Gravitational Potential Energy Calculator
Written by Thierno Sadou Diallo, formula verified per our methodology • Last checked on 9/7/2026
Gravitational potential energy is calculated with Ep = m × g × h, where m is mass, g is gravitational acceleration, and h is height. A 10 kg mass at a height of 5 m on Earth has a potential energy of about 490.5 joules.
Explanation
Gravitational potential energy represents the energy an object has purely from being positioned at a height, relative to a chosen reference level (the ground, a table, or any other arbitrary point). This energy isn't an absolute property of the object: it depends entirely on the chosen reference level — only the change in potential energy between two heights has a concrete, measurable physical meaning, independent of that choice of reference. Gravitational potential energy forms, together with kinetic energy (the energy of motion), the two components of an object's mechanical energy. In the absence of friction, the sum of these two energies stays constant: a falling object progressively converts its potential energy (which decreases as its height decreases) into kinetic energy (which increases as its speed increases), a principle called conservation of mechanical energy. This same principle explains why an object released in free fall accelerates: all the potential energy lost is fully converted into kinetic energy, as long as no friction force (air resistance, for instance) dissipates part of that energy as heat.
Example: a 10 kg mass at a height of 5 m
Inputs
Mass: 10 kg. Height: 5 m. Gravity: 9.81 m/s² (Earth).
Calculation
Ep = 10 × 9.81 × 5 = 490.5 J.
Result
This mass has a gravitational potential energy of about 490.5 joules.
Frequently asked questions
Why doesn't the choice of reference level matter?
Because only the change in potential energy between two positions has concrete physical meaning (the work needed to move the object from one height to the other), not its absolute value at a given instant. Choosing the ground, a table, or any other point as the reference changes the displayed numerical value, but never changes the calculated potential energy difference between two distinct heights, which stays the same regardless of the chosen reference frame.
What happens to the potential energy of a falling object?
It progressively converts into kinetic energy as the object accelerates downward, in the absence of friction: the loss of potential energy is exactly matched by the gain in kinetic energy, with the sum of the two (total mechanical energy) staying constant. See our kinetic energy calculator to calculate this second component from the speed reached.
Does this formula apply at any height, even a very large one?
No, this simplified formula assumes g stays constant over the entire height considered, an approximation valid near the surface of a celestial body (up to a few tens of kilometers of altitude on Earth). For much greater heights (orbit, spaceflight trajectory), where g decreases noticeably with distance from the body's center, a more complete calculation based on the law of universal gravitation becomes necessary.