Escape Velocity Calculator

The calculator uses v = √(2GM/r), derived by setting the kinetic energy needed for escape (½mv²) equal to the gravitational potential energy holding the object in place (GMm/r) and solving for v. The object's own mass (m) cancels out of the equation entirely, which is why a feather and a spacecraft need the same escape velocity from the same launch point.

G, the gravitational constant, is fixed at 6.674×10⁻¹¹ N·m²/kg² — the same value Newton's law of gravitation uses.

Mass (M) is the total mass of the body in kilograms — Earth is about 5.972×10²⁴ kg. Radius (r) is the distance from the center of mass to the point of departure, in meters — for a planet, this is usually its surface radius. Both fields accept scientific notation directly (e.g. 5.972e24), which is the natural way to enter astronomical values.

A larger mass increases escape velocity; a larger radius decreases it. That's why the Moon, despite being much less massive than Earth, still has a lower escape velocity than a hypothetical body with Earth's mass compressed into the Moon's radius.

This formula assumes a spherically symmetric, non-rotating body with no atmosphere to add drag — real launches also have to overcome air resistance and aren't fired instantaneously, so actual mission delta-v budgets are higher than the raw escape velocity number. The formula also breaks down at relativistic speeds: if you solve for the radius that gives a very massive body an escape velocity at or beyond the speed of light, you're computing something close to a Schwarzschild radius, and general relativity — not this Newtonian formula — governs the real physics there.