Gravitational Potential Energy formula
| Symbol | Quantity | SI unit | Meaning |
|---|---|---|---|
| PE | Potential energy | J | Gravitational potential energy relative to the reference level |
| m | Mass | kg | Mass |
| g | Gravitational acceleration | m/s² | Gravitational field strength (9.81 m/s² on Earth) |
| h | Height | m | Height above the reference level |
What is Gravitational Potential Energy?
Gravitational Potential Energy: Near a planet's surface, the potential energy gained by raising a mass equals its weight times the height raised.
Gravitational potential energy is the energy stored by lifting an object against gravity. Without friction, all of it converts to kinetic energy as the object falls, so mgh = ½mv², which gives an impact speed of v = √(2gh).
The formula assumes g is constant, which holds for heights much smaller than the planet's radius. Change g for other worlds: Moon 1.62, Mars 3.71 and Jupiter 24.79 m/s².
How to use this calculator
- Choose the quantity you want to find in the Calculate menu. It is highlighted as the result field.
- Enter the known values. Scientific notation such as
1.6e-11is accepted. - Select a unit for each value. Units are converted to SI automatically.
- The answer updates as you type. Open Show calculation steps to see the working, or use Copy result to share a link with your inputs.
Worked example
A 10 kg box is lifted 5 m.
- PE = 10 × 9.80665 × 5 = 490 J.
- If dropped, it lands at √(2 × 9.81 × 5) ≈ 9.9 m/s.
Frequently asked questions
Where is h measured from?
From any reference level you choose. Only differences in potential energy are physically meaningful.
How do I calculate PE far from Earth?
Use U = −GMm/r instead. See the universal gravitation calculator for the corresponding force.