Free Escape Velocity Calculator
Calculate the minimum speed needed to escape a celestial body's gravitational pull using v_esc = sqrt(2 G M / r).
kg
m
Escape Velocity
11,185.73 m/s
Escape Velocity (km/s)11.1857 km/s
Escape Velocity vs Body Mass
Deriving Escape Velocity
Escape velocity is the minimum launch speed at the surface for an object to reach infinity without further propulsion.
Formula
v_esc = √(2 G M / r)
This is exactly √2 times the circular orbital velocity at the same radius. It comes from setting kinetic energy equal to gravitational potential energy: 1/2 m v² = G M m / r.
Example Calculation
Find Earth's escape velocity (M = 5.972e24 kg, r = 6 371 km).
- 01v_esc = √(2 G M / r)
- 022 G M = 2 × 6.674e-11 × 5.972e24 = 7.972e14
- 037.972e14 / 6.371e6 = 1.251e8
- 04v_esc = √(1.251e8) ≈ 11 186 m/s ≈ 11.19 km/s