This calculator finds the escape velocity — the minimum speed an object needs to break free of a body's gravity without further propulsion. Enter the body's mass and radius.
What the symbols mean
- v — escape velocity (metres per second).
- G — gravitational constant (auto-filled).
- M — mass of the planet or star (kilograms).
- r — radius from the centre (metres).
Worked example
For Earth (M = 5.97×10²⁴ kg, r = 6.37×10⁶ m) the escape velocity is about 11,200 m/s — roughly 40,300 km/h.
How the formula works
Escape velocity is the minimum speed an object needs to break free of a body's gravity without any further propulsion. It comes from equating the kinetic energy of the launched object with the gravitational potential energy that gravity must be overcome. Notice the launched object's own mass cancels out — escape velocity depends only on the mass and radius of the body you are leaving.
Common mistakes to avoid
- Confusing it with orbital velocity. Escape velocity is higher — it is the speed to leave entirely, not to orbit.
- Using diameter instead of radius. The r in the formula is the radius from the centre.
Where it is used
Escape velocity matters for launching spacecraft, understanding why small bodies like the Moon cannot hold an atmosphere, and even defining black holes — objects whose escape velocity exceeds the speed of light.