Gravitational Potential Energy
PE = mgh — energy banked by height.
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The engineering
The humble mgh runs more of the grid than you'd guess — pumped-storage hydro is the world's dominant grid battery, and it is exactly this card at reservoir scale. The disappointment in the kWh row is instructive: a tonne raised ten meters stores only 0.027 kWh, which is why gravity storage needs mountains or absurd masses to matter.
For engineers the equation mostly runs in reverse as a hazard calculation: the impact-velocity row is what a dropped object is doing when it arrives. A 5 kg tool off a 20 m scaffold arrives at 19.8 m/s carrying a kilojoule — dropped-object programs, toe boards, and hard hats are mgh policy documents.
Where this math comes from
The intuition that height stores work is as old as the water wheel, but the bookkeeping term is Victorian: William Rankine coined 'potential energy' in 1853 to name the energy of configuration, completing the ledger that Hermann von Helmholtz's 1847 conservation memoir had opened — energy shifts between forms but the total balances.
Joule's paddle-wheel experiments of the 1840s had already priced the conversion — falling weights stirring water, warming it by an exactly predictable amount — which is why the unit that measures your mgh is named for a brewer with very good thermometers.
- 1843James Prescott JouleFalling-weight experiments price mechanical energy in heat.
- 1847Hermann von HelmholtzConservation of energy stated in full generality.
- 1853William RankineThe term 'potential energy' coined.
See the full timeline of the math behind every calculator →
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