Potential Energy CalculatorGravitational PE = mgh on any planet, and elastic spring energy ½kx²
Find stored energy, or solve for mass, height, spring constant or stretch. See how fast the object would be moving once that energy is released.
By Manzoor Ahmad, web development expert · Updated How do you calculate potential energy?
Gravitational potential energy is PE = m × g × h. Lifting a 10 kg box 5 m on Earth (g = 9.81 m/s²) stores 10 × 9.81 × 5 = 490 J. For a spring, use PE = ½kx²: a 200 N/m spring stretched 0.1 m stores ½ × 200 × 0.1² = 1 J.
If released
Potential energy formulas
Rearrangements: h = PE ÷ (mg), m = PE ÷ (gh), k = 2PE ÷ x², x = √(2PE ÷ k). For very large heights, where g changes noticeably, use −GMm/r instead; at that point the escape velocity calculator is more useful.
Worked examples
1. Lifting a box onto a high shelf
10 kg lifted 5 m on Earth: PE = 10 × 9.807 × 5 = 490 J. If dropped, it would hit the floor at √(2 × 9.807 × 5) = 9.9 m/s.
2. Climbing a flight of stairs
A 70 kg person rising 3 m gains 2,059 J, about 0.49 kcal. Muscles are only about 20–25% efficient, so the body actually burns roughly 2–2.5 kcal for that climb.
3. A compressed spring
A 200 N/m spring compressed 10 cm stores ½ × 200 × 0.10² = 1.0 J. Double the compression to 20 cm and it stores 4 J, four times as much.
Potential energy of 10 kg raised 1 m on different worlds
| World | Gravity | PE of 10 kg × 1 m | Speed after a 1 m fall |
|---|---|---|---|
| Moon | 1.62 m/s² | 16.2 J | 1.80 m/s |
| Mars | 3.7 m/s² | 37.0 J | 2.72 m/s |
| Earth | 9.807 m/s² | 98.1 J | 4.43 m/s |
| Jupiter | 23.1 m/s² | 231 J | 6.80 m/s |
Potential energy FAQs
Gravitational potential energy is PE = mgh, where m is mass in kilograms, g is gravitational acceleration (9.81 m/s² on Earth) and h is height in meters. The result is in joules.
Multiply mass by gravity by height. A 10 kg box lifted 5 m on Earth gains PE = 10 × 9.81 × 5 = 490 J.
Elastic potential energy is the energy stored in a stretched or compressed spring: PE = ½kx², where k is the spring constant in N/m and x is the stretch in meters.
Rearrange to h = PE ÷ (mg). A 2 kg object with 98 J of potential energy is 98 ÷ (2 × 9.81) = 5.0 m up.
Ignoring air resistance, v = √(2gh). From 10 m on Earth, an object reaches √(2 × 9.81 × 10) = 14.0 m/s, about 50 km/h, regardless of its mass.
Yes. Height is measured from a chosen zero level, such as the floor or the ground. Only changes in potential energy have physical meaning, so pick the zero that makes the problem simplest.
For the same mass and height, yes, because Jupiter's gravity (about 23.1 m/s²) is 2.4 times Earth's. On the Moon it is only about one-sixth as much.
Potential energy is stored because of position or shape. Kinetic energy is the energy of motion. In free fall, potential energy steadily converts into kinetic energy while their total stays the same.
Joules (J). 1 J is the energy to lift about 102 g by 1 m on Earth. Larger amounts are often given in kJ, kWh or kcal.
A 70 kg person climbing 3 m (one storey) gains 70 × 9.81 × 3 = 2,060 J of potential energy, about 0.5 kcal. The body burns several times more because muscles are only about 20–25% efficient.
A heavier object has more potential energy, but also more mass to accelerate. The two effects cancel, so without air resistance all objects reach the same speed from the same height.
The spring constant k measures stiffness in newtons per meter. A spring with k = 200 N/m needs 20 N to stretch 0.1 m, and stores ½ × 200 × 0.1² = 1 J of energy.
Sources
This potential energy calculator assumes constant gravity and ideal springs that obey Hooke’s law, with no air resistance or friction losses.