Gravitational Potential Energy Calculator
Enter any three of potential energy, mass, height, or gravity to solve for the fourth using PE = mgh. Two 3D diagrams compare an object at low and high elevation, and charts show how potential energy scales with height and how it varies across different planets.
Reviewed by the ToolNestr Editorial Team — July 2026
Enter any three values, leave one blank.
Low vs high elevation
1. Object at low elevation
Sitting close to the reference ground level, this object stores very little gravitational potential energy.
2. Object at high elevation
The same mass, lifted much higher, stores proportionally more potential energy — ready to convert into motion if released.
Potential energy graphs
How it works
The core idea in one line: gravitational potential energy is stored energy tied directly to how far an object sits above a chosen reference height, in a gravitational field of a given strength — change any one of mass, gravity, or height, and the stored energy changes proportionally.
PE = mgh
gravitational potential energy — m in kg, g in m/s², h in metres
h = PE / (mg)
rearranged to solve for height
g = PE / (mh)
rearranged to solve for gravity
PE = mgh comes directly from the work needed to lift an object of mass m against gravity g through a height h: W = F×d = (mg)×h. Because that lifting work gets stored as potential energy, PE = mgh follows immediately. Since PE depends linearly on all three of mass, gravity, and height, doubling any one of them exactly doubles the stored potential energy — no quadratic relationships here, unlike kinetic energy's dependence on velocity.
Worked example 1 — a book on a shelf (Earth)
Given: A 5 kg book sits on a shelf 2 m above the floor, on Earth (g = 9.81 m/s²).
If the book fell, essentially all of this 98.1 J would convert into kinetic energy just before it hit the floor.
Worked example 2 — the same book on the Moon
Given: The same 5 kg book at the same 2 m height, but now on the Moon (g = 1.62 m/s²).
Identical mass and height, but the Moon's much weaker gravity (about 1/6th of Earth's) means far less stored potential energy — this is also why falls on the Moon feel so much gentler.
The same object and height, across the solar system
A fixed 5 kg mass at 2 m height — only gravity changes, showing how strongly PE depends on the local gravitational field.
| Body | g (m/s²) | PE (5 kg, 2 m) |
|---|---|---|
| Moon | 1.62 | 16.2 J |
| Mars | 3.71 | 37.1 J |
| Earth ★ | 9.81 | 98.1 J |
| Jupiter | 24.79 | 247.9 J |
★ Reference row (worked example 1). The same book stores over 15× more potential energy on Jupiter than on the Moon, purely from the difference in gravity.
Where gravitational potential energy actually matters
🏗️ Civil and structural engineering
Engineers calculate the potential energy of elevated structures, dams, and retaining walls to assess stability, foundation loads, and the energy that would be released in a structural failure.
⚡ Hydroelectric power generation
The potential energy of water stored at height in a reservoir is exactly what hydroelectric plants convert into electrical energy as the water falls through turbines.
🎢 Roller coaster design
The potential energy at the top of a roller coaster's first drop directly determines the maximum speed reachable at the bottom, letting engineers design both a thrilling and a safe ride.
🎓 Teaching energy conservation
The PE-to-KE conversion during a fall is one of the clearest, most intuitive demonstrations of the conservation of mechanical energy in introductory physics.
Common misconceptions
"Potential energy is always positive."
PE can be negative depending on where the reference height is set — an object below the chosen reference point has negative PE. Only differences in PE between two states are physically meaningful.
"Gravity (g) is the same everywhere in the universe."
g depends entirely on the mass and radius of the nearby body — it's about 9.81 m/s² on Earth, but only 1.62 m/s² on the Moon and roughly 24.79 m/s² on Jupiter.
"An object always has more potential energy than kinetic energy."
PE and KE trade off during motion — as an object falls, PE converts into KE, and at the instant just before impact, nearly all the original PE has become KE.
"Height must be measured from sea level."
The reference point for height is arbitrary and can be chosen for convenience (floor, table, ground) — as long as it stays consistent throughout a single problem, the physics works out the same.
Formula sources & further reading
The formulas here are standard, traceable to:
- • OpenStax, University Physics Volume 1 — Chapter 8, "Potential Energy and Conservation of Energy" (free, peer-reviewed). openstax.org
- • Halliday, Resnick & Walker, Fundamentals of Physics — Chapter 8, Potential Energy and Conservation of Energy.
- • Serway & Jewett, Physics for Scientists and Engineers — Chapter 8, Conservation of Energy.
PE = mgh, m in kg, g in m/s², h in metres, PE in joules. Standard Earth gravity g=9.81 m/s² used by default. Results are rounded for display.
How to use this calculator
Enter any three values
Provide PE, mass, height, or gravity — leave the unknown field blank.
Read the result
The missing value solves instantly using PE = mgh.
Try other planets
Swap in different gravity values to compare potential energy across the solar system.
Related tools
Frequently asked questions
What is gravitational potential energy?
Gravitational potential energy (PE) is the energy stored in an object due to its height above a reference point. The formula is PE = m × g × h, where g is the acceleration due to gravity.
What is "g" in the formula?
g is the acceleration due to gravity. On Earth, g ≈ 9.81 m/s². On the Moon, g ≈ 1.62 m/s². The value varies slightly with latitude and altitude on Earth, and dramatically across other planets and moons.
Where is the reference point for height measured from?
The reference point is arbitrary — typically ground level, sea level, or the floor. Only the difference in potential energy between two points matters physically, not the absolute value chosen.
Can potential energy be negative?
Yes, depending on the reference point chosen. If an object sits below the reference level, h is negative and PE becomes negative — only changes in PE carry physical significance.
What happens to PE when an object falls?
As an object falls, its potential energy converts into kinetic energy. Ignoring air resistance, total mechanical energy (PE + KE) stays constant: mgh₁ + ½mv₁² = mgh₂ + ½mv₂².