How to use it
- Choose a planet or the Moon in Body, for example Earth.
- For any other body, choose Custom mass and radius, then type its Mass of the body in kilograms and its Radius of the body.
- Read Escape velocity in km/s and in metres per second.
- Look at Escape velocity of each body to compare the bodies, and open How it is worked out for the formula with the numbers.
The formula
A body of mass M and radius R holds an object with gravity. The speed an object needs at the surface to escape, with no further push, is v = √(2GM ÷ R). OpenStax gives this as equation 13.6 of its section on gravitational potential energy, with R measured from the centre of the body to the launch point.
The formula has no term for the mass of the object that leaves, so the escape speed is the same for any object from the same body. A launch from higher up uses a larger R, which lowers the speed needed.
v = √(2GM ÷ R)
G = 6.674 30 × 10⁻¹¹ m³ kg⁻¹ s⁻² (CODATA 2022)
M = mass of the body, kg
R = distance from the centre of the body to the launch point, m- The Earth's escape velocity is about 11 km/s, which is the figure OpenStax quotes for the Earth.
- The mass and radius of each planet and the Moon are from NASA's fact sheets, so the table follows NASA's values.
What the calculator does not cover
- Air drag, which slows a launch through the atmosphere and so needs more speed than the formula gives.
- A powered launch. A rocket keeps thrusting after the surface, so it does not need the escape velocity at the moment it leaves the ground.
- The orbits of the bodies and the pull of other bodies, such as the Sun, which change the speed needed to leave the solar system.
Worked example: escape velocity of the Earth
The Earth has a mass of 5.97 × 10²⁴ kg and an equatorial radius of 6378.137 km. With G = 6.674 × 10⁻¹¹, the value of 2GM ÷ R is 1.249 × 10⁸ m²/s². Its square root is 11,178 m/s, which is 11.18 km/s.
| Quantity | Value |
|---|---|
| Mass of the Earth | 5.97 × 10²⁴ kg |
| Equatorial radius | 6378.137 km |
| Escape velocity | 11.18 km/s |
Frequently asked questions
What is escape velocity?
It is the speed an object needs at the surface of a body to keep going without any further push, so that the body's gravity cannot pull it back. The formula gives that speed for a launch from the surface with no air.
Does the mass of the rocket change the escape velocity?
No. The formula depends on the mass and radius of the body being left, not on the mass of the object leaving it. A heavier rocket needs the same speed, but it needs more energy to reach it.
Why is the Earth's escape velocity about 11 km/s?
With the Earth's mass of 5.97 × 10²⁴ kg and its equatorial radius of 6378.137 km, the formula gives 11.18 km/s. OpenStax gives the same figure as about 11 km/s.
Why does Jupiter have such a high escape velocity?
Jupiter has a mass of about 1898 × 10²⁴ kg, much more than the Earth. Its escape velocity is about 59.5 km/s when the radius is taken at the 1 bar level that NASA gives.
Can I type the radius in kilometres?
Yes. Type 6378 km or 6378000 m, and the box reads either. Leave the unit out only if you mean metres.
Which radius should I use for a launch from a height?
Use the distance from the centre of the body to the launch point, because that is R in the formula. That is the surface radius plus the height of the launch.
Sources
- OpenStax University Physics Volume 1, section 13.3: Gravitational Potential Energy and Total Energy (equation 13.6, escape velocity)
- NASA planetary fact sheets: masses of the planets and the Moon
- NASA Earth fact sheet: equatorial radius 6378.137 km
- NIST CODATA 2022: Newtonian constant of gravitation G
Figures and text last checked on Thursday, November 12, 2026.