Use this gravitational potential energy calculator to find the change in stored gravitational energy from an object’s mass, vertical height, and local gravity. It returns energy in joules, compares the same setup on Earth, the Moon, and Mars, and shows the ideal fall-time and speed connection when air resistance is ignored.
Methodology. Every result is calculated locally in your browser with ΔPE = mgh. This near-surface model uses a constant gravity value and measures a change in height from the reference level you choose.
Gravitational Potential Energy Calculator
LiveWhat the result means
Gravitational potential energy is energy associated with relative height in an object–planet system. A positive result here means the object has gained energy because it is higher than the chosen reference level. In a no-loss idealization, that energy can convert into motion as the object falls. To calculate that moving energy directly from mass and speed, use the Kinetic Energy Calculator.
The formula
| Symbol | Meaning | SI unit |
|---|---|---|
| ΔPE | Change in gravitational potential energy | joule (J) |
| m | Mass | kilogram (kg) |
| g | Gravitational acceleration | m/s² |
| Δh | Vertical change in height | meter (m) |
For a 5 kg object raised 10 m on Earth, ΔPE = 5 × 9.80665 × 10 = 490.33 J. This is a change relative to the selected reference level, not an absolute universal energy value.
Check the calculation by hand
For a quick independent check, multiply mass by the selected gravity and the vertical height change. Keep the inputs in kilograms, meters, and m/s² so the result is in joules.
5 kg × 9.80665 m/s² × 10 m = 490.3325 kg·m²/s² = 490.33 J after rounding to two decimal places.
For longer expressions or a repeatable classroom check, enter 5 × 9.80665 × 10 in the Numeros Scientific Calculator. The energy calculator remains the faster choice when you also want the reference-level guidance, planet comparison, and ideal free-fall connection.
Compare the same mass and height on Earth, the Moon, and Mars
Mass and height are held constant below. Only gravity changes, so the energy changes in direct proportion to g. This comparison is useful for classroom problems; the simple mgh approximation is intended for height changes that are small relative to a planet’s radius.
| Location | Gravity | Potential energy | vs. Earth |
|---|
How height and mass affect energy
Potential energy is linear in both mass and vertical height. Doubling the mass doubles the energy. Doubling the height also doubles the energy. That is different from the kinetic-energy relationship, where speed is squared.
| Scenario | Mass | Height | Energy at selected gravity |
|---|
Potential energy and free fall: the connection
When an object drops and losses such as air resistance are negligible, its lost gravitational potential energy becomes kinetic energy. The ideal final speed depends on height and gravity, while mass cancels from the speed equation. You can model the corresponding time and final speed in the Free Fall Calculator; use the Acceleration Calculator when you need a broader constant-acceleration calculation.
Why the reference level matters
Potential energy is measured relative to a chosen zero level. You may choose the ground, a laboratory bench, or the bottom of a ramp; the important rule is to measure every compared height from the same reference. Changing the zero changes the reported value but does not change the physical energy difference between two positions.
When the mgh formula is appropriate
The mgh expression is a near-surface constant-gravity approximation. It works well for typical laboratory, building, and classroom height changes. It is not the right model for large astronomical distances, orbital mechanics, or situations where gravity changes materially with distance. The formula gives an energy change; it does not account for friction, drag, deformation, heat, or real-world stopping force.
Step-by-step guide
- Enter mass in kilograms. Do not enter weight in newtons in the mass field.
- Enter the vertical change in height. Use one consistent reference level for every comparison.
- Select Earth, Moon, or Mars gravity. The calculator uses the selected constant surface value.
- Read the energy in joules. Use the comparisons and the related calculators when you need motion or acceleration, not just stored energy.
Common mistakes
Frequently asked questions
What is gravitational potential energy?
It is energy associated with relative position in a gravitational field. Near a planet’s surface, the change in energy for a vertical height change is ΔPE = mgh.
Is gravitational potential energy always positive?
No. A positive or negative change depends on your sign convention and reference level. This calculator is designed for a positive magnitude of energy gained by raising an object through a positive height.
Does the path change the mgh result?
For this near-surface model, only the vertical change in height matters. A ramp, stairs, and vertical lift give the same change in potential energy when the start and end heights are the same.
How does potential energy become kinetic energy?
If drag and friction are negligible, a drop converts lost gravitational potential energy into kinetic energy. In real conditions, some energy may also transfer to heat, sound, deformation, or other effects.
Why is this calculator not for orbits or large altitudes?
Over very large distances, gravity is not constant. The simple mgh approximation should be replaced with a gravitational model that accounts for changing distance from the planet.
Sources
- OpenStax — Gravitational Potential EnergyDerivation of ΔPE = mgh near Earth’s surface, reference levels, and energy conversion.
- NASA Glenn — Energy ActivityEducational definitions, SI units, and the m × g × h relationship.
Related calculators
Use these tools when the next question is about motion, force, or a different physics quantity:
- Kinetic Energy Calculator — calculate energy from mass and speed.
- Free Fall Calculator — estimate ideal fall time and final speed from a height.
- Acceleration Calculator — solve constant-acceleration relationships beyond this energy model.
- Momentum Calculator — calculate momentum from mass and velocity.
- Scientific Calculator — verify a manual m × g × h expression.
- All Physics Calculators — browse the full Numeros physics collection.