# 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:

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.