The dimensional formula of force isĀ

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

where, **[M]**, **[L]**, and **[T]** represent fundamental quantity **Mass**, **Length**, and **Time**.

From this formula, we can say that the dimension of force is **1**, **1,** and **-2** in terms of fundamental quantities Mass, Length, and Time.

Now, let’s see how we can derive this formula.

## Derivation: Dimension Formula of Force

For this derivation, we need to revise some of the basic physics formulas.

Quantity | Formula |
---|---|

Force (F) | Mass (m) * Acceleration (a) |

Acceleration (a) | Velocity (v) / Time (T) |

Velocity (v) | Displacement (D) / Time (T) |

Now, let’s use these formulas to find the dimension of the force.

```
Force = Mass * Acceleration
= Mass * (Velocity / Time) [using formula of acceleration]
= Mass * (Displacement / (Time * Time) ) [using formula of velocity]
= ( Mass * Displacement ) / Time
```^{2}
= Mass^{1} * Displacement^{1} * Time^{-2}

We know that dimensionally, we use **[M]** for mass **[L]** for displacement, and **[T]** for time.

With this in mind, our dimensional formula of force becomes

Force = [ M^{1} L^{1} T^{-2} ]

And finally,

**Dimensions of Force = 1, 1, -2**

### 1. How to find the SI unit of Force using the dimensional formula?

We know that the dimensional formula of force is [ M^{1} L^{1} T^{-2} ]. Now, let’s derive the unit from it.

The unit for

- [M], Mass is kg (kilogram)
- [L], length is m (meter)
- [T], time is s (second)

Now if we use these units for respective physical quantity,

**Unit of Force = kg**^{1}** m**^{1}** s**^{-2}** = kg m s**^{-2}

**Related Articles**