About the Potential Energy Calculator
This potential energy calculator finds the gravitational potential energy stored in an object raised above a reference level, using PE = m × g × h. Enter the mass, the height and the gravity (Earth, Moon, Mars, Jupiter or a custom value) and it returns the energy in joules, kilojoules, watt-hours and food calories.
It is useful for physics homework, checking lab results, sizing a counterweight or pumped-storage idea, or simply getting a feel for how much energy is involved in lifting something. The chart shows how the stored energy rises in a straight line as height increases.
The calculator also reports the speed the object would reach if it fell the full height with no air resistance (v = √(2gh)), since all the potential energy converts to kinetic energy. Heights are measured from whatever reference level you choose — only the difference in height matters.
With the default inputs, the potential energy is 490.33 J. Change any value above to recalculate instantly.
How to use the potential energy calculator
- 1Enter the mass of the object and choose its unit.
- 2Enter the height above your reference level (floor, ground, table top).
- 3Pick the planet or enter a custom gravitational acceleration.
- 4Read the potential energy in joules, kJ, Wh and kcal.
- 5Check the impact speed to see how fast it would fall the full height.
Formula and method
Gravitational potential energy near a planet’s surface equals the mass times the gravitational acceleration times the height above the chosen reference level. Mass is converted to kilograms and height to meters first, so the result comes out in joules (1 J = 1 kg·m²/s²).
The formula assumes gravity is constant over the height involved, which is accurate for everyday heights (a few kilometres or less). For satellites and very large distances use the general form −GMm/r instead. The impact speed comes from setting mgh equal to ½mv² and assumes no air resistance.
- PE
- Gravitational potential energy (J)
- m
- Mass (kg)
- g
- Gravitational acceleration (9.80665 m/s² on Earth)
- h
- Height above the reference level (m)
Worked examples
10 kg box lifted 5 m on Earth
PE = 10 kg × 9.80665 m/s² × 5 m = 490.33 J. If the box fell back down it would reach √(2 × 9.80665 × 5) ≈ 9.90 m/s just before landing.
1,000 kg of water pumped up 100 m
A tonne of water raised 100 m stores 1000 × 9.80665 × 100 = 980,665 J, about 272 Wh (0.27 kWh). This shows why pumped-storage hydro needs huge volumes of water to store grid-scale energy.
80 kg astronaut on a 2 m ledge on the Moon
With lunar gravity of 1.62 m/s², PE = 80 × 1.62 × 2 = 259.2 J — about one sixth of the Earth value. A fall from the ledge would end at only √(2 × 1.62 × 2) ≈ 2.55 m/s.
150 lb person climbing 10 ft of stairs
150 lb is 68.04 kg and 10 ft is 3.048 m, so PE = 68.04 × 9.80665 × 3.048 ≈ 2,034 J, just under half a food Calorie. The body burns several times more than this because muscles are only around 20–25% efficient.
Frequently asked questions
What is the formula for potential energy?+
Gravitational potential energy is PE = mgh: mass in kilograms times gravitational acceleration (9.80665 m/s² on Earth) times height in meters. The result is in joules.
What units is potential energy measured in?+
The SI unit is the joule (J), equal to one kilogram-meter squared per second squared. Larger amounts are often given in kilojoules, watt-hours (1 Wh = 3,600 J) or kilocalories (1 kcal = 4,184 J).
Where should I measure height from?+
From any reference level you choose — the floor, the ground or a table top. Potential energy is always relative, so only the change in height between two positions has physical meaning.
Can potential energy be negative?+
Yes. If the object is below your chosen reference level, h is negative and so is PE. In orbital mechanics, gravitational potential energy is defined as negative everywhere, reaching zero only at infinite distance.
How is potential energy related to kinetic energy?+
When an object falls without friction, its potential energy converts into kinetic energy: mgh = ½mv². That is why the impact speed √(2gh) does not depend on the mass.