The Weight Equation W = mg

The weight equation links weight, mass and gravitational field strength. It is one of the simplest and most frequently examined equations in IGCSE Physics.

The equation

$W = mg$

Symbol	Quantity	Unit
$W$	Weight	N (newtons)
$m$	Mass	kg (kilograms)
$g$	Gravitational field strength	N/kg

Rearranging

To find mass: $m = \frac{W}{g}$

To find gravitational field strength: $g = \frac{W}{m}$

Worked example

An astronaut has a mass of 75 kg. Calculate the astronaut’s weight on Mars, where $g = 3.7\ \text{N/kg}$. [2]

Step 1. $W = mg = 75 \times 3.7$

Step 2. $W = 277.5\ \text{N}$

Marking points: M1 for $W = mg$ and correct substitution. A1 for 277.5 N (or 280 N to 2 s.f.) with unit.

These marking points are for this original example and are not an official Cambridge mark scheme.

A second example: finding mass

An object weighs 49 N on Earth ($g = 9.8\ \text{N/kg}$). Calculate its mass. [2]

$m = \frac{W}{g} = \frac{49}{9.8} = 5.0\ \text{kg}$

Common errors and how to correct them

• Substituting weight in kg. Weight must be in newtons. If the question says “a weight of 500 g”, this is actually giving mass (0.5 kg). Read the question carefully to see if it gives mass or weight.
• Using the wrong value of g. Check which planet or moon the question is set on. On the Moon, $g = 1.6\ \text{N/kg}$, so a 60 kg person weighs only 96 N.
• Forgetting the unit in the answer. Weight must be given in newtons. Mass must be given in kilograms. The unit is part of the answer.

How to apply this in an exam

This equation often appears as part of a multi-step calculation. You may need to find weight first, then use it in another equation (such as pressure $P = F/A$ where $F$ is the weight). Show the intermediate step clearly.