Escape Velocity Calculator

Escape velocity is the minimum initial speed an object needs to move away from a gravitating body without further propulsion and without eventually falling back. This calculator uses the classical spherical-body equation v = sqrt(2GM divided by r), where G is the universal gravitational constant, M is the mass of the celestial body, and r is the distance from its center. When launch begins at the surface, r is the body's mean radius. The result assumes the object starts with kinetic energy and coasts outward while gravity converts that kinetic energy into gravitational potential energy. The equation follows from conservation of mechanical energy. At the threshold escape speed, the traveling object's speed approaches zero only at an infinite distance, so its total specific energy is zero. The mass of the escaping spacecraft cancels from the derivation. A small probe and a large spacecraft therefore have the same ideal escape velocity from the same location, although the larger craft requires proportionally more energy and fuel in practice. Real launches are more complicated than this ideal model. Atmospheric drag, engine efficiency, changing thrust, planetary rotation, and gravity losses all affect the required launch profile. Rockets do not normally receive escape speed instantaneously; they build velocity over time and may first enter a parking orbit. The displayed value is best understood as an energy threshold rather than a complete mission-planning number. It also ignores the gravity of nearby bodies and assumes a non-rotating, spherically symmetric source. Mass must be entered in kilograms and radius in meters. If the starting point is above the surface, use the body's radius plus that altitude. Increasing mass raises escape velocity because the gravitational field is stronger. Increasing the starting radius lowers it because the object begins higher in the gravitational potential. Escape velocity is sqrt(2) times circular orbital velocity at the same radius under the same two-body assumptions. The calculator is useful for comparing planets and moons, checking astronomy coursework, and estimating the scale of spaceflight requirements. Earth's surface value is about 11.2 km/s, the Moon's is about 2.38 km/s, and Mars lies between them at roughly 5.03 km/s. Compact stars produce far greater values, but classical Newtonian calculations become inaccurate near extremely compact objects where relativistic gravity is important.