# Dimensional Formula of Torque

The dimensional formula of Torque is

[ M1  L2  T-2 ]

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

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

## How to calculate the dimensional formula of torque?

We can derive this formula using the definition of torque.

In physics, we can define torque as the tendency of a force to rotate a body about some axis. So, mathematically, torque is given as:

``````
Torque = Force * lever arm
``````

Here, lever arm is the perpendicular distance from the axis of rotation to the line drawn along the direction of the force applied. Hence, we can also say

``````
Torque = Force * distance
``````

We know that Force = mass * acceleration. Substituting the value of Force in the above formula, we get

``````
Torque = mass * acceleration * distance
``````

We know

• acceleration = speed / time
• speed = distance / time
• acceleration = distance / time2

Therefore,

``````
Torque = ( mass * distance / time2 ) * distance

Torque = ( mass * distance2 ) / time2

Torque = mass1 * distance2 * time-2``````

Dimensionally, we use

• [M] for mass
• [L] for distance and displacement
• [T] for time

Now the formula becomes

``````
Torque = [M1] * [L2] * [T-2]
``````

Hence, the dimensional equation of torque is τ = [ M1 L2 T-2 ].

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