Donaldson R F Orbital & Escape Velocity Calculator
How fast do you need to go to stay in orbit, or to leave a planet altogether? Pick a body and a height, or enter your own mass and radius.
The formulas
For a circular orbit at distance r from the centre of a body of mass M: orbital speed = √(GM / r). To leave the body's gravity altogether from the same distance: escape velocity = √(2GM / r) — always exactly √2 (about 1.41) times the circular orbital speed at that same height. G is the Newtonian gravitational constant; r is measured from the centre of the body, so a "height above the surface" is added to its radius first.
Low Earth orbit (a few hundred km up, where the International Space Station flies) needs about 7.8 km/s; leaving Earth's gravity from the surface needs about 11.2 km/s. Try 0 km height with Earth selected to see both figures.
Frequently asked questions
Does height above the surface matter much?
A little: both speeds fall slowly as height increases, since gravity weakens with distance, but low Earth orbit (a few hundred km) is not dramatically different from the surface value.
Why is escape velocity always √2 times orbital velocity?
It falls straight out of the two formulas above — the 2 inside the escape-velocity square root, against nothing extra in the orbital one, is the only difference between them, at the same distance from the same body.
Related tools: Planet Facts Table, Kepler's Third Law Calculator, Rocket Equation Calculator.
Source / Last verified: the two formulas are classical Newtonian mechanics. The gravitational constant G = 6.674 30 × 10&supminus;¹&sup9; m³kg&supminus;¹s&supminus;² is the CODATA 2022 value (NIST, physics.nist.gov). Body masses and diameters are from NASA/GSFC, "Planetary Fact Sheet – Metric" (nssdc.gsfc.nasa.gov/planetary/factsheet), marked "Last Updated: 18 March 2025, DRW". All read and checked on 27 September 2026; Earth's own figures reproduce the fact sheet's own escape velocity of 11.2 km/s at the surface.