Potential Energy Calculator (PE = mgh)
Solve the gravitational potential energy formula PE = mgh for energy, mass, or height. Enter any two values and get the third with steps shown.
The potential energy formula
Gravitational potential energy is the energy an object has because of its height above a reference point:
- PE — potential energy, in joules (J)
- m — mass, in kilograms (kg) — always positive
- h — height above the reference point, in metres (m) — can be negative if below the reference
- g — acceleration due to gravity, fixed at 9.8 m/s²
Enter any two values and leave the third blank; the calculator solves for it and shows the substitution step.
Worked example
A 10 kg object sits 5 m above the ground. What is its potential energy?
- Formula: PE = mgh
- Substitute: PE = 10 × 9.8 × 5
- Result: PE = 490 J
Solving in reverse
The same formula rearranges to find mass or height when potential energy is known:
- Mass: m = PE / (gh) — enter PE and h, leave m blank.
- Height: h = PE / (mg) — enter PE and m, leave h blank.
For example, 490 J of potential energy at 5 m means m = 490 / (9.8 × 5) = 10 kg. And 490 J stored in a 10 kg mass means h = 490 / (10 × 9.8) = 5 m.
Common mix-ups
- Forgetting g. PE = mh (without gravity) is a common slip — the acceleration due to gravity, 9.8 m/s², is always part of the formula.
- Using the wrong reference height. Potential energy depends on the height above a chosen reference point — measuring from the wrong baseline gives a different (but not necessarily wrong) answer, as long as you are consistent.
- Mixing units. Feet or pounds must be converted to metres and kilograms before using this calculator.
Where this shows up
Potential energy is the storage counterpart to kinetic energy: as an object falls, its potential energy converts into kinetic energy (ignoring air resistance, the total stays constant). Lifting a mass against gravity is exactly the work W = Fs done against the force of gravity, W = mgh — the same formula as potential energy, since weight is F = mg (see the weight calculator).
Frequently asked questions
- What is the formula for gravitational potential energy?
- Gravitational potential energy is PE = mgh, where PE is energy in joules (J), m is mass in kilograms (kg), g is the acceleration of gravity (9.8 m/s²), and h is height above a reference point, in metres (m).
- How do I find height from potential energy?
- Rearrange the formula to h = PE / (mg). Enter the potential energy and mass, leave height blank, and the calculator solves it for you automatically.
- What value of g does this calculator use?
- It uses the standard Earth surface value g = 9.8 m/s². This is a fixed constant in the formula, not a field you enter.
- Can potential energy be negative?
- Yes, if the height is measured as negative — for example, a height below your chosen reference point (like a ball at the bottom of a well relative to ground level).
- What is "height" measured relative to?
- Any reference point you choose — the ground, a table top, sea level. Potential energy is always relative to that reference; only differences in height (and therefore energy) between two points are physically meaningful.
- Why must mass be positive?
- Mass represents a physical amount of matter, which cannot be zero or negative. A zero mass would make the PE = mgh formula meaningless for finding height (division by zero).
- What units does this calculator use?
- SI units — joules (J) for energy, kilograms (kg) for mass, and metres (m) for height. Convert other units (pounds, feet) to SI before entering them.