Gravitational potential energy is the energy an object has stored because of its height above a reference point. This works it out from mass and height, using the internationally fixed value of standard gravity rather than a rounded approximation.
How it works
Gravitational potential energy
PE = m g h
m is mass in kilograms, h is height in metres, g is 9.80665 m/s² — standard gravity, fixed by international agreement in 1901 rather than measured locally. Real gravitational acceleration varies slightly with latitude and altitude (roughly 9.78 to 9.83 m/s²), which is exactly why a fixed reference value exists.
The same energy, seen from the kinetic side
An object dropped from a height converts its potential energy entirely into kinetic energy just before it lands, ignoring air resistance — which means mgh and ½mv² give the same number for the same drop. The free fall calculator works out the landing velocity for a given height directly; running that velocity back through the kinetic energy calculator should land on the same figure this page gives for the starting height, which is a genuine check that both calculators agree with each other rather than a coincidence.
How to use this calculator
- Enter the mass in kilograms.
- Enter the height above the reference point in metres.
- Read the potential energy in joules or kilojoules.
Frequently asked questions
Height above what, exactly?
Whatever reference point you choose — the ground, a table top, sea level. Potential energy is always relative to a chosen zero point; there is no absolute height with an absolute energy attached to it.
Why isn’t g exactly 9.8 or 10?
Because the internationally fixed value is 9.80665 m/s² precisely, chosen to represent a reasonable mid-latitude average when it was defined in 1901. Real gravity varies by location — slightly stronger at the poles, slightly weaker at the equator and at altitude — which is why physics problems use the fixed reference value rather than expecting a locally measured one.
Does this work on other planets?
The formula does, if you use that planet’s own gravitational acceleration instead of Earth’s 9.80665 — the Moon’s is roughly a sixth of Earth’s, for instance. This calculator uses Earth’s standard gravity throughout.
Why does potential energy grow linearly with height, but kinetic energy grows with the square of speed?
Because they come from different relationships — potential energy is a direct product of mass, gravity and height, while kinetic energy comes from integrating force over distance for something accelerating from rest, which is where the square in ½mv² comes from. They are related but built differently.
Is this the “stored energy” people mean when they say an object “has potential”?
Yes, in the literal physics sense — an object higher up has more capacity to do work (or damage) once it starts falling, precisely because it has more potential energy to convert into kinetic energy on the way down.
