Mass tells you how much matter a body contains. Weight tells you how hard gravity is pulling on that matter. Carry a brick to the Moon and its mass is untouched, but it becomes far easier to lift.
The comparison table
| Mass | Weight | |
|---|---|---|
| What it is | Quantity of matter in a body | Force of gravity acting on the body |
| Quantity | Scalar | Vector — it points toward the centre of the planet |
| SI unit | kilogram (kg) | newton (N) |
| Changes from place to place? | No | Yes, it follows the local value of g |
| Can it be zero? | Not for a material body | Yes, where g is zero |
| Measured with | Beam balance, by comparison with known masses | Spring balance, by how far the spring stretches |
| Formula | — | W = m × g |
The link between them
Weight is mass multiplied by the acceleration due to gravity:
W = m g
Near the Earth's surface g is about 9.8 m/s², so every kilogram is pulled down with a force of about 9.8 N. Many school problems round this to 10 m/s² to keep the arithmetic light; use whichever value the question gives.
This is Newton's second law with a particular acceleration put in. If F = ma is not yet comfortable, read Newton's second law explained first, because weight is simply that law applied to a falling body.
Example 1 — the same person on Earth and on the Moon
A student has a mass of 60 kg.
- On Earth: W = 60 × 9.8 = 588 N.
- On the Moon, gravity at the surface is about one-sixth as strong, so W ≈ 588 ÷ 6 = 98 N.
The mass is 60 kg in both places. Nothing was removed from the student; the pull on them is simply weaker.
Example 2 — working back from the weight
A stone weighs 49 N on Earth. What is its mass?
m = W ÷ g = 49 ÷ 9.8 = 5 kg
Take that same stone to a place where g is 3.7 m/s² and its weight becomes 5 × 3.7 = 18.5 N. The mass you calculated does not need recalculating.
Why the two balances disagree off Earth
A beam balance compares the object with standard masses on the other pan. Gravity pulls on both pans equally, so it cancels, and the reading is the same wherever you take it. That is why a beam balance measures mass.
A spring balance measures how far the object stretches a spring, which depends on the force pulling it down. Weaker gravity means less stretch. That is why a spring balance measures weight, and why it would read low on the Moon.
Mass also measures inertia
Mass has a second meaning that has nothing to do with gravity: it measures how strongly a body resists a change in its motion. A loaded trolley is harder to start and harder to stop than an empty one, and that would remain true in deep space where both trolleys weigh almost nothing. Weightless does not mean effortless to push.
Where marks are lost
- Writing weight in kilograms. In a physics answer, weight is a force and takes newtons.
- Changing the mass when g changes. Only the weight follows g.
- Saying an astronaut in orbit has no gravity acting on them. Gravity is what keeps the station in orbit. The astronaut is in continuous free fall, so the apparent weight is zero.
- Dropping the direction. Weight acts vertically downward, toward the centre of the Earth.
Quick check
A bag of rice has a mass of 25 kg. Taking g as 10 m/s², what is its weight? What would a spring balance and a beam balance each read for it on a planet where g is 5 m/s²?
On Earth the weight is 250 N. On the other planet the spring balance shows 125 N, while the beam balance still balances against 25 kg.