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Gravitational Potential Energy (U = mgh)

Also known as PE = mgh · potential energy of height

U=mghU = m g h
sig figs

Worked example: 2 kg lifted 10 m → 196.133 J. Press Try an example to run it live, then adjust anything.

Enter your known values, leave one input blank, and solves for the missing one. Tap a variable’s symbol to see what it means, with a typical value. Change any unit and the answer follows.

Constant used: built into this formula, no need to enter
gn=9.80665 m/s2g_{n} = 9.80665\ \text{m/s}^{2}Standard acceleration of gravity · exact

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See also

Conservation of Mechanical Energy (½mv² + mgh): What this stored energy becomes on the way down, and the speed it arrives with.
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Gravitational Potential Energy (U = mgh) explained

mhU

Lifting a mass banks energy in the gravitational field, and near Earth's surface the deposit is simply mgh, with g = 9.80665 m/s². A roller coaster earns its entire ride on the first climb: a 500 kg car hauled 30 m up stores 500 × 9.80665 × 30 ≈ 147 kJ, which the drops and loops then spend as speed. Only differences in height matter: you are free to call the ground floor, the table top, or sea level "zero", as long as you stay consistent.

The same idea runs entire power grids: pumped-storage hydro plants push water uphill when electricity is cheap and let it fall through turbines at peak demand, storing gigawatt-hours as nothing more than elevated water. The formula is a near-surface approximation: it treats g as constant, excellent for heights small compared with Earth's radius.

Gravitational Potential Energy (U = mgh) formula

U=mghU = m g h
Where
  • UU= Potential energy (J)
  • mm= Mass (kg)
  • hh= Height (m)
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Work, energy and power

8 formulasWork, the two stores of mechanical energy, the theorem that connects them to speed, and the two ways of writing power.

Revised 16 October 2026
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formula.expert. (2026, October 16). Gravitational Potential Energy (U = mgh) Calculator. https://formula.expert/solvers/gravitational-potential-energy

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