Planet escape velocity calculator

Escape velocity is the lowest speed a projectile needs at a given distance from a massive body so that, if it coasts without thrust and without drag, it never falls back. This planet escape velocity calculator takes body mass in kilograms and radius (or centre distance) in metres and returns the classical result v equals the square root of two G M over r, both in metres per second and kilometres per second, using the CODATA 2018 gravitational constant. Students, mission planners sketching rough delta-v budgets, game developers, and unit-test authors all need the same deterministic number for Earth, Moon, Mars, or a custom sphere.

What escape velocity means for a spherical body

In Newtonian gravity a point mass or a spherically symmetric body of mass M produces a potential that falls as minus G M over radial distance. Mechanical energy of a test particle of mass m is one half m v squared minus G M m over r. Setting total energy to zero at infinity and solving for speed at radius r yields the escape speed v equals the square root of two G M over r.

That speed is independent of the test mass m, which cancels, and it assumes a non-rotating spherical body with no atmosphere. Atmosphere and planetary rotation change the practical launch problem: atmospheric drag dissipates kinetic energy, and launching eastward from an equatorial site already contributes some horizontal speed, so real rockets need less propulsive delta-v than the pure surface escape figure—but textbooks and homework still ask for the ideal surface value first.

The same formula applies not only at the surface: if you stand at altitude h above a body of radius R, use r equals R plus h. Black holes have an event horizon where escape speed formally reaches the speed of light, but this tool stays classical and will simply return a very large finite number for extreme M over r ratios still inside double precision.

Teachers should emphasise that escape velocity is a scalar speed threshold for ballistic free flight, not a required direction; any trajectory whose speed at that radius meets or exceeds the threshold and is not aimed into the body can leave the gravitational well in the ideal model.

Practical tips, limits, and related searches

Use SI base units only: convert solar masses, Earth masses, kilometres, or miles before you call. Prefer numbers rather than pre-formatted strings when you control the client; string numbers are accepted only when they match a strict finite numeric pattern.

For Earth, mass about five point nine seven two times ten to the twenty-four kilograms and mean radius about six point three seven one times ten to the six metres yields roughly eleven point two kilometres per second; for the Moon and Mars the same workflow with published mass and radius gives the familiar lower figures used in exam problems. Keep mass over radius ratios inside double range: absurdly large M with tiny r can overflow the intermediate two G M over r into non-finite values that the solver rejects.

This landing targets people searching for a planet escape velocity calculator, escape speed from a body, or v equals square root of two G M over r online; it is not an orbital period tool, not a Hohmann transfer planner, not a rocket equation delta-v budget, and not a general relativity geodesic solver. Prefer this capability when you already have M and r and only need the classical escape speed; if your source gives density and diameter, convert to mass and radius first.

Round-trip checks are easy: recompute two times G times M over r by hand, take the square root, divide by one thousand for km/s, and confirm both published fields match within the same twelve-decimal rounding.