✓ Sources checked · 10 September 2026 · View verification
Gravitational potential energy describes the configuration of a gravitational system. Near Earth’s surface, a height change gives ΔU = mgΔh when g can be treated as constant.
By Matan · Updated
Choosing the right equation
For a small change in height in a nearly uniform field, U = mgh after choosing U = 0 at h = 0. Here m is mass in kilograms, g is acceleration in m/s² and h is height in metres; U is in joules. The zero is a reference choice, so negative potential energy is possible. Physical predictions use differences in potential energy. [1]
Worked example
Raise a 0.50 kg object by 10 m using g = 9.8 m/s². Its gravitational potential energy increases by 0.50 × 9.8 × 10 = 49 J. This is an illustrative calculation. It is the minimum external work for a slow lift with negligible losses and no net change in kinetic energy.
Large distances require another model
Outside a spherical mass M, U = −GMm/r when zero potential energy is assigned at infinite separation. The separation r is measured from the centre, not from the surface. Moving from r₁ to r₂ changes the energy by GMm(1/r₁ − 1/r₂). This is the suitable ideal two-body expression for large altitude changes; mgh should not be extended across an entire orbit. [1]
Energy belongs to the interaction
“Energy stored in the object” is useful shorthand, but gravitational potential energy depends on the interacting masses and their relative positions. A location alone does not determine energy without specifying a reference and the gravitational field.
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How this article was checked
Sources checked; calculations checked where shown. The definitions, model assumptions and main explanatory claims were cross-checked against the sources below. Worked-example arithmetic and units were checked separately. These examples are illustrative calculations, not experimental measurements.
Source cross-check and editing assisted by AI. No independent human scientific review is recorded for this revision. The check applies to the version dated 10 September 2026; it is not a guarantee that every possible interpretation is correct.
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Sources and further reading
- OpenStax: Gravitational potential energy — Gravitational potential energy.
Cite this article
Matan. “Gravitational Potential Energy Equation.” Your Physicist. Originally published 2023-03-17; updated 2026-09-10. https://your-physicist.com/gravitational-potential-energy-equation/
Revision history
: Clarified system energy, reference height and the limits of mgh; retained and checked the 49 J example. Added linked sources and a transparent verification record.
