Schwarzschild Radius Calculator

Karl Schwarzschild derived the radius of a black hole event horizon in 1916 — just weeks after Einstein published general relativity, while Schwarzschild was serving on the Russian front. He did not survive the war, but his solution remains one of the most elegant results in physics.

The formula

r_s = 2GM / c^2

G = 6.674 x 10^-11 N·m²/kg², c = 2.998 x 10^8 m/s.

This simplifies to: r_s (km) ≈ 2.954 x M / M_sun, where M_sun = 1.989 x 10^30 kg.

So the Schwarzschild radius of 1 solar mass is about 2.95 km — roughly the size of a small town.

Famous values

Earth (5.972 x 10^24 kg): r_s ≈ 8.87 mm — smaller than a marble. The entire Earth would need to be compressed into a sphere smaller than 9 mm to become a black hole.

Sun (1.989 x 10^30 kg): r_s ≈ 2.95 km. The Sun compressed to the size of a city.

Sagittarius A* (Milky Way center, ~4 million solar masses): r_s ≈ 11.8 million km — about 17 times the Sun’s actual radius.

M87* (the black hole photographed in 2019, ~6.5 billion solar masses): r_s ≈ 19 billion km — larger than our solar system.

What the Schwarzschild radius means

An object compressed below its Schwarzschild radius forms a black hole. Light itself cannot escape from within this radius. The event horizon is not a physical surface — it is a mathematical boundary where escape velocity exceeds the speed of light. A falling observer crosses the event horizon without feeling anything special; only later (when they cannot communicate back) is the crossing significant.

The formula also applies to ordinary objects — it just tells you how small you would need to make them, not that they will spontaneously collapse.