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    Orbital mechanics

    Escape Velocity Calculator

    Minimum speed to escape a body's gravity from its surface or any altitude, without further thrust.

    vₑ = √(2μ / r)

    Inputs

    Results

    Escape velocity
    11.1861 km/s
    Circular orbit speed at same radius
    7.90979 km/s
    Worked solution
    1. r = 6,371,000 m
    2. vₑ = √(2 × 3.986 × 10^14 / 6,371,000) = 11,186 m/s
    3. vₑ = √2 × v_circular

    How the result changes

    Escape speed (km/s) plotted against Altitude (km), from one quarter to four times your input, with your input marked.789101102,0004,0006,0008,00010,000Altitude (km)Escape speed (km/s)your input
    Escape speed vs altitude

    How it works

    Escape velocity is the speed at which kinetic energy ½mv² exactly equals the gravitational binding energy GMm/r. A projectile launched faster than this follows a hyperbolic path and never returns.

    Earth's surface escape speed is about 11.2 km/s. Rockets do not need to reach it instantly: thrust over time can raise a spacecraft gradually, but the total energy requirement is the same.

    Variables

    • vₑ — escape speed
    • μ — gravitational parameter GM
    • r — distance from the body's centre

    Assumptions and limits

    • Spherical, non-rotating body with no atmosphere
    • Ballistic trajectory: all kinetic energy is supplied at the start
    • Ignores the Sun's gravity and other bodies

    For education only. These models are simplified and are not suitable for spacecraft navigation or safety-critical engineering. See our scientific accuracy policy.