Potential Energy Calculator
Find the gravitational potential energy of a mass at a height — mgh — and the speed it would reach if it fell.
The energy stored by lifting something up.
How the potential energy calculator works
Lifting a mass m through a height h against gravity stores m × g × h joules. Let it fall and that energy becomes kinetic energy, so the landing speed is √(2gh) regardless of mass (ignoring air). The calculator reports the energy in joules, kilojoules and kilowatt-hours and the equivalent fall speed.
Hydro dams, lift counterweights and pumped storage all trade on this: a tonne of water 100 m up stores 0.27 kWh.
Formula: PE = m g h
Worked examples
| Inputs | Potential energy | Note |
|---|---|---|
| 10 kg at 5 m | 490.3 J | 490 J |
| 1,000 kg of water at 100 m | 980,665 J | 0.27 kWh — the hydro-dam sum |
| 70 kg person up 3 m of stairs | 2,059.4 J | 2.06 kJ per flight |
FAQFrequently asked questions
Where does the energy go when the object falls?
Into kinetic energy (½mv²) until it lands, then into heat, sound and deformation. Energy is conserved; it only changes form.
Is potential energy absolute?
No — it is relative to a chosen reference height. Only differences in height matter.
How much energy does a hydroelectric dam store?
mgh for every kilogram of water above the turbines. A 100 m head gives 981 J per kilogram — about 0.27 kWh per tonne.
Does the formula hold at any height?
Near the Earth's surface, where g is nearly constant. For orbits and rockets the full form −GMm ÷ r is needed.
Where these figures come from
- NIST — CODATA 2018 fundamental physical constants — G, g₀, R, c
- NIST Special Publication 811 — Guide for the use of the International System of Units — unit conversions
- The Engineering ToolBox — material properties — specific heats, expansion coefficients, densities
- National Institute of Standards and Technology — the US measurement authority
Last checked: September 2026. Constants are the CODATA 2018 values; formulas are the standard textbook forms.