Potential Energy Calculator
Gravitational PE = mgh — solve for energy, mass or height, on any planet.
Results update as you type.
About this calculator
Gravitational potential energy is the energy an object stores by virtue of its height in a gravitational field: PE = m × g × h, in joules, where m is mass in kilograms, g is the gravitational acceleration and h is the height it is raised. On Earth g is the standard 9.80665 m/s²; under advanced options you can switch to the Moon (1.62), Mars (3.72), Jupiter (24.79) and other bodies to see how the same lift stores very different amounts of energy. Choose which quantity to solve for — energy, mass or height — and the tool also reports the free-fall impact speed from that height, v = √(2gh).
As a worked example, lifting a 2 kg mass 10 m on Earth stores PE = 2 × 9.80665 × 10 ≈ 196 joules. Let it fall back and, ignoring air resistance, all of that converts to kinetic energy, so it lands at v = √(2 × 9.80665 × 10) ≈ 14 m/s. Take the identical lift to the Moon and only about 32 J is stored, because lunar gravity is roughly one-sixth of Earth’s.
Potential energy is measured relative to a chosen reference level — usually the ground — so only differences in height carry physical meaning. The concept underlies hydroelectric dams, pumped storage, pendulums, roller coasters and any situation where raising a mass banks energy that can later be released, and it pairs directly with kinetic energy through conservation of energy as objects rise and fall.
Frequently asked questions
What is gravitational potential energy?
It is the energy an object gains by being raised against gravity, PE = m × g × h. A 2 kg mass lifted 10 m on Earth stores 2 × 9.80665 × 10 ≈ 196 joules.
Does potential energy depend on the reference height?
Yes. PE is measured relative to a chosen zero level, usually the ground. Only differences in height between two points are physically meaningful.
How does gravity on other planets change the result?
PE is proportional to g, so the same lift stores far more on Jupiter (g ≈ 24.8) and far less on the Moon (g ≈ 1.62). Raising a 2 kg mass 10 m stores about 196 J on Earth but only around 32 J on the Moon.
How is the free-fall impact speed calculated?
Dropping from height h, all the potential energy becomes kinetic energy, so ½mv² = mgh gives v = √(2gh) — independent of mass. From 10 m on Earth that is about 14 m/s, and the calculator shows this alongside the energy.
How does potential energy relate to kinetic energy?
As an object falls, potential energy converts to kinetic energy while the total (ignoring air resistance) stays constant. That conservation of energy is why the impact speed depends only on the drop height, not the mass.
What is the difference between mass and weight here?
The formula uses mass in kilograms; the weight (the gravitational force) is m × g and is already baked into the PE = mgh expression through the g term, so you enter mass, not weight.
API — use this calculator from code
Call this calculator as a free JSON endpoint — no key required. Send the field values below as query parameters or JSON. Read the full API docs →
Endpoint
GET https://calculator.free/api/v1/potential-energy/curl
curl "https://calculator.free/api/v1/potential-energy/?solve=energy&mass=2&height=10"JavaScript fetch()
const r = await fetch(
"https://calculator.free/api/v1/potential-energy/?" + new URLSearchParams({
"solve": "energy",
"mass": "2",
"height": "10"
}));
const data = await r.json();
console.log(data.results);Results are estimates for general guidance only, not financial, medical or tax advice.