Rankwise

Dimensional formula of Boltzmann constant k

The dimensional formula of Boltzmann constant k is [ML²T⁻²K⁻¹].

[ML²T⁻²K⁻¹]Dimensional formula
[M¹L²T⁻²K⁻¹]With every power shown
J K⁻¹SI unit
E = (3/2) kTDefining relation

How to derive it

Start from a formula that defines Boltzmann constant k, then replace each quantity with its dimensions. M is mass, L is length, T is time, K is temperature.

  1. Rearrange: k = E ÷ T (3/2 has no dimensions)
  2. = [ML²T⁻²] ÷ [K]
  3. So [Boltzmann constant k] = [ML²T⁻²K⁻¹], also written [M¹L²T⁻²K⁻¹].

Same dimensions as Boltzmann constant k: entropy. JEE often asks which pairs match.

Dimensional formulas of other quantities

QuantityDimensional formula
velocity[LT⁻¹]
acceleration[LT⁻²]
force[MLT⁻²]
momentum[MLT⁻¹]
impulse[MLT⁻¹]
work[ML²T⁻²]
energy[ML²T⁻²]
power[ML²T⁻³]
pressure[ML⁻¹T⁻²]
stress[ML⁻¹T⁻²]
Young's modulus[ML⁻¹T⁻²]
density[ML⁻³]
torque[ML²T⁻²]
moment of inertia[ML²]
angular momentum[ML²T⁻¹]
angular velocity[T⁻¹]
frequency[T⁻¹]
gravitational constant G[M⁻¹L³T⁻²]
acceleration due to gravity g[LT⁻²]
gravitational potential[L²T⁻²]
surface tension[MT⁻²]
spring constant[MT⁻²]
coefficient of viscosity[ML⁻¹T⁻¹]
Planck's constant h[ML²T⁻¹]
heat[ML²T⁻²]
specific heat capacity[L²T⁻²K⁻¹]
latent heat[L²T⁻²]
entropy[ML²T⁻²K⁻¹]
universal gas constant R[ML²T⁻²K⁻¹mol⁻¹]
Boltzmann constant k[ML²T⁻²K⁻¹]
thermal conductivity[MLT⁻³K⁻¹]
Stefan–Boltzmann constant σ[MT⁻³K⁻⁴]
Wien's constant b[LK]
coefficient of linear expansion[K⁻¹]
electric charge[TA]
electric potential (voltage, EMF)[ML²T⁻³A⁻¹]
resistance[ML²T⁻³A⁻²]
resistivity[ML³T⁻³A⁻²]
conductance[M⁻¹L⁻²T³A²]
capacitance[M⁻¹L⁻²T⁴A²]
electric field[MLT⁻³A⁻¹]
electric flux[ML³T⁻³A⁻¹]
permittivity of free space ε₀[M⁻¹L⁻³T⁴A²]
electric dipole moment[LTA]
magnetic field B[MT⁻²A⁻¹]
magnetic flux[ML²T⁻²A⁻¹]
permeability of free space μ₀[MLT⁻²A⁻²]
inductance[ML²T⁻²A⁻²]
magnetic moment[L²A]
intensity of a wave[MT⁻³]
wave number[L⁻¹]
Rydberg constant[L⁻¹]
power of a lens[L⁻¹]
strain[M⁰L⁰T⁰]
refractive index[M⁰L⁰T⁰]
coefficient of friction[M⁰L⁰T⁰]
time constant RC[T]

The full searchable list, with SI units, is on the dimensional formula page.

Questions students ask

What is the dimensional formula of Boltzmann constant k?

[ML²T⁻²K⁻¹] (or [M¹L²T⁻²K⁻¹]), from E = (3/2) kT. Its SI unit is J K⁻¹.

What are the dimensions of Boltzmann constant k?

M: 1, L: 2, T: -2, K: -1.

What is the SI unit of Boltzmann constant k?

J K⁻¹.

Which quantities have the same dimensions as Boltzmann constant k?

entropy, all [ML²T⁻²K⁻¹].

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