The dimensional formula of Stress is

**[ M**^{1}** 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 / time
^{2}

After substituting the value of acceleration, our formula becomes

```
Stress = (mass * displacement / time
```^{2} ) / Area

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

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

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

## Frequently Asked Questions

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