What gravitational potential energy is
An object raised above the ground stores energy because gravity can make it fall. This stored energy is the gravitational potential energy. Lift a box onto a shelf and the work you do is stored in it; let it fall and that energy turns into motion. The calculator gives the energy stored by a mass at a given height, on Earth, the Moon, Mars or Jupiter.
The formula
PE = m × g × h
- m is the mass in kilograms,
- g is the acceleration of gravity, 9.80665 m/s² on Earth,
- h is the height above the reference level, in meters.
The result is in joules (J). The calculator also converts it to watt-hours and food calories, and gives the speed the object would reach if dropped, v = √(2gh), ignoring air resistance.
Worked example
A person weighing 150 lb climbs to a platform 30 ft high.
- In SI units: 68.0 kg and 9.14 m.
- PE = 68.0 × 9.81 × 9.14 = 6,101 J.
- That is 1.69 Wh, or 1.46 kcal: climbing stairs stores surprisingly little energy, although the body burns about four to five times more because muscles are not very efficient.
- A fall from that height would end at about 30 mph (13.4 m/s).
Energy at a glance
| Example | Potential energy |
|---|---|
| 1 kg book raised 1 m | 9.8 J |
| 150 lb person, one floor (10 ft) | 2,034 J |
| 1 ton of water raised 100 m | 0.27 kWh |
| Car (1,500 kg) parked at the top of a 50 m hill | 0.2 kWh |
The third line explains pumped-storage hydropower: storing large amounts of electricity requires lifting huge volumes of water over large heights.
Potential and kinetic energy
In a fall without friction, potential energy turns entirely into kinetic energy: m g h = ½ m v². The mass cancels out, which is why a heavy and a light object dropped from the same height reach the same speed. In real life air resistance slows light, bulky objects much more than dense ones.
Choosing the reference level
Potential energy is always measured from a reference height you choose, usually the ground or the floor. Only differences matter: an object on a 10 m high roof has the same potential energy relative to the street whether the street is at sea level or in the mountains.
Other forms of potential energy
This calculator covers gravity near a planet’s surface. Springs, rubber bands and stretched cables store elastic potential energy, ½ k x², and charges store electric potential energy. The idea is the same: energy stored by position, ready to be released.