Gravitational potential energy formula: E = m g h
Gravitational potential energy = mass × gravitational field strength × height, or Ep = m g h. Ep is in joules (J), m is the mass in kilograms (kg), g is the gravitational field strength in newtons per kilogram (N/kg) and h is the height in metres (m). You will find it on the equation sheet in AQA, Edexcel and OCR physics papers.
Equation
Ep = m g h
| Symbol | Quantity | Unit |
|---|---|---|
Ep | gravitational potential energy | J |
m | mass | kg |
g | gravitational field strength | N/kg |
h | height | m |
What each specification says
| Exam board | Status | Equation |
|---|---|---|
| AQA Physics (8463) | Recall | Ep = m g h |
| AQA Combined Science (8464) | Recall | Ep = m g h |
| Edexcel Physics (1PH0) | Recall | ΔGPE = m g Δh |
| Edexcel Combined Science (1SC0) | Recall | ΔGPE = m g Δh |
| OCR Gateway Physics A (J249) | Recall | E = m g h |
| OCR Twenty First Century Physics B (J259) | Recall | E = m g h |
Calculator: Ep = m g h
Energy from height
When you lift something, you do work against gravity. That energy goes into the object's gravitational potential energy store, often shortened to GPE. Let the object fall and the store empties again, usually into kinetic energy.
The equation only cares about the change in height. A book lifted from the floor to a 1.5 m shelf gains the same energy whether you lift it straight up or carry it the long way round. What counts is how far it rises.
g is the gravitational field strength: the force of gravity on each kilogram. The examples on this page use g = 9.8 N/kg. Your exam question tells you which value to use, so read it before you start.
Three ways the boards write it
- AQA (8463 and 8464): Ep = m g h.
- Edexcel (1PH0 and 1SC0): ΔGPE = m g Δh, the change in GPE from a change in vertical height.
- OCR Gateway (J249) and OCR Twenty First Century (J259): E = m g h.
Each course, in Physics and in Combined Science, lists this one to recall. That is how the specifications sort it. The sheet you get in the exam prints it all the same, as it has since 2025, and the sheets carry on after 2028. See how the lists compare on the physics equation sheet page.
Rearranging and linking
- h = Ep ÷ (m g)
- m = Ep ÷ (g h)
Notice that m g is the weight of the object. So GPE is weight × height, which is the same as the work done to lift it.
Many questions link this page to kinetic energy. A falling object loses GPE and gains the same amount of kinetic energy, if you ignore air resistance.
Worked examples
Ep
- Change 500 g to 0.5 kg
- Ep = m g h
- Ep = 0.5 × 9.8 × 1.5
- Ep = 7.35 J
7.35 J
h
- 17.64 kJ = 17 640 J
- h = Ep ÷ (m g)
- h = 17 640 ÷ (60 × 9.8)
- h = 17 640 ÷ 588
- h = 30 m
30 m
m
- m = Ep ÷ (g h)
- m = 294 ÷ (9.8 × 2)
- m = 294 ÷ 19.6
- m = 15 kg
15 kg
Common mistakes
- Using the weight in place of the mass. If the question gives 600 N, that is already m × g, so do not multiply by g again.
- Measuring height from the wrong place. Use the change in height, from where the object starts to where it ends.
- Dividing by m and forgetting g when you solve for height. Divide by the whole product m × g, in one step or two.
Solve m g h for h or m against the clock in the Equation Rearranger.
Questions people ask
Why do some questions use 10 N/kg?
Some questions round g to make the numbers easier. Always use the value printed in the question you are answering.
Is GPE the same on the Moon?
No. The Moon's field is weaker, so g is smaller. Lifting the same box by the same height stores less energy there.