# 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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