Potential Energy Calculator
Choose gravitational potential energy to lift a mass through a height on the planet you pick, or elastic energy for a spring stretched or compressed by a given distance. Results are in joules and foot-pounds.
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Formula
- Gravitational:
PE = m × g × h - Elastic spring:
U = ½ × k × x², with forceF = k × x
Surface gravity g (m/s²): Earth 9.80665 (standard gravity), Moon 1.62, Mars 3.71, Mercury 3.70, Venus 8.87, Jupiter 24.79, Saturn 10.44 (NASA Planetary Fact Sheet). Inputs are converted exactly: 1 lb = 0.45359237 kg, 1 ft = 0.3048 m, 1 in = 0.0254 m, and 1 ft·lbf = 1.3558179 J.
Worked example
A 10 kg mass is lifted 5 m on Earth.
- PE = 10 × 9.80665 × 5 = 490.3325 J
- Weight = 10 × 9.80665 = 98.0665 N
On the Moon the same lift gives 10 × 1.62 × 5 = 81 J.
A spring with k = 200 N/m stretched 0.5 m: U = ½ × 200 × 0.5² = 25 J, with a pull of 200 × 0.5 = 100 N.
Frequently asked questions
What is the gravitational potential energy formula?
PE = m × g × h, with mass in kilograms, g in m/s² and height in metres. Lifting 10 kg by 5 m on Earth stores 10 × 9.80665 × 5 = 490.33 J.
How much potential energy does the same mass have on the Moon or Mars?
Only g changes. The same 10 kg lifted 5 m stores 81 J on the Moon (g = 1.62), 185.5 J on Mars (g = 3.71) and 1,239.5 J on Jupiter (g = 24.79), against 490.33 J on Earth.
What is the spring potential energy formula?
U = ½ × k × x², where k is the spring constant in N/m and x is the stretch or compression in metres. A 200 N/m spring stretched 0.5 m stores ½ × 200 × 0.25 = 25 J, and pulls back with F = kx = 100 N.
Why is the height measured from a reference level?
Only changes in potential energy matter physically, so you choose where the height is zero, such as the floor or the ground. This calculator measures the energy gained by lifting the mass from that level up by the height you enter.
Is the energy the same if I use pounds and feet?
Yes, the inputs are converted exactly (1 lb = 0.45359237 kg, 1 ft = 0.3048 m). Lifting 10 lb by 10 ft on Earth stores 135.58 J, which is exactly 100 ft·lbf.