β¬οΈ Potential Energy Calculator
Calculate PE = mgh from mass, gravity, and height.
Result
How to Use This Calculator
This calculator finds the gravitational potential energy of an object at a given height. Enter the mass, the height above your reference point, and the gravitational acceleration.
Enter the mass in kilograms.
Enter the height in meters, measured from whatever reference level you choose.
Check g: 9.81 m/s^2 is the Earth default. Change it for the Moon, Mars, or a custom planet.
Click Calculate. The stored energy appears in joules.
Gravitational Potential Energy
Potential energy is stored work: the energy you invested lifting the object, waiting to be released. Lift a mass m through height h against gravity g and you do work mgh, which parks itself as PE. Let go, and gravity pays it back as kinetic energy. The formula is linear in all three quantities: double any one and you double the stored energy.
This simple form assumes g is constant, which holds for heights tiny compared to Earth's radius. It breaks down for satellites, where gravity weakens with altitude and you need the full GMm/r form. For buildings, cliffs, roller coasters, and homework, mgh is exact enough.
Worked Example
Where This Comes Up
Hydroelectric dams are gravitational potential energy at civilizational scale: water held behind a dam at height h carries mgh per kilogram, converted to electricity as it falls through turbines. Pumped-storage plants run the formula in reverse, lifting water uphill at night to store cheap energy. Roller coaster designers trade PE for KE and back, sizing each hill so the train always has enough energy to crest the next one.
Students usually stumble on the reference point, worrying about the correct zero. There is none: a book on a table has one PE relative to the floor and another relative to the ceiling, and both are correct because physics only ever uses the difference. Pick the datum that makes your problem simplest and move on.
Frequently Asked Questions
Does the choice of reference height matter?
No. Only differences in height matter physically, so pick whatever datum is convenient: the floor, sea level, or the bottom of the ramp. Moving the zero just adds the same constant everywhere.
Can potential energy be negative?
Yes, if the object sits below your chosen reference height. A book on the floor has negative PE relative to a tabletop datum. Negative values are fine because only changes in PE do physical work.
What about the energy in a stretched spring?
That is elastic potential energy, a different formula: PE = 1/2kx^2. Gravitational PE = mgh applies to height in a gravitational field.
How does potential energy become kinetic energy?
When the object falls, gravity does positive work and PE converts to KE. Dropped from height h with no air resistance, it lands with exactly 1/2mv^2 = mgh.
Why 9.81 for g?
It is Earth's gravitational acceleration near the surface. Use 1.62 for the Moon or 3.71 for Mars, or type any value into the g field.