Gravitational potential energy (GPE)

Gravitational potential energy (GPE) is the energy an object has because of its height in a gravitational field. The GPE equation is Ep = mgh: gravitational potential energy = mass × gravitational field strength × height. On Earth g is about 9.8 N/kg, so lifting a 1 kg mass by 1 m gives it about 9.8 J of gravitational potential energy. When the object falls, that energy is transferred to kinetic energy.

The GPE equation

The equation really gives the change in gravitational potential energy when the height changes by h. That is all you ever need, because only changes in energy can be measured. You can choose any level as zero, such as the floor or the ground, as long as you stick with it.

Rearranging the potential energy formula

The Potential Energy Calculator works out any one of these from the others, and does elastic potential energy too.

Why mgh? GPE and work done

To lift an object steadily you must push up with a force equal to its weight, mg. The work done is force × distance moved in the direction of the force, so lifting it through a height h takes mg × h of work. That work is stored as gravitational potential energy, which is why the formula is mgh.

The graph shows this for a 2 kg mass. Here x is the height in metres and y is the gravitational potential energy in joules.

The line is straight, so GPE is proportional to height: double the height, double the energy. The gradient is mg = 2 × 9.8 = 19.6 J per metre, which is the object's weight in newtons.

Height means vertical height

Only the vertical rise counts. Pushing a trolley up a long gentle ramp or a short steep one to the same top gives it the same gain in gravitational potential energy.

How to calculate gravitational potential energy: worked examples

Example 1: lifting a book

A 2 kg book is lifted from the floor onto a shelf 1.5 m high. How much gravitational potential energy does it gain? Use g = 9.8 N/kg.

Example 2: a climber

A 60 kg climber climbs 300 m up a hill. Find the gain in GPE.

That is about 176 kJ. The climber's body would use far more energy than that, because muscles waste much of it as heat.

Example 3: finding the height

A 0.5 kg ball has 24.5 J of gravitational potential energy compared with the ground. How high is it?

Example 4: up a ramp

A 40 kg trolley is pushed up the ramp in the diagram, along the 8.54 m slope to a point 3 m higher. Find its gain in GPE.

Use the vertical height, not the slope: Ep = 40 × 9.8 × 3 = 1176 J.

Example 5: on the Moon

The same 2 kg book is lifted 1.5 m on the Moon, where g is about 1.6 N/kg. Its GPE gain is 2 × 1.6 × 1.5 = 4.8 J, about a sixth of the gain on Earth. NASA's fact sheet gives the Moon's surface gravity as 1.6 m/s², which is the same as 1.6 N/kg.

GPE to kinetic energy

When an object falls freely, its gravitational potential energy is transferred to its kinetic energy store. If air resistance is small enough to ignore, all of it is transferred:

The mass cancels, which is why, without air resistance, a heavy ball and a light ball dropped together hit the ground together.

Example 6: a falling ball

A ball is dropped from 20 m. Ignoring air resistance, how fast is it going when it hits the ground?

In reality it would be a little slower, as some energy is transferred to the thermal store of the air and the ball through air resistance.

Lifting and power

Power is the rate of transferring energy. For a crane, motor or person lifting something, the useful energy transferred is the gain in GPE, so power = mgh ÷ t.

Example 7: a crane

A crane lifts a 500 kg load through 12 m in 20 s. Find the GPE gained and the useful power output.

The crane's useful power output is 2940 W, about 2.9 kW. Its motor would need a higher input power, because some energy is wasted.

Here is a quick check.

When mgh is not enough (A-level)

Ep = mgh assumes g is constant, which is true to a very good approximation near Earth's surface. Over large distances, such as lifting a satellite into orbit, g gets weaker as you go up, and mgh overestimates the energy needed. A-level Physics then uses the gravitational potential, V = −GM/r, and the potential energy Ep = −GMm/r. Our guide to gravitational potential explains why it is negative and how to use it, and the Gravitational Potential Calculator does the sums.

Common mistakes

• Using the distance along a slope. h is the vertical height.
• Mass in grams. Convert to kilograms: 250 g is 0.25 kg.
• Using weight as the mass. If you are given a weight in newtons, it is already mg, so Ep = weight × h.
• Height in centimetres. 80 cm is 0.8 m.
• Using the wrong value of g. Use the value the question gives: 9.8 N/kg, 9.81 N/kg or sometimes 10 N/kg.
• Forgetting air resistance in an explanation. If a falling object is slower than √(2gh) predicts, some GPE went to the thermal store of the air.

Is the GPE equation on the equation sheet?

Yes. AQA's GCSE Physics equations sheet, checked in November 2026, gives gravitational potential energy = mass × gravitational field strength × height, Ep = mgh, for both Foundation and Higher. It also gives kinetic energy, work done and power, which you often combine with it. Other boards publish their own sheets, so check yours. Our guide to energy stores shows how GPE fits with the other stores.

Practise energy questions in a short timed paper

GCSE Physics Foundation and GCSE Physics Higher each give you a short timed paper every day, with 8 questions worth 25 to 35 marks across the course, so energy questions come up regularly.

Read next

Physics · EnergyPotential energy calculator: mgh and ½kx² with stepsFree potential energy calculator: gravitational energy from mgh and elastic energy from ½kx², or rearrange for mass, height, gravity or extension.