Gravitational Potential Energy Calculator
Calculate gravitational potential energy near Earth's surface (mgh) or in the general case (-GMm/r).
Includes body presets and escape velocity.
Gravitational potential energy comes in two forms:
Near Earth’s surface (simple approximation): U = mgh
General formula (exact, valid anywhere): U = −GMm/r
Where:
- U = Gravitational potential energy (joules)
- m = Mass of the smaller object (kg)
- g = Local gravitational acceleration (9.81 m/s² on Earth’s surface)
- h = Height above reference point (m)
- G = Gravitational constant = 6.674 × 10⁻¹¹ N·m²/kg²
- M = Mass of the central body
- r = Distance between centers (m)
Why is U = −GMm/r negative? The convention is that U = 0 at r → ∞ (infinitely far apart). Since gravity is attractive, you must add energy to separate masses — so bound systems have negative potential energy.
Escape velocity: The escape velocity from distance r is: v_esc = √(2GM/r) This is derived by setting kinetic energy equal to the magnitude of potential energy: ½mv² = GMm/r
Body mass reference:
| Body | Mass (kg) | Radius (km) | Surface g |
|---|---|---|---|
| Earth | 5.972 × 10²⁴ | 6,371 | 9.81 m/s² |
| Moon | 7.342 × 10²² | 1,737 | 1.62 m/s² |
| Mars | 6.417 × 10²³ | 3,390 | 3.72 m/s² |
| Sun | 1.989 × 10³⁰ | 695,700 | 274 m/s² |
How we build and check this calculator
This calculator runs entirely in your browser, so the numbers you enter stay on your device. The math behind it is written by hand and tested against worked examples and standard references before the page goes live.
SuperGlobalCalculator is independently built and maintained. See how we build and verify our calculators.