What this calculator does
Find out how much energy an object stores just by being lifted up, or work backward to its mass, height or gravity. This stored energy is called gravitational potential energy. When you lift something, you work against gravity. That work is stored, and it turns back into motion when the object falls. Near a planet's surface, the stored energy is mass × gravitational acceleration × height, written PE = mgh.
This calculator solves that formula in any direction. Enter a mass and a height to get the energy. Or enter an energy to find the mass, the height or the gravity that fits. You can choose Earth's standard gravity, the Moon or Mars. You can also type your own value, such as 9.8 or 9.81 m/s², to match a textbook.
Where it's used
Why this math matters outside the classroom:
- Hydropower. Hydro engineers estimate that 1,000 kg of water falling 50 m releases about 1,000 × 9.81 × 50 ≈ 490 kJ.
- Roller coasters. Coaster designers use the first hill's height to set how much energy the train has for the rest of the ride.
- Climbing stairs. A 60 kg student climbing 3 m of stairs gains about 60 × 9.81 × 3 ≈ 1,766 J of potential energy.
- On the Moon. Students compare lifting a box on the Moon, where g is about 1.62 m/s², and find it takes roughly a sixth of the energy.
Grade level and standards: Grades 8–9; Common Core State Standards for Mathematics HSA.CED.A.4. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.
How to use it
- Choose whether to solve for potential energy, mass, height or gravity.
- Enter the values you know and pick a unit for each one.
- Pick the gravity: Earth (9.80665 m/s²), Moon (1.62 m/s²), Mars (3.71 m/s²) or a custom value.
- Choose the unit for the answer. The result is also listed in other units.
What the inputs mean
- Height above the reference level (h)
- Potential energy is always measured from a starting level you choose, such as the floor or the ground. Only differences in height matter, so pick the level the object could fall to.
- Gravity (g)
- 9.80665 m/s² is the internationally agreed standard value. Real gravity on Earth ranges from about 9.78 to 9.83 m/s², depending on how far north or south you are and how high up. Moon and Mars values are rounded surface averages.
- Custom gravitational acceleration
- Enter a positive value. 32.174 ft/s² is standard gravity in US units.
Formula and method
PE = m × g × h m = PE ÷ (g × h) h = PE ÷ (m × g) g = PE ÷ (m × h)
PE is the potential energy, m is the mass, g is the pull of gravity (how fast things speed up as they fall) and h is the height. The last three lines are the same formula, turned around to find each of the other values.
With mass in kilograms, g in meters per second squared and height in meters, the energy comes out in joules. The calculator converts your inputs to those units, does the math, and converts the answer to the unit you pick.
PE is just three numbers multiplied together. So doubling any one of them doubles the energy. Lifting the same object to the same height on the Moon stores about one sixth of the energy it would on Earth.
Worked example
A 70 kg climber stands on a ledge 10 m above the ground on Earth. How much gravitational potential energy do they have compared with the ground?
- Use standard gravity: g = 9.80665 m/s².
- PE = 70 × 9.80665 × 10.
- PE = 6,864.655 J.
Result: The climber has 6,864.655 J (about 6.86 kJ, or 5,063.11 ft·lbf) of potential energy compared with the ground. On the Moon, the same climb would store 1,134 J.
Understanding the result
If the object falls freely, all of this energy becomes kinetic energy (energy of motion) by the time it reaches the starting level. That ignores air resistance. It's also how you can find the impact speed v: v = √(2gh).
A negative result just means the object is below the starting level you chose. It would need energy to be lifted back up to that level.
Assumptions and limitations
- Gravity is the same at every height. That holds when the height is small compared with the planet's radius.
- The mass is treated as a single point at its center of mass, and the height is measured to that point.
- Only gravitational potential energy is calculated.
- For satellites and other great heights, use the universal gravitation form, PE = −GMm ÷ r, instead.
- Elastic (spring) and chemical potential energy are different things and aren't covered here.
- Moon and Mars values are rounded averages; local surface gravity differs slightly.
Frequently asked questions
Which value of g should I use?
Use the standard 9.80665 m/s², unless your course or textbook uses 9.8 or 9.81. In that case, choose Custom and enter that value so your answers match the book exactly.
Can potential energy be negative?
Yes. It's measured from a starting level you choose. An object below that level has negative potential energy. That only means it sits lower than your chosen zero.
How is potential energy related to kinetic energy?
When an object falls without air resistance, the potential energy it loses becomes kinetic energy. Setting mgh equal to ½mv² gives the speed after a drop of height h: v = √(2gh). Notice the mass cancels out, so the speed doesn't depend on it.
What is 1 joule in everyday terms?
About the energy needed to lift a 100 g apple by 1 meter on Earth: 0.1 × 9.80665 × 1 ≈ 0.98 J.
How this calculator is checked
Method: Gravitational potential energy in a uniform field, PE = mgh, rearranged for m, h and g. Standard gravity 9.80665 m/s² (CGPM). The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-18. Found a problem? Tell us.
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