Potential Energy Calculator
Gravitational potential energy, mgh, or the energy stored in a spring, ½kx², and the mass, height, spring constant or stretch from an energy.
Result
Potential energy: 1,500 ft·lbf
Uses standard gravity unless you change it. Energy is measured from the level you call zero.
- Mass
- 150 lb
- Height above the zero level
- 10 ft
https://calcgallery.com/physics/potential-energy-calculator/
Results come from the published equations applied to the values you enter. They are not electrical design, conductor sizing, laboratory safety or medical guidance. Weather indices describe a standard person in standard conditions and are not a forecast. Where codes apply, local rules vary and must be checked. Read the full disclaimer
How to use the Potential Energy Calculator
- Choose gravitational energy (a mass at a height) or elastic energy (a stretched or compressed spring), and which value to find.
- Enter the values you know. Heights are measured from whatever level you choose as zero, and can be negative below it.
- Gravity starts at standard gravity. Change it under more options to match a textbook’s rounded value or another planet.
The formulas
gravitational: U = m × g × h m = U ÷ (g × h), h = U ÷ (m × g)elastic: U = ½ × k × x² k = 2U ÷ x², x = √(2U ÷ k)g is standard gravity, 9.80665 m/s², unless you change it. Real gravity at the Earth’s surface differs slightly from place to place.
Limits
mgh assumes gravity is the same at every height, which holds near a planet’s surface but not for a satellite’s orbit, where the energy falls off with distance instead. The spring formula assumes an ideal spring that obeys Hooke’s law; a real spring stops doing so if it is stretched too far or coils bind, and its maker’s rating says where that is.
With your numbers
- U = m × g × h = 150 lb × 32.174 ft/s² × 10 ft = 1,500 ft·lbf
Quick reference
Uses standard gravity unless you change it. Energy is measured from the level you call zero.
| Example | Result |
|---|---|
| 150 lb lifted 10 ft | Potential energy: 1,500 ft·lbf |
| 75 kg hiker 147 m up a hill | Potential energy: 108,118 J |
| The same hiker 48 m below the base | Potential energy: -35,304 J |
| Height 50 kg reaches with 1,000 J | Height above the zero level: 2.039 m |
| Spring of 4 N/cm stretched 6 cm | Potential energy: 0.72 J |
| Spring of 20 lbf/in compressed 2 in | Potential energy: 3.333 ft·lbf |
| Spring constant storing 0.72 J at 6 cm | Spring constant: 400 N/m |
Where the numbers come from
The fixed figures this calculator relies on, and the published source each one was checked against. How the calculators are built and checked
1 source
SI Brochure, 9th ed. (BIPM, 2019), Appendix 1, 3rd CGPM (1901), Declaration on the unit of mass and on the definition of weight, p. 154: "The value adopted in the International Service of Weights and Measures for the standard acceleration due to gravity is 980.665 cm/s2", https://www.bipm.org/documents/20126/41483022/SI-Brochure-9-EN.pdf
Used for
- Standard acceleration of gravity, gₙ, a conventional value fixed by definition. Real gravity differs slightly from place to place, and on other worlds far more, so pages let you change it.
Common questions about the Potential Energy Calculator
- What is the formula for gravitational potential energy?
- U = mgh: mass times gravitational acceleration times height. A 75 kg hiker 147 m above the base of a hill has 75 × 9.80665 × 147 ≈ 108,000 J more energy than at the base. OpenStax University Physics example 8.2 gets 108 kJ with g rounded to 9.8.
- Why can potential energy be negative?
- Only differences in potential energy matter, so the zero level is yours to pick: the floor, the ground or sea level. Anything below it has negative potential energy. The same hiker 48 m below the base has about −35,300 J measured from the base.
- What is the formula for the energy stored in a spring?
- U = ½kx², where k is the spring constant and x the stretch or compression from the spring’s natural length. A spring of 4 N/cm, which is 400 N/m, stretched 6 cm stores ½ × 400 × 0.06² = 0.72 J. Doubling the stretch stores four times the energy.
- How do I find the height from the energy?
- Divide the energy by the mass and gravity: h = U ÷ mg. 1,000 J lifts a 50 kg mass about 2.04 m. The page also finds a mass from an energy and a height, a spring constant from an energy and a stretch, or a stretch from an energy and a spring constant.
- Why do foot-pounds match pounds times feet?
- A pound-force is defined as the weight of a pound under standard gravity, so lifting 150 lb through 10 ft stores exactly 1,500 ft·lbf when g is standard. With any other g the two part company.