Gravitational potential energy calculator
Choose what to find, enter the other two values and pick the gravity. The calculator applies PE = m × g × h and also shows the weight and the speed an object would reach falling that height without air resistance.
Runs in your browser: nothing you enter is sent anywhere.
How to use it
- Choose what to find: energy, mass or height.
- Enter the other two values and pick their units.
- Choose the gravity: Earth, the Moon, Mars, Jupiter or a custom g.
- Read the result, the weight in newtons and the fall speed.
PE = m × g × h
- m = PE ÷ (g × h), h = PE ÷ (m × g);
- weight W = m × g;
- fall speed v = √(2 × g × h).
The surface gravity values are 9.80665 m/s² (standard gravity) for Earth, 1.62 m/s² for the Moon, 3.71 m/s² for Mars and 24.79 m/s² for Jupiter.
Worked example
A 2 kg box lifted 10 m on Earth gains PE = 2 × 9.80665 × 10 = 196.133 J. Dropped from there it would hit the ground at √(2 × 9.80665 × 10) = 14.005 m/s.
How high does 1 kJ lift a 50 kg person? h = 1000 ÷ (50 × 9.80665) = 2.0394 m, or 6.6911 ft.
Common mistakes
- Using grams as kilograms. 500 g is 0.5 kg; pick the mass unit instead of converting by hand.
- Using weight for mass. If you know the weight in newtons, divide by g first.
- Large heights. PE = mgh assumes g stays the same. For rockets and satellites the change in gravity with distance matters.
Frequently asked questions
What is the formula for potential energy?
Near a planet's surface, gravitational potential energy is PE = m × g × h, with mass in kilograms, g in m/s² and height in metres. The result is in joules.
Which value of g is used for Earth?
Standard gravity, 9.80665 m/s². Real gravity varies a little with latitude and altitude, from about 9.78 to 9.83 m/s², so the result changes by less than 0.5%.
How is the fall speed found?
If all the potential energy turns into kinetic energy, m × g × h = ½ × m × v², so v = √(2 × g × h). Mass cancels out, and air resistance is ignored.
Height measured from where?
From any level you choose as zero, usually the floor or the ground. Only the difference in height matters for the energy released or needed.