Gravitational Potential Energy Calculator (PE = mgh)
Solve PE = mgh for energy, mass, or height.
SI units: joules, kilograms, m/s², metres.
Gravitational potential energy is PE = m × g × h: mass times gravity times height. A 2 kg object held 10 m above the ground stores PE = 2 × 9.81 × 10 = 196.2 J. Rearrange to m = PE ÷ (g × h) or h = PE ÷ (m × g) to solve for either of the others.
What gravitational potential energy is
Gravitational potential energy (GPE) is the energy an object stores because of its position in a gravitational field. Lift something higher and you do work against gravity; that work is banked as potential energy and released the moment the object falls. It depends on just three things — the object’s mass, the local gravity, and its height above a chosen reference level — so knowing any two of PE, m, and h (with g) gives the third.
PE = energy (J), m = mass (kg), g = gravity (≈ 9.81 m/s²), h = height (m)
Worked example
A 2 kg book sits on a shelf 10 m above the floor. How much gravitational potential energy does it store relative to the floor?
- 1 Write the formula. PE = m × g × h, with mass in kilograms, g ≈ 9.81 m/s², and height in metres.
- 2 Choose a reference height. Measure h from where PE = 0 — here the floor — so h = 10 m.
- 3 Substitute the known values. PE = 2 kg × 9.81 m/s² × 10 m.
- 4 Compute the energy. PE = 196.2 J — the energy stored relative to the floor.
Surface gravity on different worlds
Same mass and height, very different stored energy. PE for a 2 kg object at h = 10 m.
| Body | g (m/s²) | PE of 2 kg at 10 m |
|---|---|---|
| Earth | 9.81 | 196.2 J |
| Moon | 1.62 | 32.4 J |
| Mars | 3.72 | 74.4 J |
| Jupiter | 24.79 | 495.8 J |
Reference height, falling, and the value of g
The zero point of height is arbitrary. Only changes in height carry physical meaning, so you may set h = 0 wherever it’s convenient — the floor, a tabletop, sea level. The same object has different PE values against different references, but the difference as it moves is what matters.
Falling converts PE into kinetic energy. As the object drops, height decreases and its stored PE is traded for motion. Ignoring air resistance, the 196.2 J above becomes 196.2 J of kinetic energy (KE = ½mv²) just before impact, giving a speed of about 14 m/s — a tidy demonstration of conservation of energy.
Use the right g. Near Earth’s surface g ≈ 9.81 m/s², but it weakens slightly with altitude and differs on other worlds. Swap in the local value — the calculator’s g field is editable — when you leave Earth.