Potential energy calculator
Mass times gravity times height. The interesting term is the middle one: 9.80665 m/s² is a defined value with no uncertainty at all, and it is not the gravity anywhere in particular. Nothing you type here leaves your browser — it is worked out on your own device, so there is nothing to send and nothing to log.
9.80665 is a definition, not a measurement
Standard gravity was fixed at exactly 9.80665 m/s² by the 3rd General Conference on Weights and Measures in 1901. It has no uncertainty, no error bars, and will never be revised, because it is not a claim about the world — it is an agreement about a number.
What it is not is the gravity at any particular place. Earth is not a sphere, it spins, and its density varies:
| The equator | about 9.7803 |
|---|---|
| London | about 9.8158 |
| The poles | about 9.8322 |
| Standard | 9.80665 exactly, and nowhere |
A spread of 0.53% between the extremes — larger than most people's sense of how constant a constant is, and larger than the precision anyone quotes mgh to. Altitude moves it again: gravity falls by about 0.3% at the top of Everest.
Those figures are measurements, unlike the 9.80665, and the selector says which is which. If you need the gravity at a specific place to better than a few parts in ten thousand, it has to be measured there; there is no formula on this page that will tell you.
Measured from where?
Potential energy has no absolute value. Only changes in it mean anything, so the height has to be measured from somewhere you have chosen — the floor, the ground, sea level, the bottom of the shaft. This page takes your height as a rise above whatever you are calling zero, and the answer is only meaningful once you have decided what that is.
This is why a ball on a table has a different potential energy depending on whether you are about to roll it off the table or drop it out of the window, without anything about the ball changing.
Where mgh stops working
mgh assumes gravity is the same all the way up, which is true enough for anything you can build and false for anything in orbit. Gravity falls off with the square of the distance from the centre of the Earth, so for heights that are a noticeable fraction of the planet's 6,371 km radius the straight-line formula overstates the energy.
At 10 km — cruising altitude — the error is about 0.3%. At 400 km, the space station's orbit, mgh is out by roughly 6% and the honest calculation needs the inverse-square form. This page does the simple one and tells you where it stops being simple.