Dimensional Formula of Power

The dimensional formula of Power is

[ M1  L2  T-3 ]

where [M], [L], and [T] are the fundamental quantities: Mass, Length, and Time.

From the above formula, we can derive the dimensions of power as (1, 2, -3).

How to calculate the dimensional formula of power?

For this derivation, we first need to know some of the formulas:

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)
Requirements to compute the dimensional formula of Power

Now, let’s use these formulas to find the dimension of power.


The dimension formula of Power includes 1 dimension of Mass, 2 dimension of Length and -3 dimension of Time.
Derivation of Dimension Formula of Power

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]


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.