Weight formula: W = mg
Weight = mass × gravitational field strength, or W = m g. W is the weight in newtons (N), m is the mass in kilograms (kg) and g is the gravitational field strength in newtons per kilogram (N/kg). Each board lists it for recall in its specifications, and the equation sheet in every GCSE physics paper includes it.
Equation
W = m g
| Symbol | Quantity | Unit |
|---|---|---|
W | weight | N |
m | mass | kg |
g | gravitational field strength | N/kg |
What each specification says
| Exam board | Status | Equation |
|---|---|---|
| AQA Physics (8463) | Recall | W = m g |
| AQA Combined Science (8464) | Recall | W = m g |
| Edexcel Physics (1PH0) | Recall | W = m g |
| Edexcel Combined Science (1SC0) | Recall | W = m g |
| OCR Gateway Physics A (J249) | Recall | W = m g |
| OCR Twenty First Century Physics B (J259) | Recall | W = m g |
Calculator: W = m g
Mass and weight are different things
Mass is how much stuff an object is made of. It is measured in kilograms and stays the same wherever you take the object. Weight is the pull of gravity on that mass. It is a force, so it is measured in newtons.
Take a 60 kg astronaut to the Moon. Their mass is still 60 kg. Their weight drops to about a sixth of its Earth value, because the Moon's gravitational field is much weaker.
Gravitational field strength, g, tells you how many newtons of pull act on each kilogram. Near the Earth's surface it is close to 10 N/kg. The worked examples below use 9.8 N/kg. In an exam, use whatever value the question gives you.
How AQA, Edexcel and OCR show it
The symbols are the same on every board: W = m g. AQA and Edexcel call it weight = mass × gravitational field strength. OCR Gateway (J249) calls the left side gravitational force instead of weight. OCR Twenty First Century (J259) uses the word weight.
It is a recall equation in all six specifications, including the combined science courses. For exams from 2025 onwards, every board's sheet prints it next to the rest. The OCR Gateway list shows the J249 wording.
Rearranging and linked equations
- m = W ÷ g
- g = W ÷ m
Weight is a special case of the force equation. When nothing but gravity acts, an object accelerates at g, and its weight is the force that causes that fall.
You also meet m g inside the gravitational potential energy equation. The weight times the height gives the energy you store by lifting something. If a question gives a density and a volume, find the mass first with the density equation.
Worked examples
W
- Change the mass to kilograms: 500 g = 0.5 kg
- W = m × g
- W = 0.5 × 9.8
- W = 4.9 N
4.9 N
m
- m = W ÷ g
- m = 196 ÷ 9.8
- m = 20 kg
20 kg
g
- g = W ÷ m
- g = 112 ÷ 70
- g = 1.6 N/kg, which is about the value on the Moon
1.6 N/kg
Common mistakes
- Giving a weight in kilograms. Bathroom scales say kilograms, but physics weight is a force and its unit is the newton.
- Forgetting to turn grams into kilograms. A 250 g apple has a mass of 0.25 kg, so its weight is about 2.5 N, not 2450 N.
- Saying your mass changes on the Moon. Only the weight changes, since g is smaller there and the amount of matter is the same.
- Mixing up g, the field strength, with g, the short form for grams. In W = m g the letter g is always the field strength.
Train yourself to spot m = W ÷ g quickly in the Equation Rearranger.
Questions people ask
Why do bathroom scales show kilograms?
They measure the force you push down with, then divide by the field strength for Earth. That gives a mass reading, which only works on Earth.
Would I weigh anything in space?
Gravity reaches a long way. On the space station, g is still about nine tenths of its value at the ground, so astronauts have weight. They float because they are falling around the Earth all the time.