Calculators
Gravitational Potential Energy Calculator
Solve gravitational potential-energy change, mass, or height.
Use ΔU = mgΔh for gravitational potential-energy change near a body's surface where gravitational acceleration can be treated as constant. Height is measured relative to your chosen reference level.
Calculated potential-energy change
58.8399 J
ΔU = mgΔh
Default g = 9.80665 m/s² is standard gravity. A negative height change gives a negative change in potential energy relative to the chosen reference.
About This Tool
Near a planet or other body's surface, when gravitational acceleration is approximately constant over the height change, gravitational potential-energy change can be modeled as ΔU = mgΔh. This calculator solves that relationship for energy change, mass, or height. It uses standard Earth gravity by default but lets you enter another positive gravitational acceleration. Height and energy changes may be signed because potential energy is defined relative to a chosen reference level.
How To Use It
- Choose whether to solve for potential-energy change, mass, or height change.
- Enter the known quantities and units. The default gravitational acceleration is standard gravity, 9.80665 m/s².
- Use a positive height change for movement upward relative to your reference direction and a negative height change for movement downward. Keep your sign convention consistent when solving backward from energy.
- Choose the result unit and interpret the answer as a change relative to the reference level, not an absolute universal potential energy.
Examples
Raise a 2 kg object
Raising 2 kg by 3 m at standard gravity changes gravitational potential energy by about 58.8399 J.
One kilogram by one meter
For 1 kg raised 1 m using standard gravity, ΔU = 1 × 9.80665 × 1 = 9.80665 J.
Find height
An energy increase of 98.0665 J for a 2 kg mass at standard gravity corresponds to a height increase of 5 m.
Move downward
For a positive mass and gravity, a negative height change produces a negative potential-energy change relative to the chosen reference.
Useful Notes
The near-surface formula
For approximately constant gravitational acceleration, ΔU = mgΔh, where m is mass, g is gravitational acceleration, and Δh is vertical height change. Rearrangements are m = ΔU/(gΔh) and Δh = ΔU/(mg).
Reference level matters
Gravitational potential energy can be assigned zero at a convenient reference height. The mgh relationship is most clearly interpreted as a change in potential energy between two nearby heights.
Standard gravity
The default 9.80665 m/s² is the defined value of standard gravity. Local gravitational acceleration on Earth varies slightly, and other celestial bodies have different values.
Units
Using kilograms, meters, and m/s² produces joules. The calculator converts grams and pounds for mass, centimeters and feet for height, and joules or kilojoules for energy.
Limitations
The constant-g mgh approximation is appropriate when gravitational acceleration does not change meaningfully across the height interval. For very large altitude changes or orbital/astronomical problems, use the gravitational potential based on distance from the body's center instead.
FAQ
Why is potential energy relative to a reference height?
Only differences in potential energy affect many ordinary mechanics calculations, so a convenient height can be chosen as the zero reference.
Can gravitational potential-energy change be negative?
Yes. With upward defined as positive, moving to a lower height gives a negative Δh and therefore a negative ΔU.
What value of g should I use on Earth?
9.80665 m/s² is standard gravity and is a useful default. Use a known local value when the problem specifically provides one.
When does mgh stop being a good approximation?
When the height range is large enough that gravitational acceleration changes significantly, a distance-dependent gravitational potential model is more appropriate.
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