Dimensional Formula of Pressure

The dimensional formula of Pressure is 

[ M1  L-1  T-2 ]

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

From the above formula, it’s clear that the dimension of pressure is 1, -1, and -2.

How to calculate the dimensional formula of pressure?

We can derive this formula using the definition of pressure.

In physics, we can define force as the total measure of the force exerted on a unit area. Hence, mathematically,


  Pressure = Force / Area

We know, Force = mass * acceleration and Area = length * breadth. So, our formula becomes


  Pressure = ( mass * acceleration ) / ( length * breadth )

We know 

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

Therefore,


  Pressure = ( mass * (distance / time2 ) / ( length * breadth )

  Pressure = ( mass * distance ) / ( time2 * length * breadth )

  Pressure = mass1 * distance1 * time-2 * length-1 * breadth-1 

Dimensionally, we use

  • [M] for mass
  • [L] for distance, length, and breadth
  • [T] for time

Now, the formula becomes


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

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

Hence, the dimensional formula of Pressure becomes [ M1 L-1 T-2 ].

Derivation of Dimensional Formula of Pressure

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