Gravitational Potential Energy (U = mgh)

Also known as PE = mgh · potential energy of height

U = m g h

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

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Constant used — built into this formula, no need to enter

g_{n} = 9.80665\ \text{m/s}^{2}

Standard acceleration of gravity · exact

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UniversityEngineering Mechanics

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Gravitational Potential Energy (U = mgh) explained

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 = m g h

Where

$U$ = Potential energy (J)
$m$ = Mass (kg)
$h$ = Height (m)

Missing one of these? Work it out first, then come back

Potential energy — Gravitational Potential Energy (Orbital), Elastic Potential Energy
Mass — Newton's Second Law, Kinetic Energy
Height — Area of a Triangle, Body Mass Index (BMI)

Part of this formula set

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.