The dimensional formula of Power in terms of Mass [M], Length [L], and Time [T] is:
[ M1 L2 T-3 ]
By looking at this formula, we can identify that Power is made up of 3 fundamental quantities: Mass, Length, and Time.
Here, the powers of these fundamental quantities (1, 2, -3) are the dimensions.
Now, let’s see how we can derive this formula.
How to derive the dimensional formula of Power
For this derivation, we first need to know some of the formulas:
Quantity | Formula |
Power (P) | Work (W) / Time (T) |
Work (W) | Force (F) * Displacement (D) |
Force (F) | Mass (m) * Acceleration (a) |
Acceleration (a) | Velocity (v) / Time (T) |
Velocity (v) | Displacement (D) / Time (T) |
Now, let’s use these formulas to find the dimension of power.
Derivation

Power = Work / Time
= (Force * Displacement) / Time {using formula of Work}
= (Mass * Acceleration * Displacement) / Time {using formula of Force}
= (Mass * (Velocity / Time) * Displacement / Time {using formula of Acceleration}
= (Mass * (Displacement / (Time * Time) ) * Displacement ) / Time {using the formula of Velocity}
= (Mass * Displacement * Displacement ) / (Time * Time * Time)
= (Mass * Displacement2 ) / Time3
Power = Mass * Displacement2 * Time-3
Now, let’s convert this formula in terms of fundamental quantity [M] (Mass), [L] (Length), and [T] (Time)
- Mass is represented in terms of [M]
- Displacement is represented in terms of [L]
- Time is represented in terms of [T]
Hence,
Dimensional Formula of Power = [M1 L2 T-3]
From the formula, the dimensions are
- 1 for Mass
- 2 for Length
- -3 for Time
If you want to learn more about dimensional analysis, visit Dimensional Formula and Equations of Physical Quantity.