Potential Energy Calculator — gravitational (mgh)

How it works

Gravitational potential energy is the stored energy an object gains by being lifted against gravity — the work done to raise it to a height h:

PE = m × g × h

where m is the mass, g is the gravitational field strength and h is the height above a chosen reference level. In SI units — kilograms, m/s² and metres — the result is in joules (J).

Gravity g is an input here, defaulting to Earth's 9.8 m/s², so you can change it for the Moon (about 1.6 m/s²) or another planet. Potential energy is always measured relative to a reference height: raise the object and PE increases; below the reference, the height — and the potential energy — is negative. This calculator is unit-agnostic, so any consistent units work.

Worked example

OpenStax lifts a 0.500 kg book 1.00 m at g = 9.80: PE = 0.5 × 9.8 × 1 = 4.90 J. A 2 kg object 10 m up has 2 × 9.8 × 10 = 196 J on Earth, but the same object at the same height on the Moon (g ≈ 1.6) stores only 2 × 1.6 × 10 = 32 J. A 70 kg diver on a 10 m platform has 70 × 9.8 × 10 = 6860 J ready to become kinetic energy on the way down.

Frequently asked questions

What is the formula for gravitational potential energy?

PE = mgh: mass times the gravitational field strength times the height above a reference level. With mass in kilograms, g in m/s² and height in metres, the energy comes out in joules.

Why does gravity appear as an input?

Because potential energy depends on where you are. On Earth g ≈ 9.8 m/s², but on the Moon it is about 1.6 m/s² and on Mars about 3.7 m/s², so the same lift stores different amounts of energy. Leaving g adjustable lets the calculator work anywhere.

What is the reference height, and can potential energy be negative?

The height is measured from a reference level you choose (often the ground or a table top). Only *changes* in potential energy matter physically, so the zero point is arbitrary. Below the reference, the height is negative and so is the potential energy.

What units does potential energy use?

The SI unit is the joule (J), the same as every other energy. Kilograms, m/s² and metres give joules directly. This calculator treats the inputs as plain numbers, so keep the units consistent.

How does potential energy turn into kinetic energy?

As an object falls, gravity does work on it and its potential energy (mgh) converts into kinetic energy (½mv²). Ignoring air resistance, the energy lost as height drops exactly equals the kinetic energy gained, so the two always sum to the same total.

Is this the only kind of potential energy?

No — this is *gravitational* potential energy. There are others: elastic potential energy stored in a stretched spring, electrical potential energy between charges, and chemical potential energy in bonds. This calculator covers only the height-based gravitational form, PE = mgh.