Find the escape velocity of a planet, moon, star or black hole from its mass and radius using v = √(2GM/r) — the minimum speed needed to break free of gravity without further propulsion.
Escape velocity is the minimum speed an object needs to permanently escape a body's gravity, with no further thrust. It comes from setting kinetic energy equal to the gravitational potential energy binding the object: ½ m v² = GMm/r, which rearranges to v = √(2GM/r).
Notice the escaping object's own mass cancels out — a pebble and a spaceship need the same escape speed. Escape velocity depends only on the mass and radius of the body you are leaving. For a black hole, the radius at which this speed equals the speed of light is the Schwarzschild radius.
For the underlying physics, read our explanation of black hole event horizons.
About 11.2 km/s (11,186 m/s, or roughly 25,000 mph). This is the speed needed to leave Earth's gravity without further propulsion, ignoring air resistance.
Use v = √(2GM/r), where G is the gravitational constant (6.674×10⁻¹¹), M is the body's mass in kilograms and r is its radius in metres. Enter M and r above to get v.
No. The escaping object's mass cancels out of the equation, so a small probe and a large spacecraft have the same escape velocity from a given body.
At the event horizon (the Schwarzschild radius), the escape velocity equals the speed of light, which is why not even light can escape from inside it.