What is escape velocity?

Escape velocity is the minimum speed an object must have at the surface of a body (planet, moon, or other massive object) to escape its gravitational pull without any additional thrust. It is derived by equating kinetic energy to gravitational potential energy: 0.5 times m times v squared equals G times M times m divided by r. Solving for v gives ve = square root of (2GM/r), where G is the gravitational constant (6.674e-11 N m2 per kg2), M is the mass of the body, and r is its radius.

What is the escape velocity of Earth?

The escape velocity at Earth's surface is approximately 11.18 km/s (about 40,250 km/h or 25,000 mph). This is the minimum speed needed to launch an object from Earth's surface on a trajectory that will take it infinitely far away (ignoring atmospheric drag and Earth's rotation). Rockets do not actually need to reach this speed all at once; continuous thrust allows escape at lower instantaneous speeds.

Why does the Moon have a lower escape velocity than Earth?

The Moon has both a smaller mass and a smaller radius than Earth. The escape velocity formula ve = sqrt(2GM/r) means that a lower mass reduces escape velocity directly, while a smaller radius (which means you are closer to the centre of gravity at the surface) increases it. For the Moon, the mass effect dominates: the Moon's mass is about 1/81 of Earth's, and its radius is about 1/3.67 of Earth's, giving an escape velocity of about 2.38 km/s, roughly 21% of Earth's.

Escape Velocity Calculator

Escape velocity is the minimum speed an object at the surface of a planet or moon must achieve to break free from its gravitational field, without any additional thrust after launch. Below this speed, gravity will eventually pull the object back. At or above it, the object will travel on an open trajectory and never return, assuming no further forces act on it. The formula is derived by equating the kinetic energy of the object at the surface with the gravitational potential energy it needs to overcome: the result is escape velocity equals the square root of two times the gravitational constant G times the planet's mass M divided by the radius r of the planet. The value of G is 6.674 times 10 to the power of negative 11 N m squared per kg squared. For Earth, with a mass of about 5.97 times 10 to the 24 kg and a radius of about 6.37 times 10 to the 6 m, the escape velocity works out to about 11.18 km/s. The Moon, which is far less massive, needs only about 2.38 km/s. Jupiter, being far more massive, requires about 59.5 km/s. This calculator accepts planet mass and radius as inputs and returns the escape velocity. Presets for the major solar system bodies make it easy to compare. The tool also shows the escape velocity in different units and the specific kinetic energy (energy per kilogram of spacecraft) required at launch.

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Planet preset

Planet mass M

Planet radius r

11.18 km/s

escape velocity

In m/s11,180 m/s

In km/h40,248 km/h

KE per kg62.5 MJ/kg

Surface gravity9.83 m/s²

Assumes a spherical body with uniform density and no atmosphere. Earth's actual escape velocity at the surface is approximately 11.186 km/s. Atmospheric drag increases the practical energy requirement for rockets significantly.

How it works

The escape velocity formula is v_e = √(2GM/r), where G = 6.674 × 10^-11 N m²/kg² is the gravitational constant, M is the planet's mass in kg, and r is its radius in metres. Specific kinetic energy at launch KE/m = 0.5 × v_e² in J/kg. Surface gravity g = GM/r² in m/s².

Worked example

For Earth: M = 5.97 × 10²⁴ kg, r = 6.37 × 10⁶ m. v_e = √(2 × 6.674e-11 × 5.97e24 / 6.37e6) = √(1.2503 × 10⁸) = 11.18 km/s. KE per kg = 0.5 × 11180² = 62.5 MJ/kg. Surface gravity = 6.674e-11 × 5.97e24 / (6.37e6)² = 9.83 m/s². These match the default values pre-filled in the calculator above.

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