Classical Mechanics
Gravitational Potential Energy Calculator
Calculate gravitational potential energy (PE = mgh), or solve for mass, height or gravity. Works on any planet with a live energy conversion bar.
Solve for
PE = m × g × h
Enter values to calculate.
Gravitational PE equations
Potential energy
PE = mgh
Solve for mass
m = PE / (gh)
Solve for height
h = PE / (mg)
Solve for gravity
g = PE / (mh)
Impact velocity
v = √(2gh)
PE + KE = constant
Conservation of energy
Gravitational potential energy
Gravitational potential energy is the energy stored by an object due to its position in a gravitational field. Near Earth's surface, where gravity is approximately constant at g = 9.81 m/s², this is simply PE = mgh. The height h is measured from an arbitrary reference point — usually the ground or the lowest point in the problem.
When an object falls, its PE converts to kinetic energy. At the ground (h = 0), all the initial PE has become KE = ½mv², giving v = √(2gh). This is the work-energy theorem in action. For the full treatment see our article on Kinetic Energy and Conservation of Energy.
Is PE always measured from the ground?↓
No — PE is relative to whatever reference height you choose. The absolute value of PE doesn't matter; only changes in PE matter, since ΔPE = −ΔKE in a conservative system. You can set h = 0 wherever is most convenient.
Why does the formula break down at large heights?↓
PE = mgh assumes g is constant. At significant heights above Earth's surface, g decreases as 1/r². The exact formula for gravitational PE is U = −GMm/r, which is used for orbital mechanics. Near the surface (h << R_Earth), mgh is an excellent approximation.