Gravitational Potential Energy Calculator — GPE = mgh
Lifting an object stores energy in it: gravitational potential energy, GPE = mgh. Enter any two of energy, mass and height and the calculator finds the third, using g = 9.81 m/s² unless you change it.
GPE is the energy source behind hydroelectric power and roller coasters: as the object falls, the stored energy converts into kinetic energy, which is why GPE and KE problems so often appear together.
Use the calculator
Enter any TWO of energy, mass and height. g defaults to 9.81 m/s².
The formula
GPE = mgh — so m = GPE/(gh) and h = GPE/(mg). The formula assumes g is constant, which is accurate near a planet’s surface.
Worked example
Worked example: A 5 kg mass raised 10 m gains GPE = 5 × 9.81 × 10 = 490.5 J. If it falls back, that same 490.5 J becomes kinetic energy (minus any air resistance losses).
Frequently asked questions
From where is height measured for GPE?
From any reference level you choose, usually the ground or the lowest point of the motion. Only changes in height matter, so the choice of zero level does not affect energy differences.
What is g on the Moon?
About 1.62 m/s² — roughly one sixth of Earth's. The same 5 kg mass raised 10 m on the Moon stores only about 81 J. Enter g = 1.62 in the calculator to check.
How does GPE become kinetic energy?
As the object falls it accelerates, trading height for speed. With no friction, GPE lost = KE gained, so mgh = ½mv² at the bottom — the basis of many exam questions.