Dimensional Formula Table : class 11 best notes

Dimensional Formula Table : class 11

Dimensional Formula

✅ What is Dimensional Formula?

The dimensional formula of a physical quantity shows how and which of the base quantities (Mass [M], Length [L], Time [T], etc.) are involved in its definition.

Basic Dimensions (Fundamental Quantities)

Quantity	Symbol	Dimension Symbol
Mass	m	[M]
Length	l	[L]
Time	t	[T]
Temperature	T	[K]
Electric current	I	[A]
Amount of substance	n	[mol]
Luminous intensity	Iv	[cd]

Dimensional Formula of Common Physical Quantities

Quantity	Formula	Dimensional Formula
Velocity (v)	Distance / Time	[M⁰ L¹ T⁻¹]
Acceleration (a)	Velocity / Time	[M⁰ L¹ T⁻²]
Force (F)	Mass × Acceleration	[M¹ L¹ T⁻²]
Work or Energy (W)	Force × Displacement	[M¹ L² T⁻²]
Power (P)	Work / Time	[M¹ L² T⁻³]
Pressure (P)	Force / Area	[M¹ L⁻¹ T⁻²]
Density (ρ)	Mass / Volume	[M¹ L⁻³ T⁰]
Gravitational constant (G)	F × r² / (m₁·m₂)	[M⁻¹ L³ T⁻²]
Universal gas constant (R)	PV / nT	[M¹ L² T⁻² K⁻¹ mol⁻¹]
Planck’s constant (h)	Energy / Frequency	[M¹ L² T⁻¹]
Frequency (ν)	1 / Time	[M⁰ L⁰ T⁻¹]
Angular velocity (ω)	Angle / Time	[M⁰ L⁰ T⁻¹]

Dimensional Formulas of Thermal Physical Quantities

Quantity	Symbol	Dimensional Formula
Temperature	T	[K] (Thermodynamic unit)
Heat (Energy)	Q	[M¹ L² T⁻²]
Specific Heat Capacity	c	[L² T⁻² K⁻¹]
Heat Capacity	C	[M¹ L² T⁻² K⁻¹]
Latent Heat	L	[L² T⁻²]
Thermal Conductivity	k	[M L T⁻³ K⁻¹]
Coefficient of Linear Expansion	α	[K⁻¹]
Coefficient of Superficial Expansion	β	[K⁻¹]
Coefficient of Volume Expansion	γ	[K⁻¹]
Stefan-Boltzmann Constant	σ	[M T⁻³ K⁻⁴]
Gas Constant (Universal R)	R	[M L² T⁻² K⁻¹ mol⁻¹]
Boltzmann Constant	k_B	[M L² T⁻² K⁻¹]
Thermal Energy (Kinetic)	—	[M L² T⁻²]
Entropy	S	[M L² T⁻² K⁻¹]

Electrical and Magnetic Physical Quantities – Dimensional Formulas

Quantity	Symbol	Dimensional Formula
Electric Charge	Q	[T A]
Electric Current	I	[A]
Potential Difference (Voltage)	V	[M L² T⁻³ A⁻¹]
Electric Field	E	[M L T⁻³ A⁻¹]
Electric Potential	V	[M L² T⁻³ A⁻¹]
Resistance	R	[M L² T⁻³ A⁻²]
Resistivity	ρ (rho)	[M L³ T⁻³ A⁻²]
Conductivity	σ (sigma)	[M⁻¹ L⁻³ T³ A²]
Capacitance	C	[M⁻¹ L⁻² T⁴ A²]
Inductance	L	[M L² T⁻² A⁻²]
Power (Electric)	P	[M L² T⁻³]
Magnetic Field (Magnetic Flux Density)	B	[M T⁻² A⁻¹]
Magnetic Flux	ϕ (phi)	[M L² T⁻² A⁻¹]
Permeability (μ)	μ	[M L T⁻² A⁻²]
Permittivity (ε)	ε	[M⁻¹ L⁻³ T⁴ A²]
EMF (Electromotive Force)	E	[M L² T⁻³ A⁻¹]
Current Density	J	[A L⁻²]
Surface Charge Density	σ	[T A L⁻²]
Volume Charge Density	ρ	[T A L⁻³]

Dimensional Formula of Dimensional Constants

Constant	Symbol	Dimensional Formula
Gravitational Constant	G	[M⁻¹ L³ T⁻²]
Planck’s Constant	h	[M L² T⁻¹]
Gas Constant	R	[M L² T⁻² K⁻¹ mol⁻¹]
Boltzmann Constant	k_B	[M L² T⁻² K⁻¹]
Avogadro’s Number (dimensionless)	Nₐ	— (No dimensions)
Universal Electric Constant (Permittivity of free space)	ε₀	[M⁻¹ L⁻³ T⁴ A²]
Magnetic Constant (Permeability of free space)	μ₀	[M L T⁻² A⁻²]
Coulomb’s Constant (1/4πε₀)	K	[M L³ T⁻⁴ A⁻²]
Stefan-Boltzmann Constant	σ	[M T⁻³ K⁻⁴]
Wien’s Displacement Constant	b	[L K⁻¹]
Rydberg Constant	R∞	[L⁻¹]
Electron Charge (e)	e	[T A]
Faraday Constant	F	[T A mol⁻¹]
Mobility	μ	[M⁻¹ T² A]

Dimensional Formulas of Modern Physics Physical Quantities

Quantity	Symbol	Dimensional Formula
Planck’s Constant	hhh	[M L² T⁻¹]
Energy (Photon / Quantum)	E=hνE = h\nuE=hν	[M L² T⁻²]
Frequency	ν\nuν	[T⁻¹]
Wavelength	λ\lambdaλ	[L]
Momentum	ppp	[M L T⁻¹]
De Broglie Wavelength	λ=hp\lambda = \frac{h}{p}λ=ph​	[L]
Mass–Energy (E = mc²)	EEE	[M L² T⁻²]
Charge of Electron	eee	[T A]
Work Function	ϕ\phiϕ	[M L² T⁻²]
Threshold Frequency	ν0\nu_0ν0​	[T⁻¹]
Threshold Wavelength	λ0\lambda_0λ0​	[L]
Stopping Potential	V0V_0V0​	[M L² T⁻³ A⁻¹]
Atomic Radius	—	[L]
Nuclear Radius	RRR	[L]
Binding Energy	—	[M L² T⁻²]
Half-life (T₁/₂)	—	[T]
Activity (Radioactive decay)	AAA	[T⁻¹]
Decay Constant	λ\lambdaλ	[T⁻¹]
Electric Potential	VVV	[M L² T⁻³ A⁻¹]
Electronvolt (eV)	—	[M L² T⁻²]

Dimensionless Physical Quantities

Quantity	Symbol	Dimensional Formula	Nature
Angle (plane)	θ	[M⁰ L⁰ T⁰]	Ratio of lengths
Solid Angle	Ω (omega)	[M⁰ L⁰ T⁰]	Ratio of areas
Refractive Index	n	[M⁰ L⁰ T⁰]	Ratio of velocities
Relative Density (Specific Gravity)	—	[M⁰ L⁰ T⁰]	Ratio of densities
Strain (linear, volumetric)	—	[M⁰ L⁰ T⁰]	Ratio of lengths/volumes
Poisson’s Ratio	σ	[M⁰ L⁰ T⁰]	Ratio of strains
Efficiency	η	[M⁰ L⁰ T⁰]	Ratio of energies
Coefficient of Friction	μ	[M⁰ L⁰ T⁰]	Ratio of forces
Relative Permittivity	εᵣ	[M⁰ L⁰ T⁰]	Ratio
Relative Permeability	μᵣ	[M⁰ L⁰ T⁰]	Ratio
Mach Number	M	[M⁰ L⁰ T⁰]	Ratio (v/v_sound)
Reynolds Number	Re	[M⁰ L⁰ T⁰]	Ratio (inertial/viscous)
Fineness Ratio (optics)	—	[M⁰ L⁰ T⁰]	Ratio