What this calculator does
Gravitational potential energy, GPE, is the energy an object holds because of its height above a reference point, ready to convert to motion the moment it is allowed to fall. A book on a high shelf, water held behind a dam and a raised weight in a gym machine all store energy this same way.
How to calculate GPE comes down to one formula: GPE equals mass times gravitational acceleration times height. Mass and height are things you measure directly; gravitational acceleration is a near-constant 9.81 metres per second squared at the Earth's surface, though it is left editable here in case you need a different value, such as for another planet or a more precise local figure.
The formula
GPE = mass × gravity × height. Mass in kilograms, height in metres above the reference point, and gravity in metres per second squared together give an energy result in joules.
| Term | Meaning |
|---|---|
| GPE | Gravitational potential energy, the stored energy due to height, measured in joules. |
| Mass | How much matter the object contains, in kilograms. |
| Height | The vertical distance above the chosen reference point, not the total distance travelled if the path is not straight up. |
| Gravity | Gravitational acceleration, 9.81 m/s² at the Earth's surface by default. |
The inputs explained
| Field | What to enter |
|---|---|
| Mass (kg) | The mass of the object in kilograms. |
| Height above the reference point (m) | The height above whatever point you are measuring energy relative to, in metres. |
| Gravitational acceleration (m/s²) | Gravitational acceleration. Leave at 9.81 for Earth, or change it for another planet or a more precise local value. |
When to use it
A raised object in a physics problem
Working out how much energy an object has stored at a given height, before it is released to fall, is the standard use of the GPE formula in coursework and problem sets.
Estimating energy in a mechanical system
A counterweight, a raised platform or water held at height in a pumped storage scheme all store gravitational potential energy that can later convert to kinetic energy or electrical output.
Comparing energy at different heights
Since GPE scales directly with height, doubling the height of an object above the reference point doubles the stored energy, useful for quick comparisons without recomputing from scratch.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How does GPE change with height, for a fixed mass?
A 70 kg mass, raised to a range of heights.
| Height | Gravitational potential energy |
|---|---|
| 1 | 686.70 J |
| 2 | 1,373.40 J |
| 5 | 3,433.50 J |
| 10 | 6,867.00 J |
| 20 | 13,734.00 J |
| 50 | 34,335.00 J |
How does GPE change with mass, at a fixed height?
A range of masses, all raised to the same 2-metre height.
Questions
How do you calculate GPE?
Multiply mass by gravitational acceleration by height: GPE = m × g × h. Use kilograms, metres per second squared and metres to get an answer in joules.
What units does GPE come out in?
Joules, when mass is in kilograms, height in metres and gravity in metres per second squared. The calculator also shows the same figure in kilojoules for larger values.
Why is gravity editable instead of fixed at 9.81?
9.81 m/s² is only accurate at the Earth's surface. Editing it lets the same formula work for another planet, or for a more precise local value that accounts for altitude and latitude.
Is GPE the same as kinetic energy?
No. GPE is stored energy due to height, while kinetic energy is the energy of motion. As an object falls, its GPE converts into kinetic energy, and in the absence of friction the total of the two stays constant.
For the energy of motion rather than height, see a kinetic energy calculator if one is available on the site, or the cone calculator and other geometry tools for related physical measurements.