Calculate escape velocity from a body’s mass and radius, with surface gravity, using the standard v = √(2GM/r) formula.
Earth is 5.972 × 10²⁴ kg with a 6,371 km radius; the Moon is 0.07348 × 10²⁴ kg with a 1,737 km radius. Air resistance is ignored.
Escape velocity
How to use this tool
Type the mass in units of 10²⁴ kg — Earth is 5.972, the Moon is 0.07348.
Type the mean radius in kilometres, measured from the centre to the surface.
The result is the minimum speed a projectile needs to escape to infinity, ignoring air resistance.
Try the Moon, Mars (0.6417 × 10²⁴ kg, 3,390 km) or Jupiter (1898 × 10²⁴ kg, 69,911 km) to see how mass and size trade off.
Formula & worked example
For Earth, v = √(2 × 6.67430 × 10⁻¹¹ × 5.972 × 10²⁴ / 6,371,000) ≈ 11,190 m/s, about 11.2 km/s.
Limitations — read this before you rely on it
This is the idealised vacuum result for a spherical, non-rotating body. Real rockets escape gradually with thrust, and atmospheric drag, rotation and the body’s non-sphericity all change practical launch speeds.
Frequently asked questions
The minimum speed an object needs, with no further propulsion, to escape a body’s gravity and never fall back.
Yes, about 11.2 km/s (roughly 40,000 km/h) from the surface, ignoring air resistance.
No — for a projectile it depends only on the planet’s mass and radius, not on the projectile’s own mass.
They accelerate gradually while thrusting, so they do not need the full speed instantly; the 11.2 km/s figure is for a single impulsive kick.
About 2.38 km/s — much lower, because the Moon is far less massive despite being smaller.