Escape velocity calculator

What is escape velocity?

The launch speed needed to coast away from a planet or moon forever, ignoring air resistance: v = √(2GM ÷ r), where G is the gravitational constant, M the mass and r the distance from the center (OpenStax University Physics).

What is Earth’s escape velocity?

About 11.2 km/s — roughly 25,000 mph. NASA lists 11.186 km/s at the equator.

Does it depend on the object’s mass?

No — the object’s own mass cancels out. A pebble and a spacecraft need the same launch speed.

Which values does the calculator use?

Masses and equatorial radii from NASA’s planetary fact sheets, and G = 6.67430 × 10⁻¹¹ m³/(kg·s²) (CODATA). For Jupiter, Saturn, Uranus and Neptune the radius is at the 1-bar pressure level. NASA’s own escape velocity is shown next to the result.

Why do rockets not fly at escape velocity?

A rocket keeps firing its engines as it climbs, so it does not need to reach escape speed at the surface. Escape velocity is for an object that coasts after one push.

How does escape velocity compare with orbital speed?

At the same distance from the center, escape speed is √2 (about 1.414) times the circular orbital speed. At Earth's equatorial radius, circular orbit speed is 7.91 km/s and escape speed is 11.18 km/s. The extra speed is the cost of going from a bound orbit to a free path.

How much energy per kilogram is needed to escape?

Half the speed squared: ½ × (11.180 km/s)² = 62.5 MJ per kilogram at Earth's surface, ignoring air drag and the planet's rotation. That is the kinetic energy needed for a mass starting at the surface to reach infinity with zero speed.

Where the formula comes from

An object is free of a body's gravity when its kinetic energy equals the gravitational potential energy it must climb out of: ½mv² = GMm ÷ r. The mass m cancels, giving v = √(2GM ÷ r), with G = 6.6743 × 10⁻¹¹ m³/(kg·s²), M the body's mass and r the distance from its center of mass. The derivation treats the body as a single sphere of uniform gravity, ignores the atmosphere, and considers only that one body's gravity.

Worked example: from Earth, the Moon, Mars and Jupiter

With NASA's masses and equatorial radii, the formula gives 11.18 km/s for Earth, 2.38 km/s for the Moon, 5.02 km/s for Mars and 59.5 km/s for Jupiter at its 1-bar level. Starting from a 400 km altitude above Earth, where r is 6,778 km instead of 6,378 km, the escape speed falls to 10.85 km/s, so about 0.33 km/s less is needed. NASA's own figure of 11.186 km/s for Earth corresponds to the mean radius of 6,371 km; the equatorial radius used here is slightly larger, so its result is slightly lower. Converting: 11.18 km/s is 25,009 mph.

Common mistakes

Using the planet's radius from the surface (altitude) in place of the distance from the center is the usual error; add the altitude to the radius. Entering the diameter for the radius lowers the answer by a factor of √2. Units are the third: with G in SI units the mass must be in kilograms and the distance in meters, which is why the result is in m/s. Last, escape velocity is a theoretical threshold for a single push; real launches also lose energy to air drag and gravity losses, and the Sun's gravity also still acts on anything that escapes Earth.

Sources: OpenStax University Physics, Volume 1, section 13.3 (gravitational potential energy and escape velocity); NASA Planetary Fact Sheets (masses, radii and escape velocities); G from NIST CODATA. Related: orbital period calculator, gravitational force calculator, rocket equation calculator and free fall calculator.