Gravitational Potential Energy Calculator

GCSE PhysicsAQAEdexcelOCRFoundation & Higher

Find gravitational potential energy, mass, height or g using Ep = m g h. The gravitational field strength is set to 9.8 N/kg; change it if your question uses a different value.

Quick answer

Gravitational potential energy = mass × g × height. Use mass in kg, g in N/kg and height in m to get joules (J). For example, a 2 kg book lifted 1.5 m with g = 9.8 N/kg gains Ep = 2 × 9.8 × 1.5 = 29.4 J.

By Mehmood Kakar · Updated

Ep = m × g × h
Find:

Use the value in the question. AQA usually gives 9.8 N/kg; some boards use 10 N/kg.

How to calculate gravitational potential energy

Gravitational potential energy (GPE) is the energy an object gains when it is lifted against gravity. On your equation sheet it is written as:

g.p.e. = mass × gravitational field strength × height

  • Ep is gravitational potential energy in joules (J)
  • m is mass in kilograms (kg)
  • g is gravitational field strength in newtons per kilogram (N/kg)
  • h is the change in height in metres (m)

The equation gives the change in GPE, so h is how far the object moves up or down, not its height above sea level. A book lifted from the floor to a 1.5 m shelf gains GPE for a height of 1.5 m.

The question will tell you which value of g to use. AQA questions usually give 9.8 N/kg; some other exam boards use 10 N/kg. Using a different value from the one given can cost the final mark.

GPE questions often lead on to kinetic energy. When an object falls and air resistance is ignored, the GPE it loses becomes kinetic energy, so you can set mgh equal to ½mv² to find its speed. Try that step with the kinetic energy calculator.

Common mistakes that cost marks

  1. Using the wrong value of g. Use exactly what the question gives, 9.8 N/kg or 10 N/kg.
  2. Leaving height in centimetres. 120 cm is 1.2 m. Divide by 100 before you substitute.
  3. Leaving mass in grams. 500 g is 0.5 kg. Divide by 1000.
  4. Confusing mass and weight. If you are given a weight in newtons, that is already m × g, so Ep = weight × height.
  5. Dividing by only one quantity. To find height, divide Ep by m and by g: h = Ep ÷ (m × g).
  6. Answer in the wrong unit. If the energy was given in kJ, convert to J first, or your mass or height will be 1000 times too small.

Practice questions

Try each one on paper first, then reveal the worked answer.

Q1A 2.0 kg book is lifted 1.5 m onto a shelf. Gravitational field strength = 9.8 N/kg. Calculate the increase in its gravitational potential energy.[2 marks]
  1. Ep = m × g × h
  2. Ep = 2.0 × 9.8 × 1.5
  3. Ep = 29.4 J
Q2A climber of mass 60 kg gains 35,280 J of gravitational potential energy. Gravitational field strength = 9.8 N/kg. Calculate how high she climbs.[3 marks]
  1. Rearrange: h = Ep ÷ (m × g)
  2. h = 35,280 ÷ (60 × 9.8)
  3. h = 35,280 ÷ 588
  4. h = 60 m
Q3A crane lifts a load through 25 m, giving it 125 kJ of gravitational potential energy. Gravitational field strength = 10 N/kg. Calculate the mass of the load.[3 marks]
  1. Convert: Ep = 125 kJ × 1000 = 125,000 J
  2. Rearrange: m = Ep ÷ (g × h)
  3. m = 125,000 ÷ (10 × 25) = 125,000 ÷ 250
  4. m = 500 kg

Frequently asked questions

What is the GPE equation for GCSE Physics?

Gravitational potential energy = mass × gravitational field strength × height, written Ep = mgh. Energy is in joules (J), mass in kilograms (kg), g in newtons per kilogram (N/kg) and height in metres (m).

Should I use 9.8 N/kg or 10 N/kg for g?

Use the value given in the question. AQA questions usually give 9.8 N/kg, while some exam boards use 10 N/kg. If no value is given, check your exam board’s equation sheet.

How do you find height from Ep = mgh?

Divide the energy by both the mass and g: h = Ep ÷ (m × g). Work out m × g first, then divide.

Is height measured from the ground?

Height in Ep = mgh is the change in height: how far the object moves up or down. Measure it from wherever the object started.