Dimensional formulas of physical quantities

51 quantities with their dimensional formula and SI unit, from mechanics to magnetism.

Updated 28 October 2026Free · no sign-up

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Mechanics

Velocity, speed: [LT⁻¹] · m s⁻¹
Acceleration: [LT⁻²] · m s⁻²
Momentum, impulse: [MLT⁻¹] · kg m s⁻¹ = N s
Force, weight: [MLT⁻²] · newton (N)
Work, energy: [ML²T⁻²] · joule (J)
Torque: [ML²T⁻²] · N m
Power: [ML²T⁻³] · watt (W)
Pressure, stress: [ML⁻¹T⁻²] · pascal (Pa)
Young's, bulk, shear modulus: [ML⁻¹T⁻²] · Pa
Density: [ML⁻³] · kg m⁻³
Frequency, angular velocity: [T⁻¹] · Hz, rad s⁻¹
Angular acceleration: [T⁻²] · rad s⁻²
Moment of inertia: [ML²] · kg m²
Angular momentum: [ML²T⁻¹] · kg m² s⁻¹
Gravitational constant G: [M⁻¹L³T⁻²] · N m² kg⁻²
Gravitational potential: [L²T⁻²] · J kg⁻¹
Spring constant, surface tension: [MT⁻²] · N m⁻¹
Coefficient of viscosity: [ML⁻¹T⁻¹] · Pa s

Heat and thermodynamics

Temperature: [K] · kelvin
Specific heat capacity: [L²T⁻²K⁻¹] · J kg⁻¹ K⁻¹
Latent heat: [L²T⁻²] · J kg⁻¹
Heat capacity, entropy: [ML²T⁻²K⁻¹] · J K⁻¹
Boltzmann constant k: [ML²T⁻²K⁻¹] · J K⁻¹
Gas constant R: [ML²T⁻²K⁻¹mol⁻¹] · J mol⁻¹ K⁻¹
Thermal conductivity: [MLT⁻³K⁻¹] · W m⁻¹ K⁻¹
Stefan–Boltzmann constant σ: [MT⁻³K⁻⁴] · W m⁻² K⁻⁴
Wien's constant b: [LK] · m K
Coefficient of thermal expansion: [K⁻¹] · K⁻¹

Electricity and magnetism

Charge: [AT] · coulomb (C)
Electric potential, EMF: [ML²T⁻³A⁻¹] · volt (V)
Resistance: [ML²T⁻³A⁻²] · ohm (Ω)
Resistivity: [ML³T⁻³A⁻²] · Ω m
Conductance: [M⁻¹L⁻²T³A²] · siemens (S)
Capacitance: [M⁻¹L⁻²T⁴A²] · farad (F)
Electric field: [MLT⁻³A⁻¹] · V m⁻¹ = N C⁻¹
Permittivity ε₀: [M⁻¹L⁻³T⁴A²] · C² N⁻¹ m⁻²
Electric dipole moment: [LTA] · C m
Magnetic field B: [MT⁻²A⁻¹] · tesla (T)
Magnetic flux: [ML²T⁻²A⁻¹] · weber (Wb)
Permeability μ₀: [MLT⁻²A⁻²] · T m A⁻¹
Inductance: [ML²T⁻²A⁻²] · henry (H)
Magnetic moment: [L²A] · A m²

Waves, optics and modern physics

Planck's constant h: [ML²T⁻¹] · J s
Wavelength: [L] · m
Wave number, Rydberg constant: [L⁻¹] · m⁻¹
Intensity of a wave: [MT⁻³] · W m⁻²
Power of a lens: [L⁻¹] · dioptre (D)
Time constants RC, L/R, √(LC): [T] · second

Dimensionless

Angle, solid angle: No dimensions (radian, steradian are supplementary units)
Strain, refractive index, relative density: No dimensions, no unit
Coefficient of friction, Poisson's ratio: No dimensions, no unit

Three ways dimensions save marks

Check an answer. Every term in a correct equation has the same dimensions. If an option for velocity comes out in [LT⁻²], cross it out.
Find a relation. If a pendulum's period depends on length l and g only, then T ∝ lᵃgᵇ. Matching powers of L and T gives a = ½, b = −½, so T ∝ √(l/g).
Convert units. Knowing force is [MLT⁻²] tells you 1 N = 10⁵ dyne without memorising it.

Watch out for look-alikes. Work and torque share [ML²T⁻²]; angular momentum and Planck's constant share [ML²T⁻¹]. JEE likes to ask which pairs match.

All the formulas are on the physics formula sheet.

Derivations, one quantity at a time

velocity acceleration force momentum impulse work energy power pressure stress Young's modulus density torque moment of inertia angular momentum angular velocity frequency gravitational constant G acceleration due to gravity g gravitational potential surface tension spring constant coefficient of viscosity Planck's constant h heat specific heat capacity latent heat entropy universal gas constant R Boltzmann constant k thermal conductivity Stefan–Boltzmann constant σ Wien's constant b coefficient of linear expansion electric charge electric potential (voltage, EMF)resistance resistivity conductance capacitance electric field electric flux permittivity of free space ε₀ electric dipole moment magnetic field B magnetic flux permeability of free space μ₀ inductance magnetic moment intensity of a wave wave number Rydberg constant power of a lens strain refractive index coefficient of friction time constant RC

Questions students ask

What is the dimensional formula of Planck's constant?

[ML²T⁻¹], the same as angular momentum. Its SI unit is J s.

What is the dimensional formula of the gravitational constant G?

[M⁻¹L³T⁻²], with SI unit N m² kg⁻².

Which quantities have the same dimensions?

Work, energy and torque [ML²T⁻²]; pressure, stress and modulus of elasticity [ML⁻¹T⁻²]; angular momentum and Planck's constant [ML²T⁻¹]; and the time constants RC, L/R and √(LC), which are all [T].

Can dimensional analysis find constants like 2π?

No. Dimensionless numbers can't be found this way, and it doesn't work for relations with sums, trigonometric, exponential or log functions.