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
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 |