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Potential Energy Calculator
Work out gravitational potential energy from mass, height and gravity, or the elastic energy stored in a stretched or compressed spring. Solve for any variable and see the free-fall speed or spring force alongside.
Type of potential energy
Solve for
Solve for
Height above your chosen reference level.
m/s²
Stretch or compression from the rest length.
Enter your values to see the result.
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How to use the Potential Energy Calculator
- Choose the type: gravitational (height) or spring (elastic).
- Pick what to solve for, for example potential energy, mass or height.
- Enter the known values with their units. For gravity, pick a planet or type a custom g.
- Read the answer plus the energy in other units, the free-fall speed or the spring force.
- Compare the result on other planets or at other displacements in the table and chart.
Potential energy formulas
- Gravitational: PE = m g h, so m = PE ÷ (g h) and h = PE ÷ (m g)
- Elastic (spring): PE = ½ k x², so k = 2 PE ÷ x² and x = √(2 PE ÷ k)
- Hooke's law: F = k x
- Free-fall speed when PE turns into kinetic energy: v = √(2 g h)
Example: a 70 kg climber who gains 100 m of height stores 70 × 9.807 × 100 = 68,647 J, about 68.6 kJ or 16.4 kcal of potential energy (the body burns several times more food energy because muscles are not 100% efficient).
Surface gravity reference
| Body | g (m/s²) | Relative to Earth | PE of 1 kg raised 1 m |
|---|---|---|---|
| Moon | 1.62 | 0.17× | 1.62 J |
| Mars | 3.71 | 0.38× | 3.71 J |
| Venus | 8.87 | 0.90× | 8.87 J |
| Earth (standard) | 9.80665 | 1.00× | 9.81 J |
| Jupiter (cloud tops) | 24.79 | 2.53× | 24.79 J |
Energy unit conversions
- 1 kJ = 1,000 J; 1 Wh = 3,600 J; 1 kWh = 3.6 MJ
- 1 cal = 4.184 J; 1 kcal (food Calorie) = 4,184 J
- 1 ft·lbf = 1.35582 J
Frequently asked questions
What is the formula for gravitational potential energy?
PE = m × g × h, where m is mass in kilograms, g is the gravitational acceleration (9.80665 m/s² on Earth) and h is the height in meters above a reference level. The result is in joules. A 10 kg mass raised 5 m has 10 × 9.807 × 5 ≈ 490 J.
What is the formula for spring (elastic) potential energy?
PE = ½ × k × x², where k is the spring constant in N/m and x is the stretch or compression from the spring's rest length in meters. Because x is squared, doubling the stretch stores four times the energy.
What reference level should I use for height?
Any level you choose, as long as you use it consistently. Potential energy differences are what matter physically, so measure h from the floor, the ground or the lowest point of the motion.
How fast will an object be falling if all its potential energy turns into kinetic energy?
Setting mgh = ½mv² gives v = √(2gh), independent of mass. From 5 m on Earth that is about 9.9 m/s. Air resistance makes real speeds lower, especially for light or large objects.
What value of g should I use?
Standard gravity is 9.80665 m/s², often rounded to 9.81 or 9.8. Actual g on Earth's surface varies slightly, from about 9.78 m/s² at the equator to 9.83 m/s² at the poles. The Moon's surface gravity is about 1.62 m/s² and Mars about 3.71 m/s².
Does Hooke's law apply to every spring?
Only within the spring's elastic limit. Beyond that the spring deforms permanently and force is no longer proportional to displacement, so ½kx² no longer gives the stored energy.
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