Gravitational Potential Energy — PE = mgh

Gravitational potential energy PE = mgh explained: stored energy of height, the meaning of the reference level, and a worked example.

PE = mgh

Gravitational potential energy equals mass times gravity times height.

What it means

The equation says height is stored energy. Lifting something against gravity banks energy equal to its weight times the height gained, and that bank is fully refundable: drop the object and the stored energy reappears as motion. Only changes in height matter — the reference level (h = 0) is your choice, so potential energy values are relative, but differences between two heights are absolute and physical. A heavier object or a greater height both mean more stored energy, linearly.

Variables

Symbol	Name	Unit	Meaning
$PE$	Gravitational potential energy	J	Stored energy due to position in a gravitational field
$m$	Mass	kg	Mass of the object
$g$	Acceleration of gravity	m/s²	Gravitational field strength, 9.8 m/s² near Earth
$h$	Height	m	Vertical height above the chosen reference level

Assumptions

Gravity g is uniform over the height change (true near Earth's surface)
h is measured from an arbitrary but fixed reference level
No other forces (like air drag) do significant work

Derivation

Lifting a mass $m$ through height $h$ at constant speed requires an upward force equal to the weight $mg$ over distance $h$ . Work is force times distance, so $W = mgh$ — and that work is stored as gravitational potential energy.

Worked example

Problem

A 2 kg book rests on a shelf 1.5 m above the floor. What is its gravitational potential energy relative to the floor?

Given:

m = 2 kg
g = 9.8 m/s²
h = 1.5 m

Write the formula: $PE = mgh$
Substitute: $PE = 2 \times 9.8 \times 1.5$
Multiply: $PE = 19.6 \times 1.5 = 29.4\ \mathrm{J}$

29.4 J relative to the floor

Lifting the book stored 29.4 joules. If it falls, that stored energy converts into kinetic energy (then heat and sound on impact) — which is why dropped objects hit harder from greater heights.