Mass and weight are not the same thing

Mass is the amount of matter in an object, measured in kilograms. Weight is the gravitational force acting on that mass, measured in newtons. They are linked by W = mg, where g is the gravitational field strength in N/kg.

This skill sits at the start of mass, weight and density and is used again in pressure, energy and motion questions.

What is the difference between mass and weight?

Mass belongs to the object. It is the same on Earth, on the Moon and in space, because the amount of matter does not change. Weight depends on where the object is, because gravity is stronger on some bodies than others.

Think of a bag of rice. It holds 2 kg of rice anywhere. Hold it on Earth and you feel a larger downward pull than you would on the Moon.

How do you use W = mg?

1. Decide what the question gives you. Is it a mass in kg, or a weight in N?
2. Check g. Use the value in the question. Earth is taken as 10 N/kg in this lesson.
3. Write the formula and rearrange if needed: W = mg, so m = W ÷ g.
4. Substitute with units and state the unit of the answer: N for weight, kg for mass.

Worked example

A rover has a mass of 60 kg. Find its weight (a) on Earth, where g = 10 N/kg, and (b) on the Moon, where g = 1.6 N/kg. (Values used for practice.)

Step 1: the mass is given, so use W = mg.

Step 2, Earth: W = 60 × 10 = 600 N.

Step 3, Moon: W = 60 × 1.6 = 96 N.

Step 4, state the mass: the rover’s mass is 60 kg in both places.

Check: 96 N is less than 600 N, which fits a weaker gravitational field. The ratio 96 ÷ 600 = 0.16 matches 1.6 ÷ 10 = 0.16.

The mistake to watch for

Mistaken answer: “On the Moon the rover’s mass is 96 kg.”

The student did the weight calculation and then wrote the result as a mass.

The number 96 is a force in newtons. Mass did not change, so it is still 60 kg. Before you write an answer, ask “is this a force or an amount of matter?” and attach N or kg accordingly.

Check yourself

1. A bag has a mass of 2.5 kg. Find its weight on Earth with g = 10 N/kg.

2. An object weighs 45 N on Earth (g = 10 N/kg). What is its mass?

3. On an invented planet, a 30 kg object weighs 120 N. Find g on that planet.

Where this leads next

With mass and weight separated, move on to converting density units. The same care with units carries into forces and momentum.

Some students can do each calculation but still mislabel the answer under exam pressure. Our teachers look for that in online one-to-one Physics tuition.