Lift something higher and you store more energy — that's PE = mgh. Solve for potential energy, mass, height, or velocity, with the physics explained alongside the numbers.
A gravitational potential energy calculator lets you instantly determine the stored energy an object has due to its position above a reference height, using the formula PE = mgh. Enter any two of the three values — mass, height, or potential energy — and the calculator solves for the missing one, using Earth's standard gravitational acceleration of 9.81 m/s² (adjustable for other planets and moons).
Gravitational potential energy is one of the most fundamental concepts in classical mechanics: it represents energy stored by virtue of position rather than motion. A book on a high shelf, water held behind a dam, or a roller coaster car at the top of a hill all possess potential energy that can be converted into kinetic energy — the energy of motion — as they fall or descend. This interplay between potential and kinetic energy, governed by the conservation of energy, explains everything from why a pendulum swings back and forth to how hydroelectric dams generate power.
This calculator is useful in many contexts: physics students use it to solve energy conservation problems, engineers use it to estimate the energy released by falling objects or stored water systems, and renewable energy analysts use similar calculations to evaluate the potential of pumped-storage hydroelectric facilities.
A 15 kg backpack is lifted onto a shelf 2 meters above the floor. Using PE = mgh: PE = 15 × 9.81 × 2 = 294.3 J. This is the amount of energy stored in the backpack's elevated position, which would convert into kinetic energy if it fell.
The potential energy value this calculator produces represents stored energy relative to your chosen reference height — typically the ground or the object's starting position. This is not an absolute measure; the same object at the same height could have different potential energy values depending on which reference point you choose. When comparing your result to the reference table, notice that potential energy scales linearly with both mass and height — doubling either one doubles the potential energy, unlike kinetic energy which scales with the square of velocity. If you're calculating potential energy for objects on other celestial bodies, remember that adjusting the gravity value proportionally changes the result — the same mass and height will yield very different potential energy on the Moon versus Earth or Jupiter.
Enter any two of mass, height, or potential energy, and leave the third blank — the calculator solves for the missing value using PE = mgh. Adjust gravity for other planets.
| Scenario | Mass | Height | Potential Energy |
|---|---|---|---|
| A book on a shelf | 1 kg | 1.5 m | 14.72 J |
| A backpack lifted onto a table | 10 kg | 1 m | 98.1 J |
| A person climbing a flight of stairs | 70 kg | 3 m | 2060.1 J |
| A water tank on a tower | 1000 kg | 10 m | 98100 J |
| An elevator car rising 50 m | 800 kg | 50 m | 392400 J |