Potential Energy Calculator
Work out the gravitational potential energy stored by lifting something. Enter mass (kg or lb) and height (m or ft), and pick a gravity — Earth, Moon, or Mars — to get PE = mgh in joules and foot-pounds.
Example: with Mass 10 · Mass unit kg (kilograms) · Height 5 · Height unit m (meters) · Gravity Earth (9.80665 m/s²) → Potential energy: 490.3 J (490 J).
- In foot-pounds362 ft-lb
- Comparable toLike a microwave lifted to a high shelf, or a child climbing stairs
Computed by the calculator below using its default values. Change any input to see your own numbers.
PE = mgh: mass times gravity times height. This is the energy stored by lifting something, and it is exactly the kinetic energy it will have when it falls back down (ignoring air).
What potential energy stores
Gravitational potential energy is the work you do against gravity to raise an object, banked and ready to be released. Lift a mass m by a height h and you invest mgh joules; let it fall and gravity pays that energy back as motion. This is why a raised hammer, a reservoir behind a dam, and a roller coaster at the top of the first hill all carry stored energy proportional to how high they sit.
Only the vertical change in height matters. Carrying a box across a level floor stores no potential energy, no matter how far you walk, because gravity does no net work along a horizontal path.
Gravity sets the exchange rate
The g in mgh is the local gravitational acceleration. On Earth it is 9.80665 m/s²; on the Moon it is about one sixth of that, and on Mars a bit over a third. The same lift stores far less energy on the Moon, which is why an astronaut can hop so easily — and why a dropped tool there hits the ground gently.
Potential energy is always measured relative to a chosen reference height, usually the ground or a tabletop. What physics cares about is the difference between two heights, so pick a zero level and measure from there consistently.
How it’s calculated
PE = m·g·h in SI: mass in kilograms, g in m/s², height in meters, giving joules. Pounds convert at 1 lb = 0.45359237 kg and feet at 1 ft = 0.3048 m. Gravity presets: Earth 9.80665, Moon 1.62, Mars 3.72107 m/s². Foot-pounds use 1 J = 0.7375621493 ft-lb.
Uses constant gravity, valid near a planet's surface where g barely changes with height. It ignores air resistance and treats the object as a point mass with no rotational or elastic energy.
Potential energy of everyday lifts (Earth gravity)
| Object and lift | Mass × height | Potential energy |
|---|---|---|
| Textbook onto a shelf | 2 kg × 1.8 m | ≈ 35 J |
| Full water-cooler bottle | 19 kg × 1 m | ≈ 186 J |
| Person up one story | 75 kg × 3 m | ≈ 2,207 J |
| Car onto a 2 m ramp | 1,500 kg × 2 m | ≈ 29,420 J |
Computed with PE = mgh, g = 9.80665 m/s²; masses and heights are typical values.
Common mistakes
- Using height above the ground when what matters is the change in height for the problem at hand.
- Treating weight in pounds as mass without converting to kilograms.
- Applying Earth's g on the Moon or Mars — gravity there is much weaker.
- Counting horizontal distance; only vertical rise stores gravitational potential energy.
Frequently asked questions
What is the potential energy formula?
Gravitational potential energy is PE = mgh: mass in kilograms times gravitational acceleration g (9.80665 m/s² on Earth) times height in meters. The answer is in joules.
Does potential energy depend on the path taken?
No. Only the change in vertical height matters, not the route. Lifting a box straight up or carrying it up a winding ramp to the same height stores the same potential energy.
How is potential energy related to kinetic energy?
When an object falls, its potential energy converts to kinetic energy. Ignoring air, the mgh it had at the top equals the ½mv² it has just before landing, so the two are two sides of one coin.
Why does the Moon give a smaller answer?
Because g on the Moon is about 1.62 m/s², roughly one sixth of Earth's. The same mass and height store about one sixth the potential energy there.
What height should I measure from?
From whatever reference level makes sense for your problem, usually the floor or the ground. Potential energy is defined relative to that zero point, so measure the rise above it.