Throw a ball upward and it comes back down. Throw it faster and it climbs higher before falling. Escape velocity is the launch speed at which it would never fall back: its kinetic energy exactly pays for the climb out of the gravity well, with nothing left over at infinite distance. This calculator finds that speed for the Sun, the planets, the Moon and Pluto, at the surface or at any altitude. Switch to a custom body to enter your own mass and radius, or to work backward from a known escape speed to a mass or a radius.
How to use the escape velocity calculator
- Pick a Planet, moon or star from the list, or choose Custom mass and radius.
- For a listed body, enter an Altitude above the surface if the object starts high up; leave 0 for the surface.
- For a custom body, choose what to Solve for (escape velocity, mass or radius) and fill in the other two values. Mass can be entered in kg, t, Moon, Earth, Jupiter or solar masses; distance in km, m, mi, Earth radii, solar radii or au.
- Pick the result unit (km/s, m/s, km/h, mph or ft/s).
- Compare the result with the circular orbit speed, the local gravity, Earth’s value and the body’s Schwarzschild radius. The table lists escape velocities for every preset body.
Escape velocity formula
Setting kinetic energy equal to the energy needed to climb from distance r to infinity, ½mv2 = GMm ÷ r, gives
G = 6.67430 × 10⁻¹¹ N·m²/kg², M is the mass of the planet or star and r is the distance from its center. Notice that the escaping object’s own mass is absent.
Worked example
Leaving Earth
Earth's mass is 5.9722 × 10²⁴ kg and its equatorial radius is 6,378.137 km.
ve = √(2 × 6.6743 × 10⁻¹¹ × 5.9722 × 10²⁴ ÷ 6,378,137) = 11,180 m/s ≈ 11.18 km/s
That is about 40,250 km/h or 25,010 mph. Starting 420 km up, at the altitude of the space station, r = 6,798 km and the escape velocity drops to 10.83 km/s.
Mars and the Moon. Pick Mars and the calculator gives 5.02 km/s; the Moon gives 2.38 km/s. Leaving the Moon needs less than a quarter of Earth’s escape speed, one reason why proposals for lunar launch sites keep coming up.
Escape velocities in the Solar System
| Body | Escape velocity |
|---|---|
| Moon | 2.38 km/s |
| Mars | 5.02 km/s |
| Venus | 10.36 km/s |
| Earth | 11.18 km/s |
| Saturn | 35.5 km/s |
| Jupiter | 59.5 km/s |
| Sun | 617.7 km/s |
Values use NASA fact-sheet masses and equatorial radii (the 1-bar level for the gas giants), so they match the calculator’s table.
Why real launches look different
A real rocket does not fire straight up at 11.2 km/s. It climbs through the thickest air slowly, turns sideways, reaches orbital speed of roughly 7.8 km/s and only then, if the mission is bound for the Moon or another planet, burns again to reach escape speed. Air drag would destroy anything moving at escape velocity near sea level. Launching eastward near the equator also borrows up to about 0.46 km/s from Earth’s rotation, which the formula above does not include.
Escape velocity and atmospheres
Gas molecules move at speeds set by temperature. Light gases such as hydrogen and helium move fast enough that a few always exceed escape velocity and slowly leak away. Heavy, cold planets like Jupiter keep even hydrogen, while the Moon and Mercury, with low escape velocities, hold almost no atmosphere at all.
For the energy behind the formula, see the kinetic energy calculator; for the pull at a given distance, use the gravitational force calculator; and to time an orbit instead of leaving it, try the orbital period calculator.
Frequently asked questions
What is Earth's escape velocity?
About 11.2 km/s, which is roughly 40,250 km/h or 25,000 mph. Using Earth's equatorial radius of 6,378 km the calculator gives 11.18 km/s; at the 420 km altitude of the International Space Station it falls to 10.83 km/s.
Does escape velocity depend on the mass of the rocket?
No. The object's mass cancels out because both its kinetic energy and its gravitational potential energy are proportional to it. A pebble and a space probe need the same speed to escape from the same place.
Do rockets actually reach escape velocity?
Not necessarily. Escape velocity is the speed an unpowered object needs at one instant to coast away forever. A rocket that keeps firing its engines can climb away at any speed, although interplanetary missions usually do reach escape speed after their burns.
How is escape velocity related to orbital speed?
A circular orbit at the same distance needs the escape velocity divided by √2. Near Earth's surface that is about 7.9 km/s, the speed low satellites travel at. Going 41% faster than circular orbital speed lets an object escape.
What happens when escape velocity reaches the speed of light?
The object would be a black hole. The radius where that happens is the Schwarzschild radius, 2GM/c², which the calculator lists for each body. For Earth it is about 8.9 mm. Newtonian physics no longer applies there, so the calculator rejects such inputs.