Potential Energy Calculator
Calculate gravitational potential energy from mass, height and gravity.
About the Potential Energy Calculator
Lifting something stores energy in it. Gravitational potential energy is mass × gravity × height, and it is released if the object falls: a 10 kg mass raised 10 m stores about 981 J.
Height is measured from any reference level you choose, such as the floor or the ground, because only changes in potential energy matter. Gravity defaults to standard Earth gravity, 9.80665 m/s²; change it for the Moon (about 1.62 m/s²) or Mars (about 3.71 m/s²).
The formula
PE = m g h
- PE
- potential energy, in joules (J)
- m
- mass, in kilograms (kg)
- g
- gravitational acceleration, in m/s²
- h
- height above your reference level, in metres (m)
How to read your result
- If the object falls freely with no air resistance, all of this energy becomes kinetic energy at the bottom: speed v = √(2gh). From 10 m that is about 14 m/s.
Worked example
Water falling through a hydro dam
- 1 m³ of water has a mass of 1,000 kg
- PE = 1,000 × 9.80665 × 100 m = 980,665 J
- That is about 0.27 kWh per cubic metre, before turbine losses
Things to keep in mind
- Assumes gravity is constant over the height, which holds near a planet's surface. For satellites and very large heights use GMm/r instead.
Questions people ask
Where is height measured from?
Any reference level you choose; only differences in potential energy matter. Use the lowest point the object can reach if you want the energy it can release.
Does the path matter?
No. Gravitational potential energy depends only on the change in height, whether the object is lifted straight up or carried up a ramp.
How do I convert joules to kWh?
Divide by 3,600,000. 1 kWh = 3.6 million joules.