Potential Energy Calculator

Gravitational potential energy calculator

Gravitational potential energy is the stored energy of an object raised to a height — the energy it would release if it fell. It is given by PE = m × g × h and measured in joules. This tool rearranges the formula so you can solve for potential energy, mass, or height, with an editable gravity value for other planets, making it useful for physics homework and engineering checks.

How it works

The tool solves whichever quantity you leave unknown from the same relationship:

PE = m × g × h          (joules)
m  = PE ÷ (g × h)       (kilograms)
h  = PE ÷ (m × g)       (metres)

Gravity g defaults to Earth’s standard 9.80665 m/s² but is editable, so you can model the Moon (≈1.62), Mars (≈3.72) or any other body.

Example

A 5 kg object raised 4 m on Earth (g = 9.80665):

• PE = 5 × 9.80665 × 4 = 196.13 J

Solving the other way — 196.13 J with the same mass and gravity gives back a height of 4 m.

Everything updates instantly — all in your browser.

Understanding the reference height

Potential energy is always measured relative to a chosen reference point — there is no absolute zero. You choose where h = 0, and PE is the energy stored above that baseline. In most physics problems, h = 0 is the ground or floor. In engineering, it might be sea level, the base of a structure, or a machine’s lowest travel point.

This matters practically: a ball at table height has more PE relative to the floor but zero PE relative to the table itself. The tool computes PE for whatever h you enter — make sure your h is the height above your chosen reference, not above some other baseline.

Conversion to other energy forms

PE = m × g × h is useful because gravitational potential energy converts to kinetic energy as an object falls (ignoring air resistance). At the bottom of a fall, all PE becomes kinetic energy (KE = ½ × m × v²), so you can find the speed at impact:

KE at bottom = PE at top
½ × m × v² = m × g × h
v = √(2 × g × h)

For example, a 5 kg object dropped from 4 m on Earth hits the ground at: v = √(2 × 9.80665 × 4) ≈ 8.86 m/s

This equivalence underpins roller-coaster design, hydroelectric turbines, and pendulum clocks — all systems that trade height for motion or motion back into height.

Gravity on other bodies

Use the editable gravity field for planetary engineering or space-exploration scenarios: