Potential Energy Calculator

Think of gravitational potential energy as a debt the universe owes you. When you lift something against gravity, you do work — you spend effort to move mass upward. That effort is not lost; it is stored as potential energy, ready to be collected as motion the moment the object is released. The higher and heavier the object, the larger the debt.

The formula PE = mgh captures exactly this. Mass (m) measures how much stuff you are lifting. Gravitational acceleration (g) is the local pull trying to drag it back down — 9.81 m/s squared at Earth's surface, but different on every body in the solar system. Height (h) is the vertical distance from your chosen zero level. Multiply all three and you get joules: the standard unit of energy in physics.

The reference point for height is a concept many people overlook. There is no such thing as absolute height — all potential energy is relative to a baseline you choose. A boulder 3 m above the canyon floor has different PE than the same boulder 3 m above the riverbed 50 m below. The calculation only becomes meaningful when you fix your zero and stick to it throughout the problem.

This calculator is appropriate whenever you need to quantify how much energy an object stores because of its vertical position — falling objects, water behind dams, weights on cranes, roller coasters at the top of a hill, climbers above a belay anchor, or satellites in low orbit (as an approximation). It also works for checking quick engineering estimates: if you know the potential energy stored in a raised mass, you immediately know the maximum kinetic energy (and therefore speed) it can reach when it falls, assuming no friction.

Use it for homework and lab problems involving conservation of energy, for engineering sanity checks on cranes and lifts, and for science communication when you want to translate abstract joule values into relatable real-world comparisons. It is also useful for comparing the energy stored in hydroelectric reservoirs with electrical energy equivalents, since the kWh output makes the comparison direct.

Do not use this calculator when rotational kinetic energy matters (a spinning flywheel, a rolling ball), when elastic potential energy is significant (a compressed spring at the bottom of a fall), or when the object's path involves substantial air resistance over the height in question. At those points the simple mgh model breaks down and the actual energy available at impact will be noticeably lower than the calculated value.

Using weight instead of mass. Weight is a force measured in newtons (or pounds-force in imperial). Mass is the quantity of matter in kilograms. If you read 750 N off a bathroom scale in newtons and enter it as mass, you are multiplying by g twice — overstating the energy by a factor of roughly 9.81. Always confirm whether your source gives force (newtons, pounds-force) or mass (kg, lb). Consumer scales in pounds report mass, not force, so lb inputs are correct here.

Treating height as diagonal distance. PE = mgh uses only the vertical component of displacement. A box slid 5 m up a ramp at 30 degrees rises only 2.5 m vertically. Entering 5 m as the height will overestimate stored potential energy by a factor of two. Always extract the vertical height using trigonometry if the path is angled.

Forgetting to fix the reference point. Students often calculate PE for two positions using different zero levels, then subtract results as if they are comparable. If you define the ground as zero for one calculation and the basement floor as zero for another, the numbers cannot be subtracted. Choose a single reference plane before starting and apply it consistently to every height value in the problem.

The full expression is PE = m x g x h. In SI units: m in kg, g in m/s squared, h in metres, giving PE in joules (J). One joule equals one kilogram times metre squared per second squared (1 J = 1 kg m squared/s squared). This matches the unit analysis: kg x (m/s squared) x m = kg m squared/s squared = J.

To convert joules to kilojoules, divide by 1,000. To convert to kilowatt-hours (useful for comparing with electricity), divide by 3,600,000. A kilowatt-hour is 3.6 MJ — which is why even large mechanical systems store only a tiny fraction of the energy in a single unit of electricity. A 70 kg person climbing one flight of stairs (about 3.5 m) stores roughly 2,400 J, or 0.00067 kWh — less than turning on a 60-watt bulb for 40 seconds.

For imperial units, the calculation still produces joules if you first convert: pounds to kilograms (multiply by 0.4536) and feet to metres (multiply by 0.3048). Gravitational acceleration in imperial is typically expressed as 32.174 ft/s squared — converting that to m/s squared gives 9.81, confirming the unit systems are consistent when handled carefully.

The formula PE = mgh assumes a uniform gravitational field — valid near Earth's surface but increasingly wrong as height grows. At 100 km altitude, g has dropped to about 9.50 m/s squared; at 400 km (ISS orbit), it is roughly 8.69 m/s squared. For objects spanning large altitude differences, the correct expression integrates the inverse-square gravitational force: PE = -GMm/r, where r is the distance from Earth's centre. For everyday engineering calculations below a few hundred metres, the error from using constant g is under 0.01%, so mgh is effectively exact at those scales.