How to Calculate Gravitational Potential Energy

Calculates gravitational potential energy as E = mass × gravity × height. Mass is in kilograms, height in metres, and energy in joules.

Explanation

An object held up high can do work as it comes down. That stored energy is its gravitational potential energy.

E = m g h

$E$ is the potential energy, in joules (J)
$m$ is the mass, in kilograms (kg)
$g$ is the acceleration of gravity, about 9.8 m/s² at the Earth's surface
$h$ is the height above your chosen reference level, in metres (m)

The same number is the work needed to lift the object slowly to that height: you pull up with a force of $m g$ over a distance of $h$ .

Example

The defaults are a mass of 2 kg, a height of 5 m and gravity of 9.8 m/s².

E = 2 \times 9.8 \times 5 = 98\,\mathrm{J}

The potential energy is 98 J. Drop the object and all of it turns into kinetic energy, so $\frac{1}{2} m v^2 = 98$ gives a landing speed of about 9.9 m/s.

Notes

Height is measured from a level you pick yourself. Call the tabletop zero and you get one number; call the floor zero and you get another. What carries physical meaning is the change in potential energy, that is, how far something rises or falls.

The value of $g$ varies a little with location: about 9.8 m/s² at the Earth's surface, and about 1.6 m/s² on the Moon.

The formula assumes $g$ stays the same over the whole climb, which holds close to the ground. It does not work at satellite altitudes, where gravity has noticeably weakened.