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Gravitational Potential Energy from Reference Height

Relate mass and signed height to gravitational potential energy in a uniform gravitational field.

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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

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Formula and method

A 2 kg object 5 m above the chosen reference has gravitational potential energy 98.0665 J at standard gravity.

Potential energy relative to reference = mass × gravitational acceleration × signed height

Worked example

Enter these known values and leave the other values blank.

Object mass
2 kg
Uniform gravitational acceleration
1 g
Signed height above chosen zero level
5 m
Potential energy relative to that level
98.0665 J

Assumptions and limitations

  • Mass and gravity magnitude are positive. Height and potential energy may be positive, zero or negative relative to the chosen reference.
  • Gravity is treated as uniform over the height interval. Large altitude changes require the varying gravitational-potential formula.
  • One g is standard gravity, exactly 9.80665 m/s². A zero height gives zero energy but does not uniquely determine mass or gravity.

Common questions

Can gravitational potential energy be negative?

Yes. In this model, a position below the chosen zero level has negative potential energy. The reference is a convention; energy differences determine changes.

Is energy the same as lifting force?

No. Force has units of newtons; energy has units of joules. Multiplying the constant weight force by vertical height gives the energy change.

References

The calculation equations, inverse formulas, units, and input rules were imported from this source. Bookify provides the interface and equation solver.

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