# Dimensions of Potential Energy

## Dimensional Formula of Potential Energy

The dimensional formula of Potential Energy is given by,

[M1 L2 T-2]

Where,

• M = Mass
• L = Length
• T = Time

### Derivation

Potential Energy (P.E) = Mass × Acceleration due to Gravity × Altitude . . . . . . (1)

The dimensional formula of Altitude and Mass = [M0 L1 T0] and [M1 L0 T0] respectively . . . . (2)

For acceleration due to gravity, the dimensional formula = [M0 L1 T-2] . . . . (3)

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

Potential Energy = Mass × Acceleration due to Gravity × Altitude

Or, P.E = [M1 L0 T0] × [M0 L1 T-2] × [M0 L1 T0] = [M1 L2 T-2]

Therefore, Potential Energy is dimensionally represented as [M1 L2 T-2].