# Schwarzschild radius

A measure for the size of a spherically symmetric black hole. It is defined using the area of the black hole's horizon: In usual high school geometry (the geometry of flat space), radius and area of a spherical surface are related as

area = 4 times pi times (radius)^{2}.

Area of the black hole's horizon = 4 times pi times (Schwarzschild radius)^{2}.

It is directly proportional to the black hole's mass. The Schwarzschild radius for an object the mass of the earth is 9 millimeters, for an object with the mass of the sun, 2.95 kilometers.

There is a quite general result that says: If a sphere of matter is compressed further and further, a black hole forms as soon as the sphere's radius gets smaller than the Schwarzschild radius corresponding to the matter's mass.