Potential Energy Calculator
Gravitational potential energy, mgh, and the speed it becomes if the object falls.
Last updated
Your details
Result
- Potential energy
- 490.33 J
- In kilojoules
- 0.4903 kJ
- Speed on impact
- 9.903 m/s
- Time to fall
- 1.01 s
10 kg raised 5 m
35.65 km/h, ignoring air resistance
10 kg lifted 5 m…
PE = m × g × h
m = 10 kg, g = 9.80665 m/s², h = 5 m
10 × 9.80665 = 98.0665
98.0665 × 5
PE = 490.33 J
Formula — written step by step
10 kg raised 5 metres…
PE = m × g × h
m = 10 kg, g = 9.80665 m/s², h = 5 m
10 × 9.80665 = 98.0665
98.0665 × 5
PE = 490.33 J
m is mass in kilograms, g the gravitational field strength and h the height gained. On Earth g is 9.80665 m/s²; on the Moon it is about one sixth of that, so the same lift stores a sixth of the energy.
A worked example
Water stored behind a dam
- Volume
- 1,000 m³ — 1,000,000 kg
- Head
- 80 m
- Turbine efficiency
- 90%
- PE = 1,000,000 × 9.80665 × 80
- PE = 784,532,000 J
- Usable = 784,532,000 × 0.9 = 706,078,800 J
- ÷ 3,600,000 to convert to kWh
About 196 kWh of electricity
A thousand cubic metres of water is a substantial reservoir, and it yields roughly what a typical household uses in three weeks. Gravitational storage is reliable but not dense, which is why pumped hydro needs either enormous volumes or great height.
How to use this calculator
- Enter the mass and its unit.
- Enter the height gained — the vertical distance only. Moving along a slope stores energy according to the height climbed, not the distance travelled.
- Change the gravity setting for another body if you need it; the formula is identical, only g changes.
- The impact speed row shows what the stored energy becomes if the object falls back, ignoring air resistance.
Energy stored by position
Gravitational potential energy is the work done lifting an object against gravity, and it is recoverable: let the object fall and the energy returns as motion. It equals mass times gravitational field strength times height.
Only the vertical component counts. Carrying a box up a long ramp and up a short ladder to the same floor stores identical potential energy, though the ramp requires far less force applied over a much greater distance.
Height is always relative
There is no absolute zero of potential energy. Height is measured from a reference level you choose — the floor, the ground, sea level — and the number changes with that choice.
This is not a flaw. Only differences in potential energy have physical consequences, and differences are unaffected by where the zero sits. Pick a reference, state it, and stay with it for the whole problem.
Where the energy goes
An object falling freely converts potential energy into kinetic energy: mgh becomes ½mv². Setting them equal and solving gives v = √(2gh), which is the impact speed shown above. Mass cancels entirely, which is why a heavy and a light object dropped together land together in a vacuum.
In air they do not, because drag scales with cross-sectional area and speed while gravity scales with mass. A feather and a hammer fall at the same rate on the Moon and very differently on Earth — the classic demonstration, and the reason the impact figure here is an upper bound.
Formula & methodology
What this calculator assumes
- Uses a uniform gravitational field, which is accurate near a planet’s surface but not over heights comparable to its radius.
- Height is measured from a reference level you choose. Only differences in potential energy have physical meaning.
- The impact speed ignores air resistance and is therefore an upper bound, badly so for light or large objects.
Sources
Surface gravity, and what it does to a 10 kg lift of 5 m
| Body | g (m/s²) | PE stored |
|---|---|---|
| Earth | 9.80665 | 490.3 J |
| Moon | 1.625 | 81.3 J |
| Mars | 3.721 | 186.0 J |
| Jupiter | 24.79 | 1,239.5 J |
The mass is unchanged in every row — only the field strength differs. This is the practical distinction between mass, which is a property of the object, and weight, which is a force that depends on where it is.
Frequently asked questions
Does the path taken affect the energy stored?
No. Gravity is a conservative force, so only the change in height matters. A spiral staircase and a vertical hoist to the same floor store exactly the same energy.
What height should I measure from?
Whatever reference makes the problem convenient — usually the lowest point the object could reach. Only differences matter, so the choice cannot change a physical answer.
Why is g 9.80665 and not 9.81?
9.80665 m/s² is standard gravity as defined by the SI. Actual local gravity varies with latitude and altitude, from about 9.78 at the equator to 9.83 at the poles.
Is the impact speed realistic?
It is an upper bound. It assumes all the potential energy becomes kinetic energy, which ignores air resistance. For dense compact objects over short drops it is close; for light or large ones it overstates considerably.