Dimensional Formula of Stress

The dimensional formula of Stress is 

[ M1  L-1  T-2 ]

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

Now let’s see how we can drive this formula.


How to calculate the dimensional formula of stress?

In physics, we can define stress as the force acting upon a small bounded area. So mathematically,


 Stress = Force / Area 

We know that formula of Force is mass * acceleration. Now let’s substitute this value in the above equation,


  Stress = (mass * acceleration) / Area

Also, we can further derive acceleration.

  • acceleration = speed / time
  • speed = displacement / time
  • acceleration = displacement / time2

After substituting the value of acceleration, our formula becomes


  Stress = (mass * displacement / time2 ) / Area

Similarly, we know that Area is equal to length * breadth, so our formula becomes


  Stress = (mass * displacement / time2 ) / (length * breadth)

              = (mass * displacement) (length * breadth * time2)

              = mass * displacement * length-1 * breadth-1 * time-2 

              = mass * displacement * length-1 * breadth-1 * time-2 

Dimensionally, we use

  • [M] to represent mass
  • [L] for displacement, length, and breadth
  • and [T] for time.

Now our formula becomes,


  Stress = [M1] * [L1] * [L-1] * [L-1] * [T-2]

              = [M1] * [L-1] * [T-2]

Hence, the dimensional formula of Stress is [ M1 L-1 T-2 ].


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