Escape Velocity Calculator

About this calculator

Escape velocity is the minimum speed an object needs, fired straight up with no further propulsion, to break free of a body’s gravity permanently and never fall back — the speed at which kinetic energy exactly equals the gravitational potential energy holding it down. It’s derived by setting ½mv² = GMm/r and solving for v, giving v = √(2GM/r), where G is the gravitational constant (6.674×10⁻¹¹ N·m²/kg²), M is the body’s mass, and r is the distance from its center (typically its surface radius).

This formula explains why Earth’s escape velocity is about 11.2 km/s while the Moon’s is only about 2.4 km/s (less mass, smaller radius), and why rockets need multi-stage boosters to reach it. Mission planners in astrodynamics use it to size launch vehicles, astronomers use it to determine whether a planet or moon can retain an atmosphere (comparing escape velocity to the thermal speed of gas molecules), and it’s a staple comparison in astronomy education across the solar system’s planets and moons.