Escape Velocity Calculator

Escape velocity is the minimum speed an object needs, with no further propulsion and ignoring air resistance, to break completely free of a body's gravity from a given distance: v = √(2GM/r), where G is the gravitational constant, M the body's mass, and r the distance from its center. It comes from setting the object's kinetic energy equal to the gravitational potential energy it has to overcome.

The same inputs also give the speed needed for a stable circular orbit at that exact radius, v = √(GM/r) = v_escape / √2 — found by setting gravity equal to the centripetal force circular motion requires. This is why a spacecraft only needs to gain about 41% more speed (a factor of √2) to leave a circular orbit entirely rather than just maintain it.

The gravitational constant used is G = 6.6743×10⁻¹¹ m³ kg⁻¹ s⁻², the CODATA 2022 recommended value. Mass and radius are converted to kilograms and meters before the formula runs, and results are converted back to mph for imperial display — the same convert-to-canonical-then-back pattern this site's other unit-toggled physics calculators use.