Escape Velocity Calculator
Escape Velocity11.186 km/s
In Metres per Second11,185.7 m/s
The Escape Velocity Calculator finds the minimum speed an object must reach to break free of a celestial body gravity without further propulsion. Provide the body mass in kilograms and its radius in metres, and the tool evaluates the square root of twice the gravitational constant times the mass divided by the radius. Results are shown in both metres per second and kilometres per second for planets, moons, and stars.
Formula
v = √(2GM / r)
- v
- Escape velocity (m/s)
- G
- Gravitational constant, 6.674e-11 N·m²/kg²
- M
- Mass of the body (kg)
- r
- Distance from the body centre (m)
How it works
- Enter the body mass in kilograms (scientific notation like 5.972e24 is accepted) and the radius in metres from which the object launches.
- The calculator uses the universal gravitational constant G = 6.674e-11 and evaluates v = √(2GM/r), where larger mass raises the escape speed and larger radius lowers it.
- The result is independent of the escaping object mass, so a pebble and a spaceship require the same escape speed from the same body.
Worked example
Escape velocity from the surface of Earth.
- Use M = 5.972e24 kg and r = 6.371e6 m.
- v = √(2 × 6.674e-11 × 5.972e24 ÷ 6.371e6).
- v ≈ 11,186 m/s ≈ 11.18 km/s.
About 11.18 km/s, the classic Earth escape speed.
Frequently asked questions
- Does escape velocity depend on the mass of the rocket?
- No. Escape velocity depends only on the mass and radius of the body being escaped. A small probe and a heavy spacecraft need the same speed to escape the same planet from the same altitude.
- Is escape velocity the same as orbital velocity?
- No. Escape velocity is √2 times the circular orbital velocity at the same radius. An object at orbital speed circles the body, while one at escape speed leaves it permanently.
- Why does escape velocity decrease with altitude?
- Because r appears in the denominator, a larger distance from the body centre reduces the gravitational pull and lowers the speed needed to escape from that point.
- Can light escape any body?
- If a body is so dense that its escape velocity reaches the speed of light, not even light escapes and it becomes a black hole. For ordinary planets and stars the escape velocity is far below light speed.