How fast do you need to go to leave a planet behind?
Escape velocity is the speed at which an object can coast away from a planet, moon or star and never fall back, ignoring air resistance and any other bodies. This escape velocity calculator uses v = √(2GM ÷ r). Pick the Sun, a planet or the Moon, or type any mass and radius, and it returns the escape speed in m/s, km/s, km/h and mph together with the circular orbital velocity at the same distance and the surface gravity.
The working is written out line by line, so the answer can be copied into homework or a lab report. Everything runs in your browser; nothing is sent anywhere.
How to use the Escape Velocity Calculator
- Choose a body from the list, or choose Custom and type a mass in kilograms and a radius in kilometres.
- Leave the height at 0 for the surface, or enter a height in kilometres to get the escape speed from that altitude.
- Read the escape velocity, the orbital velocity, the gravity and the worked steps.
- Use Copy result to paste the line into a document.
Escape Velocity Calculator features
Presets
The Sun, eight planets, the Moon and Pluto with NASA masses and equatorial radii.
Any mass and radius
Custom mode accepts scientific notation, so asteroids, exoplanets and homework values all work.
Height above the surface
Escape speed shrinks with distance from the centre, so a launch from orbit needs less.
Orbital speed alongside
Circular orbital velocity √(GM ÷ r) is shown, with the √2 link between the two.
Comparison table
Surface gravity, escape and orbital speed for every preset at a glance.
The formula and a worked example for Earth
Escape velocity comes from energy. A body of mass m at distance r from a mass M has kinetic energy ½mv² and gravitational potential energy −GMm ÷ r. It escapes when the total is zero, which gives vesc = √(2GM ÷ r). The mass of the escaping object cancels, so a pebble and a spacecraft need the same speed. The circular orbital velocity at the same distance is vorbit = √(GM ÷ r), so escape speed is always √2 ≈ 1.414 times the orbital speed.
Earth: GM = 6.6743 × 10−11 × 5.9722 × 1024 = 3.986 × 1014 m³/s². With the equatorial radius r = 6,378 km, vesc = √(2 × 3.986 × 1014 ÷ 6.378 × 106) ≈ 11,180 m/s, or about 11.2 km/s, which matches the value published by NASA. The Moon needs only about 2.38 km/s, and Jupiter about 59.5 km/s.
Common misunderstandings
Escape velocity is not the speed a rocket must hold all the way up. A rocket can leave Earth slowly if its engines keep pushing; the figure applies to an object moving freely after a single burst, with nothing pushing it. It is also a speed measured from the centre of the body, and it ignores the Sun and the other planets. Leaving the Solar System from Earth’s orbit needs a different calculation, so use this page for the body you are leaving. For fuel needs see the rocket equation calculator, and for orbit timing the orbital period calculator.
If the escape velocity of an object exceeds the speed of light, nothing can escape it. The black hole calculator finds the radius at which that happens for any mass.
Limits of this calculator
- Air drag, rotation of the body and the pull of other bodies are ignored.
- Masses are rounded published values; GM for Earth, the Sun and Jupiter is known more precisely than G × M here, so the fifth digit may differ from specialist tables.
- Gas giants have no surface, so their radius is the 1-bar level quoted by NASA.
Escape Velocity Calculator FAQ
What is the escape velocity of Earth?
About 11.18 km/s (roughly 40,250 km/h) from the surface, using the equatorial radius of 6,378 km. NASA lists 11.2 km/s.
What is the formula for escape velocity?
v = √(2GM ÷ r), where G is the gravitational constant, M the mass of the body and r the distance from its centre. It equals √(2gr) when the local gravity g is known.
Does the mass of the rocket matter?
No. The mass of the escaping object cancels out of the energy equation. It matters only for how much fuel is needed to reach the speed.
How is orbital velocity related to escape velocity?
Escape velocity is √2 (about 1.414) times the circular orbital velocity at the same distance.
What is the escape velocity of the Moon?
About 2.38 km/s, much lower than Earth’s because the Moon has about 1.2 per cent of Earth’s mass and a quarter of its radius.
Why does escape velocity decrease with height?
Because r in the formula grows. At 400 km above Earth the escape speed is about 10.85 km/s instead of 11.18 km/s.