Escape Velocity Calculator
Find the escape velocity and circular orbital velocity from a body's mass and radius, using v = √(2GM/r).
- Escape velocity
- 11,185.98 m/s
- Circular orbital velocity at this radius
- 7,909.68 m/s
- Escape velocity (km/s)
- 11.186 km/s
How it works
Escape velocity is the minimum speed an object needs, with no further propulsion and ignoring air resistance, to break completely free of a body's gravity from a given distance: v = √(2GM/r), where G is the gravitational constant, M the body's mass, and r the distance from its center. It comes from setting the object's kinetic energy equal to the gravitational potential energy it has to overcome.
The same inputs also give the speed needed for a stable circular orbit at that exact radius, v = √(GM/r) = v_escape / √2 — found by setting gravity equal to the centripetal force circular motion requires. This is why a spacecraft only needs to gain about 41% more speed (a factor of √2) to leave a circular orbit entirely rather than just maintain it.
The gravitational constant used is G = 6.6743×10⁻¹¹ m³ kg⁻¹ s⁻², the CODATA 2022 recommended value. Mass and radius are converted to kilograms and meters before the formula runs, and results are converted back to mph for imperial display — the same convert-to-canonical-then-back pattern this site's other unit-toggled physics calculators use.
FAQ
Why is orbital velocity always escape velocity divided by √2?
Both formulas share the same GM/r term; escape velocity's kinetic-energy balance produces a factor of 2 inside the square root that circular orbital velocity's force balance doesn't, so their ratio always reduces to exactly √2 regardless of the body's mass or radius.
Does this include atmospheric drag or the body's rotation?
No — this is the idealized two-body vacuum case from Newtonian gravity alone. A real launch from a rotating, atmosphere-bearing planet needs a somewhat different (usually lower, thanks to the planet's own spin) net speed than the idealized figure shown here.
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