Escape Velocity Calculator
Escape and orbital speed for any body, plus its black-hole radius.
Work out Escape Velocity. Escape and orbital speed for any body, plus its black-hole radius. Shows the working, not just the answer.
Earth 5.972e24, Moon 7.348e22, Mars 6.417e23, Sun 1.989e30, Jupiter 1.898e27.
Earth 6.371e6, Moon 1.737e6, Mars 3.390e6, Sun 6.957e8.
Escape velocity
11.186 km/s
Orbital velocity 7.91 km/s · surface gravity 9.82 m/s²
Escape velocity is exactly √2 times orbital velocity at the same radius — always, for every body, with no dependence on mass or size. Getting into orbit is most of the work; leaving entirely costs only 41% more speed. The mass of what is escaping never appears. A pebble and a rocket need the same 11.2 km/s from Earth's surface, which is the same reason everything falls at the same rate. Escape velocity assumes a single unpowered impulse and no atmosphere, so it is not a rocket's required speed — a rocket accelerates continuously and never needs to reach it all at once. The Schwarzschild radius is this calculation carried to its limit: compress the mass inside that radius and escape velocity would exceed the speed of light. For Earth it is under a centimetre.
How the Escape Velocity Calculator works
Enter a body's mass and radius for its escape velocity, its low orbital velocity, surface gravity and the Schwarzschild radius it would need to become a black hole. Escape velocity is always exactly √2 times orbital velocity at the same radius.
Also known as: orbital velocity calculator · schwarzschild radius calculator · surface gravity calculator · escape velocity formula
Frequently asked questions
How do I calculate escape velocity?
v = √(2GM/r). For Earth that gives 11.2 km/s, and for the Moon only 2.4 km/s — which is why the Moon has no atmosphere left.
Does escape velocity depend on what is escaping?
No. A pebble and a rocket need the same 11.2 km/s from Earth's surface, for the same reason everything falls at the same rate — the escaping object's mass cancels out.
Do rockets actually reach escape velocity?
Not as a single burst. Escape velocity assumes one unpowered impulse and no atmosphere. A rocket accelerates continuously, so it never needs the full figure all at once.
What is the Schwarzschild radius?
The radius at which escape velocity would equal the speed of light. Compress a mass inside it and nothing escapes. For Earth that is under a centimetre; for the Sun, about 3 km.
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