Quick answer
This calculator finds gravitational potential energy using GPE = mgh. It also works backwards to find mass or height. The value of g is 9.81 m/s² by default, and you can change it for the Moon or other planets.
GPE (mgh) calculator
How to Use the GPE Calculator
- Choose potential energy, mass or height.
- Enter the known values in kg, m and J.
- Keep g = 9.81 m/s² on Earth or enter another value.
- Press Calculate.
Gravitational Potential Energy Formula
GPE = mgh
GPE is in joules, m is mass in kg, g is the gravitational field strength in m/s² (or N/kg) and h is the height gained in metres.
The formula gives the change in potential energy when an object is raised by h near a planet’s surface. Learn how GPE turns into kinetic energy in our work, energy and power section.
Worked Example
Worked example: climbing stairs
Question: A 60 kg student climbs stairs 4 m high. How much gravitational potential energy does she gain?
- Choose “Potential energy (GPE)”.
- GPE = 60 × 9.81 × 4.
- GPE ≈ 2,354 J.
Answer: She gains about 2,350 J (2.35 kJ) of gravitational potential energy.
GPE on Other Worlds
| Place | g (m/s²) |
|---|---|
| Earth | 9.81 |
| Moon | 1.62 |
| Mars | 3.71 |
| Jupiter | 24.8 |
Lifting the same mass to the same height on the Moon needs only about a sixth of the energy it needs on Earth.
Learn more: read about gravitational force and Newton’s law of universal gravitation.
This gravitational potential energy calculator works for any planet: just change the value of g. Use the gravitational potential energy calculator alongside the kinetic energy calculator to check energy-conservation problems.
Frequently Asked Questions
What is gravitational potential energy?
It is the energy an object has because of its position in a gravitational field. Raising an object increases its GPE; letting it fall turns that energy into kinetic energy.
What is g in GPE = mgh?
g is the gravitational field strength. On Earth it is about 9.81 m/s², which is the same as 9.81 N/kg.
Does the path taken affect GPE?
No. Only the vertical height gained matters, not whether you take the stairs or a ramp.