Escape Velocity Calculator
Compute escape velocity (v = √(2GM/r)) for any body. Presets for Earth, Moon, Mars, Jupiter, Sun — or custom.
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.
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The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.