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Escape Velocity Calculator

Computes the escape velocity √(2GM/r) and the circular orbital velocity √(GM/r) at the surface (or a given altitude) of Earth, the Moon, Mars, Jupiter, the Sun or a custom body defined by mass and radius, plus its surface gravity GM/R².

When to use

You need the speed required to escape a planet or moon without further propulsion, the speed of a low circular orbit, or the surface gravity of a body from its mass and radius.

Do not use when: You need the period of an orbit of a given size (use orbital-period), the rocket delta-v including gravity and drag losses, or the weight of an object on a planet (use planet-weight).

Formula

v_escape = √(2 × GM / r); v_orbit = √(GM / r); g = GM / R²; r = R + altitude_m; GM(custom) = 6.67430 × 10⁻¹¹ × mass_kg

Energy conservation for a non-rotating, airless body (kinetic energy equals the gravitational binding energy). Constants: GM in m³/s² Earth 3.986004418 × 10¹⁴, Moon 4.9048695 × 10¹², Mars 4.282837 × 10¹³, Jupiter 1.26686534 × 10¹⁷, Sun 1.32712440018 × 10²⁰; mean radii 6,371 / 1,737.4 / 3,389.5 / 69,911 / 695,700 km. Real launches need extra speed for drag and gravity losses and gain from the body's rotation.

Inputs

ParameterTypeUnitRequiredDescription
bodyenum: earth | moon | mars | jupiter | sun | customyesBody to escape from; GM and mean radius are taken from the JPL/NASA constants.
mass_kgnumberkgnoMass of a custom body; only used when body is custom. Range: > 0, ≤ 1e+42
radius_mnumbermnoRadius of a custom body in metres; only used when body is custom. Range: > 0, ≤ 1000000000000000
altitude_mnumbermdefault 0Height above the surface at which the speeds are evaluated (0 = surface). Range: ≥ 0, ≤ 1000000000000000

Outputs

OutputTypeUnitDescription
escape_velocity_m_snumberm/s√(2GM / r) with r = radius + altitude.
escape_velocity_km_snumberkm/sEscape velocity / 1000.
escape_velocity_km_hnumberkm/hEscape velocity × 3.6.
circular_orbital_velocity_km_snumberkm/s√(GM / r): escape velocity / √2.
surface_gravity_m_s2numberm/s²GM / R² at the surface (altitude 0).
radius_used_kmnumberkmRadius + altitude.
gm_m3_s2numberm³/s²Standard gravitational parameter of the body.

Example

Earth, surface: {"body":"earth"} → {"escape_velocity_m_s":11186.1,"escape_velocity_km_s":11.186,"escape_velocity_km_h":40270,"circular_orbital_velocity_km_s":7.91,"surface_gravity_m_s2":9.82}

Moon, surface: {"body":"moon"} → {"escape_velocity_km_s":2.376,"circular_orbital_velocity_km_s":1.68,"surface_gravity_m_s2":1.625}

GET https://tttkmbb.com/api/v1/calculate/escape-velocity?body=earth

Machine access

Sources

FAQ

Why is 11.2 km/s different from the speed rockets reach?

Escape velocity is the speed needed at the surface with no further thrust and no atmosphere; rockets accelerate gradually, lose speed to drag and gravity, and usually enter orbit (7.9 km/s at low altitude) rather than escaping.

Why does the value change with altitude?

Both speeds fall with distance from the centre as 1/√r: at 400 km above Earth the escape velocity is about 10.85 km/s and the orbital speed 7.67 km/s.

How does surface gravity relate to escape velocity?

v_escape = √(2 g R): two bodies with the same g but different radii have different escape speeds, which is why the Moon's small radius gives only 2.38 km/s.

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