Gravitational Potential Energy Calculator
Gravitational potential energy is the energy an object holds because of its height in a gravitational field. Near a planet's surface it equals the mass times the gravitational field strength times the height above the reference level, U = m times g times h. With mass in kilograms, gravity in metres per second squared, and height in metres, the result is in joules. Potential energy is always relative to a chosen zero, so the height you enter is measured from whatever reference you pick. This calculator returns the energy in joules and kilojoules, the equivalent in kilowatt-hours, and the free-fall impact speed that energy would produce. Gravity is a user-editable input so you can model other bodies.
Potential energy formula
Potential energy U = m * g * h
Energy (kJ) = U / 1,000
Energy (kWh) = U / 3,600,000
Impact speed = square root of (2 * g * h)
The impact speed follows from energy conservation: all the potential energy becomes kinetic energy in free fall, ignoring air resistance, so v equals the square root of 2 g h.
Potential energy context
- The m g h formula is the near-surface approximation where gravity is constant.
- Standard gravity is about 9.80665 m/s^2; it differs on the Moon and Mars.
- Only differences in potential energy matter; the zero level is your choice.
- In free fall, potential energy converts fully to kinetic energy.
- One kilowatt-hour equals 3,600,000 joules.
Potential energy: frequently asked questions
What is the gravitational potential energy formula?
Near a planet's surface gravitational potential energy is U = m times g times h, the mass times the gravitational field strength times the height above the reference level. With mass in kilograms, gravity in metres per second squared, and height in metres, the energy comes out in joules.
What value of gravity should I use?
Standard gravity at Earth's surface is about 9.80665 metres per second squared, the default here, but it varies slightly with latitude and altitude and differs on other bodies. Gravity is a user-editable input so you can model the Moon, Mars, or a precise local value.
What is the reference level for height?
Potential energy is always measured relative to a chosen zero, usually the ground or the lowest point of motion. Only differences in potential energy are physically meaningful, so enter the height above whatever reference you select. The same object has different U values for different chosen zeros.
How does potential energy relate to kinetic energy?
When an object falls freely, gravitational potential energy converts to kinetic energy while their sum stays constant, ignoring air resistance. So the potential energy at a height equals the kinetic energy the object would gain falling to the reference level, which lets you find impact speed.
Is U = m g h valid far from Earth?
No. The simple m g h formula assumes gravity is constant, which holds only for heights small compared with Earth's radius. For satellites or large distances you need the full gravitational potential, which falls off with distance. This calculator uses the near-surface approximation.
Official sources
Reviewed by the CalculatorHub team, edited by James Graham, 17 June 2026. See our methodology.