March 26, 20263 min read

Potential Energy Calculator — Gravitational PE = mgh

Calculate gravitational potential energy using mass, gravity, and height. Explore energy conservation, height vs mass effects, and real physics examples.

potential energy gravitational PE mgh physics calchub

Potential energy is stored energy — the energy an object has because of its position rather than its motion. Hold a rock over a cliff and it has potential energy. Release it and that PE converts to kinetic energy as it falls. The conversion between these two forms is one of the most fundamental ideas in all of physics.

Use the CalcHub potential energy calculator to compute gravitational PE for any mass, height, and gravitational field.

The Formula

PE = m × g × h

PE = gravitational potential energy (Joules, J)
m = mass (kg)
g = gravitational acceleration (9.81 m/s² on Earth's surface)
h = height above reference point (m)

The reference point (h = 0) is arbitrary — what matters is the change in height. Setting the ground as zero is most common, but you could set sea level or any other convenient baseline.

Energy Conservation in Action

When an object falls from height h with no air resistance:

All PE converts to KE at the bottom:
mgh = ½mv²

Solving for final velocity: v = √(2gh)

A ball dropped from 10 m hits the ground at v = √(2 × 9.81 × 10) ≈ 14 m/s. Notice mass cancels out entirely — a pebble and a bowling ball dropped from the same height hit the ground at the same speed (ignoring air resistance).

PE on Other Planets

Body	g (m/s²)	PE for 10 kg at 5 m
Earth	9.81	490.5 J
Moon	1.62	81 J
Mars	3.72	186 J
Jupiter	24.8	1240 J

The calculator lets you input custom gravitational acceleration for problems involving other planets or non-Earth environments.

Worked Example

A 75 kg hiker climbs from base camp at 2000 m to a peak at 3400 m. How much gravitational PE have they gained?

Height change = 3400 − 2000 = 1400 m

PE = 75 × 9.81 × 1400 = 1,030,050 J ≈ 1030 kJ

That's roughly 246 food calories — just from the height gain, not accounting for metabolic inefficiency (the body is only about 25% efficient, so the actual calorie burn is around 1000 kcal).

Is potential energy "real"?

It's a useful model rather than a physical substance. PE represents the work that a system could do if released. The concept becomes precise when you're careful about reference points, but the energy itself is real in the sense that it accurately predicts outcomes.

What if height is negative?

If an object moves below your reference point, h is negative and so is the change in PE. This is common in problems involving objects falling into wells or below sea level — perfectly fine physically.

Does gravitational PE use mass or weight?

Mass (in kg). Weight is the force (mg in Newtons). The formula PE = mgh uses mass and separately incorporates g. Don't substitute weight for mass, or you'd effectively square gravity.