Mass times gravity times height
Gravitational potential energy is the energy an object has because of its height. Multiply mass in kilograms, gravity in metres per second squared, and height in metres, and you get joules. On Earth g is 9.81, so a 10 kg box lifted 5 m stores 10 × 9.81 × 5 = 490.5 J. Height is measured from whatever level you call zero.
Gravity is not the same everywhere
The g in the formula changes with the body you are on, so the same lift stores different energy on the Moon than on Earth. The last column is the energy to raise 1 kg by 1 m.
| Body | g (m/s²) | vs Earth | PE per kg per metre |
|---|---|---|---|
| Moon | 1.62 | 0.17× | 1.62 J |
| Mars | 3.71 | 0.38× | 3.71 J |
| Earth | 9.81 | 1.00× | 9.81 J |
| Saturn | 10.44 | 1.06× | 10.44 J |
| Neptune | 11.15 | 1.14× | 11.15 J |
| Jupiter | 24.79 | 2.53× | 24.79 J |
The mental-math shortcut, and where mgh trips people up
- Round g to 10. For a quick estimate on Earth, PE is roughly 10 times mass times height. A 70 kg person up 3 m stores about 2100 J, close to the exact 2060 J.
- Zero height is your choice. Potential energy has no absolute value; it is always relative to the level you call h = 0. Pick that reference point first, then measure heights from it.
- Use the right g off Earth. On the Moon or Mars the same lift stores far less energy. Plugging in 9.81 everywhere is a common error.
- It converts to motion. As an object falls, PE turns into kinetic energy. Ignoring friction, mgh = ½mv², so drop height sets impact speed: v = √(2gh).
Common questions
What is the formula for gravitational potential energy?
PE = m times g times h. Mass is in kilograms, g is the gravitational acceleration (9.81 metres per second squared on Earth), and h is the height above your chosen reference level in metres. The result is in joules.
What are the units of potential energy?
Joules. A joule is one kilogram times metre squared per second squared. Lifting a 1 kg object 1 metre on Earth stores about 9.81 joules.
Can potential energy be negative?
Yes, if the object sits below the level you picked as zero height, such as the bottom of a well. The negative sign is just a bookkeeping convention. What matters physically is the change in potential energy, not its absolute value.
