# Definition:Weight (Physics)

*This page is about Weight in the context of Physics. For other uses, see Weight.*

## Definition

The **weight** of a body is the magnitude of the force exerted on it by the influence of a gravitational field.

The context is that the gravitational field in question is usually that of the Earth.

### Weigh

To **weigh** a body is to determine its **weight**, and thence its **mass**.

Similarly we can say that:

to mean:

and both mean the same thing.

### Dimension of Weight

The dimension of **weight** is $\mathsf M \mathsf L \mathsf T^{-2}$: mass times acceleration, that is, a force.

### Units of Weight

The SI unit of **weight** is $\mathrm N$ (newton).

The CGS unit of **weight** is $\mathrm {dyn}$ (dyne).

## Warning

There is a certain amount of confusion in the common mind between **weight** and **mass**.

The latter is usually determined by measuring its **weight**.

But while the **mass** of a body is (under normal circumstances) constant, its **weight** varies according to its position relative to the gravitational field it is in, and so is not a constant property of that body.

However, under usual terrestrial conditions the gravitational field is more or less constant (any differences being detectable only by instruments).

This means that the **weight** and **mass** of a body are commonly considered "the same".

Thus a weighing machine, while indicating the **mass** of a body, does so by measuring its **weight**.

## Sources

- 1998: David Nelson:
*The Penguin Dictionary of Mathematics*(2nd ed.) ... (previous) ... (next):**weight** - 2008: David Nelson:
*The Penguin Dictionary of Mathematics*(4th ed.) ... (previous) ... (next):**weight** - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next):**weight** - 2021: Richard Earl and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(6th ed.) ... (previous) ... (next):**weight**