About the Escape Velocity Calculator
This escape velocity calculator finds the minimum speed an unpowered object needs to break free of a body’s gravity and never fall back, using v = √(2GM/r). Choose a planet, moon or the Sun, or enter your own mass and radius, and optionally an altitude above the surface.
Alongside escape velocity it shows the circular orbital speed at the same distance and the local gravitational acceleration, which makes it useful for astronomy and physics students, science fiction writers checking their worlds, and space enthusiasts comparing launch difficulty across the solar system.
Escape velocity ignores air resistance and the body’s rotation, and assumes a spherically symmetric mass. It does not depend on the escaping object’s mass or direction (as long as it does not hit the surface), and it falls with distance from the centre.
With the default inputs, the escape velocity is 11.186 km/s. Change any value above to recalculate instantly.
How to use the escape velocity calculator
- 1Pick a planet, the Moon or the Sun — or choose Custom.
- 2For a custom body, enter its mass (Earth masses, solar masses or kg) and radius in km.
- 3Optionally enter an altitude above the surface.
- 4Read the escape velocity in km/s, m/s, km/h and mph.
- 5Compare with the circular orbit speed and the bar chart of other worlds.
Formula and method
Escape velocity is the speed at which an object’s kinetic energy exactly equals the gravitational energy binding it: ½mv² = GMm/r. The object’s own mass cancels out, leaving v = √(2GM/r), where r is the distance from the body’s centre (radius plus altitude).
The calculator uses G = 6.6743 × 10⁻¹¹ m³·kg⁻¹·s⁻² (CODATA 2018) and NASA fact-sheet masses and mean radii. The circular orbital speed at the same distance is escape velocity divided by √2, and the local gravity is GM/r².
- v_esc
- Escape velocity (m/s)
- G
- Gravitational constant, 6.6743 × 10⁻¹¹ m³·kg⁻¹·s⁻²
- M
- Mass of the planet, moon or star (kg)
- r
- Distance from the centre = radius + altitude (m)
Worked examples
Escape velocity of Earth
v = √(2 × 6.6743e-11 × 5.9722e24 ÷ 6,371,000) ≈ 11,186 m/s, the familiar 11.2 km/s. A low circular orbit needs about 7.9 km/s.
Escape velocity of the Moon
With 1.2% of Earth’s mass and a 1,737 km radius, the Moon’s escape velocity is only about 2.38 km/s — one reason Apollo’s lunar module could lift off with a small engine.
From the International Space Station’s altitude (400 km)
At r = 6,771 km, v = √(2GM/r) ≈ 10.85 km/s. The ISS already moves at about 7.67 km/s, so it would need roughly 3.2 km/s more to leave Earth.
Escape velocity of the Sun
The Sun’s mass of 1.988 × 10³⁰ kg and radius of 695,700 km give about 617.7 km/s at its surface.
Frequently asked questions
What is the escape velocity of Earth?+
About 11.2 km/s (40,270 km/h or 25,020 mph) from the surface, ignoring air resistance. It drops with altitude — about 10.85 km/s at the height of the International Space Station.
Does escape velocity depend on the mass of the object?+
No. Both kinetic energy and gravitational potential energy scale with the object’s mass, so it cancels. A pebble and a spacecraft need the same speed; the spacecraft just needs far more energy.
Do rockets actually reach escape velocity?+
Not necessarily at launch. Escape velocity applies to an unpowered object. A rocket that keeps firing its engines can leave slowly; in practice missions reach orbit first and then burn to escape speed.
What is the difference between orbital velocity and escape velocity?+
Circular orbital velocity √(GM/r) keeps an object circling at a fixed distance. Escape velocity √(2GM/r) is √2 ≈ 1.414 times larger and lets it leave for good.
Which planet has the highest escape velocity?+
Jupiter, at about 60 km/s, because of its huge mass. Among solid planets Earth has the highest; Mercury and Mars are around 4.3 and 5.0 km/s.