# Dimensions of Boltzmann Constant

## Dimensional Formula of Boltzmann Constant

The dimensional formula of Boltzmann constant is given by,

[M1 L2 T-2 K-1]

Where,

• M = Mass
• K = Temperature
• L = Length
• T = Time

### Derivation

Boltzmann Constant (k) = Energy × [Temperature]-1 . . . (1)

Since, Energy = M × a × displacement = [M1 × ML1 T-2 × L1]

Therefore, the dimensions of energy = [M1 L2 T-2] . . . (2)

And, the dimensional formula of temperature = [M0 L0 T0 K1] . . . . (3)

On substituting equation (2) and (3) in equation (1) we get,

Boltzmann Constant = Energy × [Temperature]-1

Or, k = [M1 L2 T-2] × [M0 L0 T0 K1]-1 = [M1 L2 T-2 K-1].

Therefore, the Boltzmann constant is dimensionally represented as [M1 L2 T-2 K-1].