How to Calculate Gravitational Potential Energy
Gravitational potential energy (PE, sometimes written Ep or GPE) is the energy an object holds because of its position in a gravitational field, measured relative to a reference height. Lifting an object stores energy that can later convert into motion — a raised hammer, a drawn pendulum, or water held behind a dam. The formula is PE = m × g × h, where m is mass, g is gravitational acceleration, and h is height above the reference point. This calculator also derives the impact velocity the object would reach if it fell freely from that height, plus the same energy expressed in foot-pounds and kilocalories.
How the calculation works
Enter the mass and its unit, the height and its unit, and the gravitational acceleration (default 9.80665 m/s², Earth's standard gravity at sea level). The calculator converts mass to kilograms and height to meters, then multiplies m × g × h to get energy in joules. It converts that figure to foot-pounds (× 0.737562) and kilocalories (÷ 4,184) for comparison, and — using conservation of energy, m × g × h = ½ × m × v² — solves for the velocity the object would reach after falling that height from rest: v = √(2 × g × h).
Common mistakes
- Forgetting the reference point: PE is always relative — raising an object from a 2 m ledge to 5 m above the ground only adds energy for the 3 m difference, not the full 5 m, unless the ground is your zero point.
- Mixing units: keep mass and height in one consistent system before comparing results — convert pounds to kilograms or feet to meters rather than mixing them in the formula.
- Assuming Earth gravity everywhere: the Moon's gravity (about 1.62 m/s²) and Mars's (about 3.71 m/s²) are far lower than Earth's, so the same mass and height store much less potential energy off-world.
- Confusing potential with kinetic energy: PE describes stored energy from position; kinetic energy (½mv²) describes energy of motion. They are equal only when energy converts fully between the two, as in idealized free fall.
Real-world applications
- Hydroelectric dams convert the gravitational potential energy of stored water into electricity as it falls through turbines.
- Roller coasters store potential energy at the top of the first hill and convert it into kinetic energy — speed — on the way down.
- Pile drivers and drop hammers use a raised weight's potential energy to drive stakes or forge metal on impact.
- Pendulum clocks and weight-driven elevators release stored potential energy slowly and steadily over time.