# Dimensions of Joule

## Dimensional Formula of Joule

The dimensional formula of Joule is given by,

[M1 LT-2]

Where,

• M = Mass
• L = Length
• T = Time

### Derivation

Joule is the SI unit of work done. Therefore, the dimensional formula of Joule is the same as that of the work done.

Since, Work done (W) = Force × Displacement . . . . (1)

And, Force = Mass × acceleration = M1 × [ML T-2]

∴ The dimensions of force = M1 L1 T-2 . . . . (2)

Also, the dimensions of displacement = [MLT0] . . . . (3)

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

Work (Joule)= F × D = [MLT-2] × [L1] = [M1 LT-2].

Therefore, Joule is dimensionally represented as [M1 LT-2].