The dimensional formula of Pressure is

**[ M**^{1}** L**^{-1}** T**^{-2}** ]**

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

From the above formula, itâ€™s clear that **the dimension of pressure is 1, -1, and -2**.

## Derivation of 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, 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 / time
^{2}

Therefore,

```
Pressure = ( mass * (distance / time
```^{2} ) / ( length * breadth )
Pressure = ( mass * distance ) / ( time^{2} * length * breadth )
Pressure = mass^{1} * distance^{1} * 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 = [M
```^{1}] * [L^{1}] * [T^{-2}] * [L^{-1}] * [L^{-1}]
Pressure = [M^{1}] * [L^{-1}] * [T^{-2}]

Hence, the **dimensional formula of Pressure becomes [ M**^{1}** L**^{-1}** T**^{-2}** ]**.

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