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Escape Velocity Calculator

Enter a body's mass and radius to find its escape velocity.

How it is calculated

The tool uses v = √(2·G·M / r). M is the body's mass in kilograms, r is the distance from its centre in metres (normally the surface radius), and G = 6.674 × 10⁻¹¹ N·m²/kg² is fixed inside the tool. Because masses of planets are huge, you can type scientific notation such as 5.972e24. The speed is shown in m/s (one decimal), km/s (two decimals) and km/h (one decimal). Mass and radius must both be above zero. The number is the speed needed at the surface to coast away without further thrust; it ignores air drag, the body's rotation and the pull of other bodies such as the Sun, so it is an idealised figure.

Worked example

Earth: mass 5.972e24 kg and radius 6,371,000 m. Multiply 2 × 6.674e-11 × 5.972e24 ≈ 7.97e14. Divide by the radius: 7.97e14 ÷ 6,371,000 ≈ 1.251e8. The square root gives 11,185.7 m/s. That equals 11.19 km/s, or 40,268.6 km/h.

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Common mistakes

  • Entering the radius in kilometres. The field expects metres, so 6371 instead of 6,371,000 gives an answer about 30 times too large.
  • Entering mass in tonnes or Earth masses instead of kilograms. Earth is about 5.972e24 kg, not 1.
  • Using altitude above the surface as the radius. The formula needs the distance from the centre of the body; for a launch from a height, add the body's radius to the altitude.
  • Confusing escape velocity with orbital velocity. Staying in a low orbit needs only about 1/√2 (roughly 71%) of the escape speed.
  • Typing the diameter instead of the radius, which makes the result too small by a factor of about 1.4.

About this calculator

Escape velocity is the minimum speed an object needs, fired straight up with no further propulsion, to break free of a body’s gravity permanently and never fall back — the speed at which kinetic energy exactly equals the gravitational potential energy holding it down. It’s derived by setting ½mv² = GMm/r and solving for v, giving v = √(2GM/r), where G is the gravitational constant (6.674×10⁻¹¹ N·m²/kg²), M is the body’s mass, and r is the distance from its center (typically its surface radius).

This formula explains why Earth’s escape velocity is about 11.2 km/s while the Moon’s is only about 2.4 km/s (less mass, smaller radius), and why rockets need multi-stage boosters to reach it. Mission planners in astrodynamics use it to size launch vehicles, astronomers use it to determine whether a planet or moon can retain an atmosphere (comparing escape velocity to the thermal speed of gas molecules), and it’s a staple comparison in astronomy education across the solar system’s planets and moons.

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