Escape Velocity Calculator

What is escape velocity?

Escape velocity is the minimum initial speed an object needs to break free of a planet's gravity and never fall back. Launched at this speed, the object keeps slowing down but never stops and returns.

The formula

It follows from conservation of energy. At the surface the kinetic energy must just match the gravitational potential energy: ½ × m × v² = G × M × m / R. The mass of the object cancels:

v = √(2 × G × M / R)

M is the mass of the planet, R the distance from its centre and G = 6.6743 × 10⁻¹¹ m³/(kg·s²). The result does not depend on the mass of the object or on the launch direction.

Example

For the Earth, with M = 5.9722 × 10²⁴ kg and R = 6371 km, v = √(2 × 6.6743 × 10⁻¹¹ × 5.9722 × 10²⁴ / 6.371 × 10⁶) = 11 186 m/s, which is 11.2 km/s or about 40 270 km/h. The escape velocity is 2.38 km/s on the Moon, 5.03 km/s on Mars and 617.7 km/s at the surface of the Sun.

How it relates to orbital speed

The speed needed to stay in a circular orbit at the same height is 1 / √2 times the escape velocity. At the level of the Earth's surface that is 7.9 km/s. Increase the speed of an orbiting object by 41 percent and it escapes.

Schwarzschild radius

Setting the escape velocity equal to the speed of light gives R = 2 × G × M / c². That is about 2.95 km for the Sun and about 9 mm for the Earth. A body squeezed inside this radius becomes a black hole.

Limits

Air resistance and the rotation of the planet are not included. Only the gravity of the selected body is considered. Masses and radii are NASA Planetary Fact Sheet values.