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Escape Velocity Calculator

Find the escape velocity.

Result

11,186 m/s
11.19 km/s

How it is calculated

The tool applies v = √(2·G·M / r), where M is the mass of the body in kilograms, r is the distance from its centre in metres, and G = 6.674×10-11 N·m²/kg² is fixed inside the engine. The result is in metres per second, rounded to a whole number, and the same speed is repeated in km/s with two decimals. Radius must be greater than zero; a mass of zero simply gives 0 m/s. The formula is the Newtonian one for a point-like or spherically symmetric body, ignoring air drag and rotation.

Worked example

For Earth, enter a mass of 5.972e24 kg and a radius of 6371000 m. First 2·G·M = 2 × 6.674e-11 × 5.972e24 ≈ 7.97e14. Dividing by the radius gives 7.97e14 / 6.371e6 ≈ 1.251e8 m²/s². The square root of that is the escape velocity: 11,186 m/s, which the tool also shows as 11.19 km/s.

Try this example →

Common mistakes

  • Typing the radius in kilometres. The field expects metres, so 6371 instead of 6371000 gives a speed about 32 times too high.
  • Entering Earth's mass in tonnes or grams. The mass must be in kilograms; use scientific notation such as 5.972e24.
  • Using the altitude above the surface instead of the distance from the centre. For a spacecraft at height h the radius is the body's radius plus h.
  • Confusing escape velocity with orbital velocity. Staying in a low circular orbit needs only about 1/√2 (roughly 71%) of the escape speed.

About this calculator

This calculator finds escape velocity — the minimum speed an object needs to break free of a planet or moon's gravity without further propulsion — using v = √(2GM/r), where G is the gravitational constant, M is the body's mass, and r is the distance from its center. Earth's escape velocity works out to about 11.2 km/s.

It's a staple of astronomy and physics courses, used by students checking textbook problems and by space enthusiasts comparing how much harder it is to leave a massive planet like Jupiter versus a small moon. Rocket engineers use the same formula, in more detailed form, to plan how much thrust a launch needs.

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