Escape velocity is the minimum launch speed an object needs to break free of a body's gravity and coast away forever, with no further push — given by v = √(2GM/r). It comes from setting the object's kinetic energy equal to the gravitational potential energy holding it down, and remarkably the object's own mass cancels out, so a pebble and a rocket need the same speed. It depends only on the planet's mass M and radius r, which is why Earth's value is a fixed 11.2 km/s while the lighter Moon needs just 2.4.
Reviewed: June 20, 2026 · Author: Naveen P N, Founder — AI Calculator · Verified against: the energy derivation of escape velocity v = √(2GM/r).
The escape velocity equations
Put the mass in kilograms and the radius in metres, multiply by twice the gravitational constant, and take the square root to get metres per second. If you know the surface gravity instead of the mass, the equivalent form v = √(2gr) is handier. Escape velocity is always √2 ≈ 1.414 times the circular orbital speed at the same radius, because escaping needs twice the kinetic energy of orbiting.
Worked example — escaping Earth
Scenario: Earth has mass 5.972×10²⁴ kg and radius 6.371×10⁶ m. What is its escape velocity?
Earth's escape velocity is about 11.2 km/s — roughly 40,300 km/h. Notice nothing about the escaping object appears in the formula, so this speed is the same for a satellite or a stray atom. Repeat the calculation for the Moon (M = 7.35×10²² kg, r = 1.74×10⁶ m) and you get ≈ 2.38 km/s; for Mars, ≈ 5.03 km/s — both far easier to leave than Earth, which is exactly why low-gravity worlds are attractive launch points.
Frequently Asked Questions
v = √(2GM/r), G = 6.674×10⁻¹¹. Earth: √(2×6.674e-11×5.972e24/6.371e6) ≈ 11,186 m/s.
About 11.2 km/s (≈ 40,300 km/h) at the surface, ignoring air resistance.
No — the object's mass cancels. A pebble and a spaceship need the same 11.2 km/s for Earth.
Moon ≈ 2.38 km/s, Mars ≈ 5.03 km/s — both far below Earth's, so easier to launch from.
Escape is √2 × orbital. Orbit = √(GM/r); escape = √(2GM/r), about 41% faster.