Escape Velocity Calculator

Escape velocity: v_e = √(2GM/r)

Escape velocity is the minimum speed an unpowered object needs to escape the gravitational pull of a body, with no further propulsion: v_e = √(2GM/r), where G = 6.674·10⁻¹¹ N·m²/kg² is the universal gravitational constant, M is the body's mass and r the distance from its center. Example for Earth (M = 5.972·10²⁴ kg, r = 6,371 km): v_e ≈ 11,180 m/s ≈ 11.2 km/s. For the Moon it's only 2.38 km/s, for Mars 5.03 km/s, and for the Sun (escaping the Solar System from Earth's orbit) 42.1 km/s. For a black hole, v_e equals the speed of light c — that's the definition of the event horizon. Rocket design uses the Tsiolkovsky equation Δv = v_exhaust · ln(m₀/m_f) to stack stages until total Δv exceeds escape velocity.

Applications

Rocket launches (Saturn V reached ~11 km/s to send Apollo 11 to the Moon), geostationary satellites (35,786 km altitude, orbital speed ~3 km/s — orbit, not escape), interplanetary probes (Voyager, New Horizons) that need Earth's escape velocity plus a gravitational assist, and astrophysics for stellar wind and black hole modelling.

FAQ

Does escape velocity depend on the object's mass? No — only on the central body's mass and the distance r. A pebble and a rocket need the same speed to escape from the same altitude.

Why don't rockets just hit v_e on the pad? v_e assumes a single instantaneous impulse with no atmosphere. Real rockets accelerate gradually and lose energy to drag, so total Δv ends up well above 11.2 km/s.

What's the link with black holes? When the radius is small enough that v_e equals c, not even light can escape — that radius is the Schwarzschild radius and defines the event horizon.