Potential Energy Calculator
Gravitational potential energy from mass and height.
Defaults to Earth's 9.81 m/s². Use 1.62 for the Moon, 3.71 for Mars.
Results update as you type.
How it works
Potential energy is the energy an object stores because of its position in a gravitational field, and this potential energy calculator finds it from the mass, the height, and the strength of gravity. It uses the classic PE = mgh relationship and reports the result in joules, the SI unit of energy. Gravitational potential energy matters because it converts directly into other forms. A raised weight in a grandfather clock, water held behind a hydroelectric dam, and a roller-coaster car at the top of a hill all bank potential energy that becomes kinetic energy as they descend. Estimating that stored energy is essential for engineers sizing a dam, physics students solving conservation-of-energy problems, and anyone analysing how much work it takes to lift a load. The formula works because lifting an object against gravity does work equal to the constant gravitational force, m times g, multiplied by the height climbed. Doubling either the mass or the height doubles the stored energy. By letting you change the gravity value, this potential energy calculator also handles the Moon, Mars, or any other body, so you can compare how much energy the same lift stores in different gravitational environments.
PE = m × g × h
Gravitational potential energy is the work done against gravity to lift an object, and work equals force times distance. The downward force of gravity on a mass is m times g, so raising it through a height h stores exactly m·g·h joules of energy. The formula works because the gravitational field near Earth's surface is effectively uniform, making the force constant over the lift, so the energy stored grows in direct proportion to both the mass raised and the height it is raised through.
Source:Standard physics (gravitational potential energy)
We review all our tools from time to time to ensure accuracy.
Worked example
How to use this calculator
- 1
Enter your values
Enter mass and height.
- 2
Adjust the options
Adjust gravity if they apply — sensible defaults are already set.
- 3
Read your result
Potential energy updates instantly as you type — no button to press.
Frequently asked questions
What value of gravity should I use?
For everyday problems on Earth, use 9.81 m/s², the standard average surface gravity, which is already the default. On the Moon use about 1.62 m/s², on Mars about 3.71 m/s², and on Jupiter roughly 24.79 m/s². Changing this field lets the same mass and height give different stored energy, which is why potential energy depends on the gravitational environment, not just the object.
Where is the height measured from?
Height is measured from whatever reference level you choose to call zero, usually the ground, a tabletop, or the lowest point of the motion. Potential energy is always relative to that reference, so only differences in height carry physical meaning. As long as you are consistent about where zero sits, the change in potential energy between two positions comes out correctly.
Why is potential energy measured in joules?
The joule is the SI unit of energy, defined as one newton of force acting over one metre. Because PE = mgh multiplies a mass in kilograms by an acceleration in metres per second squared and a height in metres, the units combine to kilogram-metres-squared per second-squared, which is exactly a joule. Keeping your inputs in kilograms and metres therefore returns energy directly in joules.
How does potential energy relate to kinetic energy?
When an object falls, its potential energy converts into kinetic energy while total mechanical energy stays constant, ignoring air resistance. At the top of a drop the energy is all potential; at the bottom it is all kinetic. This is the principle of conservation of energy, and it lets you find the speed at the bottom by setting mgh equal to one-half m v squared.
Does the mgh formula work for very tall heights?
The mgh formula assumes gravity is constant, which holds well near a planet's surface but breaks down over very large heights, such as satellite orbits, where gravity weakens with distance. For those cases physicists use the more general gravitational potential energy formula involving the inverse of distance. For buildings, hills, and everyday lifts, mgh is accurate and this calculator is appropriate.