Escape Velocity Calculator

Calculate the escape velocity needed to break free from a planet or star from its mass and radius. Pick a preset such as Earth, the Moon, Mars, Jupiter or the Sun, or enter your own values, and also get the orbital velocity and surface gravity.

Input

Enter a body mass and radius to compute the escape velocity needed to leave it. Pick a preset to fill in the values for a well-known body.

Body

Choose a preset, or select custom to enter your own values.

Mass M

Mass of the body. Scientific notation such as 5.972e24 is accepted.

Radius r

Distance from the center. For escape from the surface, use the body radius.

Result

Escape velocity

11.185726km/s

= 11,185.726492 m/s

Orbital velocity (circular)

7.909503 km/s

Surface gravity

9.819532 m/s²

Escape velocity v=√(2GM/r), orbital velocity v=√(GM/r), surface gravity g=GM/r². Computed with G=6.674e-11.

How it works

Escape velocity is v=√(2GM/r), where G is the gravitational constant, M is the body mass and r is the distance from the center (the radius at the surface).
The circular orbital velocity is v=√(GM/r), which is 1/√2 of the escape velocity, so the escape velocity is about 1.414 times the orbital velocity.
Surface gravity is g=GM/r^2.
Constants used: gravitational constant G=6.674e-11 m^3 kg^-1 s^-2. Presets are Earth mass 5.972e24 kg and radius 6.371e6 m, Moon 7.342e22 kg and 1.7374e6 m, Mars 6.417e23 kg and 3.3895e6 m, Jupiter 1.898e27 kg and 6.9911e7 m, Sun 1.989e30 kg and 6.9634e8 m.
These are idealized values that ignore atmospheric drag, the body rotation and the gravity of other bodies. A real rocket needs more speed and energy than this.

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