

[M0 L T–2]

( Energ/area × time) ( Temperature) 4

[M L0 T–3 K–4]

54 . 55 . 56 .

Wien constant

Wavelength × temperature

[M0 LT0 K]

Boltzmann constant

Energy/temperature

[ML2 T–2 K–1]

Universal gas constant

Pressure × volume mole × temperature

[ML2 T–2 K–1 mol–1]

57 . 58 . 59 .

Charge

Current × time

[M0 L0 TA]

Current density

Current/area

[M0 L–2 T0A]

Voltage, electric potential, electromotive force Resistance

Work/charge

[ML2 T–3A–1]

Potential difference Current

[ML2 T–3A–2]

Capacitance

Charge/potential difference

[M–1 L–2 T4A2]

Electrical resistivity or (electrical conductivity)–1 Electric field

Resistance × area length

[ML3 T–3A–2]

Electrical force/charge

[MLT–3A–1]

Electric flux

Electric field × area

[ML3 T–3A–1]

Electric dipole moment Electric field strength or electric intensity Magnetic field, magnetic flux density, magnetic induction Magnetic flux

Torque/electric field

[M0 LTA]

Potential difference distance Force Current × length

[MLT–3 A–1]

Magnetic field × area

[ML2 T–2A–1]

Inductance

Magnetic flux Current

[ML2 T–2A–2]

Magnetic dipole moment Magnetic field strength, magnetic intensity or magnetic moment density

Torque/magnetic field or current × area

[M0 L2 T0A]

60 . 61 . 62 . 63 . 64 . 65 . 66 . 67 . 68 . 69 . 70 . 71 .

Magnetic moment Volume

[ML0 T–2A–1]

[M0 L–1 T0A]

3

Charge × charge

[M–1 L–3 T4A2]

72 .

Permittivity constant (or free space)

73 .

Permeability constant (of free space)

74 .

Refractive index

Speed of light in vacuum Speed of light in medium

[M0 L0 T0]

75 . 76 . 77 . 78 .

Faraday constant

Avogadro constant × elementary charge 2π/wavelength

[M0 L0 TA mol– 1 ] [M0 L–1 T0]

Radiant flux, Radiant power Luminosity of radiant flux or radiant intensity Luminous power or luminous flux of source Luminous intensity of illuminating power of source Intensity of illumination or luminance Relative luminosity

Energy emitted/time

[M L2 T–3]

Radiant power or radiant flus of source Solid angle

[M L2 T–3]

Luminous energy emitted time

[M L2 T–3]

Luminous flux Solid angle

[M L2 T–3]

Luminous intensity

[M L0 T–3]

Luminous flux of a source of given wave length luminous flux of peak sensitivity wavelength ( 555nm ) sourc e of same power

[M0 L0 T0]

Luminous efficiency

Total luminous flux Total radiant flux Luminous flux incident area (sum of masses of nucleons) – (mass of the nucleus) Mass defect × (speed of light in vacuum)2 0.693/half life

[M0 L0 T0]

79 . 80 . 81 . 82 .

83 . 84 . 85 . 86 . 87 . 88 . 89 . 90 . 91 .

Wave number

Illuminance or illumination Mass defect Binding energy of nucleus Decay constant

4π × electric force × ( distance ) 2π × force × distance current × current length

2

[MLT–2A–2]

( distance) 2

[M L0 T–3] [M L0 T0] [ML2 T–2] [M0 L0 T–1]

Resonant frequency

( Inductance × capacitance) − 2

[M0 L0 A0 T–1]

Quality factor or Qfactor of coil Power of lens

Resonant frequency × inductance Resistance

[M0 L0 T0]

(Focal length)–1

[M0 L–1 T0]

Image distance Object distance

[M0 L0 T0]

Magnification

1

4

92 .

Fluid flow rate

( π/8) ( pressure) × ( radius) 4 ( viscosity coefficient ) × ( length )

[M0 L3 T–1]

93 . 94 .

Capacitive reactance

(Angular frequency × capacitance)–1 (Angular frequency × inductance)

[ML2 T–3A–2]

Inductive reactance

[ML2 T–3A–2]

5