Escape Energy Calculator
To leave a planet or star behind for good, an object needs enough kinetic energy to climb out of its gravity well to infinity. That minimum is the escape energy, equal to the depth of the gravitational potential energy where the object starts. This calculator takes the central body's mass, the object's mass, and the starting radius, and returns the escape energy in joules along with the corresponding escape velocity. The gravitational constant defaults to its CODATA value and stays editable.
Escape energy formula
escape energy E = (G * M * m) / r
escape velocity v = sqrt((2 * G * M) / r)
check: E = (1/2) * m * v^2
The escape energy equals the magnitude of the gravitational potential energy at radius r. The two outputs are consistent: the energy is exactly the kinetic energy at escape velocity.
Worked example
For a 1,000 kg craft at Earth's surface (M = 5.972e24 kg, r = 6,371,000 m): E = (6.674e-11 * 5.972e24 * 1,000) / 6,371,000 = 6.256e10 joules. The escape velocity is sqrt((2 * 6.674e-11 * 5.972e24) / 6,371,000) = 11,185.73 m/s, about 11.2 km/s.
Escape energy: frequently asked questions
What is escape energy?
Escape energy is the minimum kinetic energy an object needs at a given distance from a massive body to escape its gravity entirely, ending with zero speed infinitely far away. It equals the magnitude of the gravitational potential energy at that point: G times the central mass times the object's mass, divided by the radius.
How does escape energy relate to escape velocity?
Escape energy is the kinetic energy corresponding to escape velocity. Escape velocity is the square root of 2GM divided by r, and the escape energy is one half of the object's mass times that velocity squared, which simplifies to GMm divided by r. This calculator reports both so you can cross-check them.
Does escape energy depend on direction?
No. Escape energy depends only on the magnitudes: the central mass, the object's mass, and the radial distance. Direction does not appear because gravitational potential energy is a function of distance alone for a spherical body. In practice, launching in the direction of a planet's rotation reduces the energy you must supply, but the escape energy itself is direction independent.
Sources
- Gravitational constant G: NIST CODATA, Newtonian constant of gravitation. Escape energy equals the gravitational potential energy magnitude GMm/r.
Reviewed by the CalculatorHub team, edited by James Graham, 19 June 2026. See our methodology.