Potential Energy Calculator
Solve PE = mgh for energy, mass or height, on Earth or any other body's gravity — with the rearranged formula shown for whichever direction you pick.
PE = m·g·h
Potential energy
Formula used for this direction
PE = m·g·h
Your values
m = 10 kg, h = 20 m, g = 9.807 m/s²
Energy Stored by Height
Lifting something takes work, and that work does not vanish — it is stored as gravitational potential energy, PE = m·g·h. Release the object and gravity hands the energy straight back as motion.
All three quantities are solvable here. Rearranged, h = PE ÷ (m·g) gives the height a known energy corresponds to, and m = PE ÷ (g·h) gives the mass. The gravity value is an input too, so the same page works for any world.
Worked example — three very different scales
A 2 kg book on a 1.2 m desk: PE = 2 × 9.80665 × 1.2 = 23.54 J.
A 70 kg person on a 10 m diving platform: 6,865 J, or 6.865 kJ.
A thousand tonnes of water behind a dam, 50 m above the turbines: 136.2 kWh — this is precisely how pumped storage works, and why hydroelectric reservoirs are built high.
The conversion, checked. Drop a 10 kg mass 20 m. Its starting potential energy is 1,961 J. It arrives at 19.81 m/s, carrying kinetic energy of 1,961 J. The two agree exactly — energy is conserved, and that agreement is computed live by this page rather than asserted.
Going the other way: 1,961 J stored in a 10 kg mass means it was lifted 20 m.
The Same Lift on Other Worlds
Raising 10 kg by 20 m, under each body's surface gravity:
| Body | Gravity | Energy stored | Relative to Earth |
|---|---|---|---|
| Mercury | 3.7 m/s² | 740 J | 0.378× |
| Venus | 8.9 m/s² | 1,780 J | 0.908× |
| Earth | 9.8 m/s² | 1,960 J | 1× |
| Moon | 1.6 m/s² | 320 J | 0.163× |
| Mars | 3.7 m/s² | 740 J | 0.378× |
| Jupiter | 23.1 m/s² | 4,620 J | 2.36× |
| Saturn | 9 m/s² | 1,800 J | 0.918× |
| Uranus | 8.7 m/s² | 1,740 J | 0.888× |
| Neptune | 11 m/s² | 2,200 J | 1.12× |
| Pluto | 0.7 m/s² | 140 J | 0.0714× |
Gravity figures from the NASA NSSDC Planetary Fact Sheet, fetched 2026-09-19. The relative column compares against NASA's rounded Earth figure of 9.8 m/s² for consistency within the table.
Keep going
- Drop the object and its potential energy converts into exactly that much kinetic energy; the kinetic energy calculator shows the other end of the exchange. Kinetic Energy Calculator
- The height in mgh is the same height a free fall starts from; the free fall calculator gives the time and impact speed for that drop. Free Fall Calculator
Frequently Asked Questions
What is gravitational potential energy?
The energy an object holds because of its height in a gravitational field: PE = m·g·h. Lift something and you do work against gravity; that work is stored, and released the moment you let go. It is 'potential' in the literal sense — energy waiting to become motion.
Potential energy relative to what height?
Whatever reference you choose, which is the subtlety most explanations skip. Only differences in potential energy are physically meaningful. A book on a desk has one PE relative to the desk and a larger one relative to the floor, and both are correct — what matters is the height it would actually fall through.
What happens to potential energy when something falls?
It converts into kinetic energy, joule for joule, if air resistance is negligible. An object dropped from height h arrives with exactly m·g·h of kinetic energy, which is why √(2gh) gives the impact speed — set ½mv² equal to mgh and solve for v, and the mass cancels out entirely.
Does potential energy depend on mass?
Yes, directly — double the mass and you double the stored energy. This is why heavier objects do more damage falling from the same height even though they fall at the same speed. Speed is mass-independent; energy is not.
Is this the same formula on the Moon or Mars?
Yes, but with a different g. The formula PE = m·g·h is unchanged; only the gravity value differs. On the Moon at 1.6 m/s², the same lift stores roughly a sixth of the energy it would on Earth, which is why the Apollo astronauts could hop so easily in heavy suits.
Related Calculators
- Kinetic Energy Calculator — Energy, Work & Power
- Work Calculator — Energy, Work & Power
- Acceleration Calculator — Motion & Kinematics
- Velocity Calculator — Motion & Kinematics