Schwarzschild Radius (Black Hole) Calculator

The Schwarzschild radius is the critical radius below which an object becomes a black hole. It defines the event horizon, the boundary from which nothing, not even light, can escape.

Karl Schwarzschild derived this radius in 1916, just weeks after Einstein published general relativity, while Schwarzschild was serving on the Russian front during World War I. He did not survive the war, but his solution remains one of the most elegant results in physics.

Formula:

r_s = 2GM / c²

Simplified:

r_s = 2.953 km × (M / M☉)

Where:

• G = 6.674 × 10⁻¹¹ N·m²/kg²
• c = 3 × 10⁸ m/s
• M☉ = 1.989 × 10³⁰ kg (solar mass)

Famous examples:

• The Sun (1 M☉): r_s ≈ 2.95 km, against an actual radius of 695,700 km, so nowhere near collapse
• The Earth (M_E = 5.97×10²⁴ kg): r_s ≈ 8.87 mm (about the size of a marble)
• Milky Way center black hole (Sgr A*, ~4 million M☉): r_s ≈ 11.8 million km
• M87* (the black hole photographed by the Event Horizon Telescope in 2019, ~6.5 billion M☉): r_s ≈ 19.2 billion km, which is 3.25 times the radius of Pluto’s orbit

Physical meaning: Any object compressed inside its Schwarzschild radius becomes a black hole. Stellar-mass black holes (5–100 M☉) form from collapsing massive stars. Supermassive black holes (millions to billions of M☉) lurk at the centers of most galaxies.

Density at event horizon: For stellar-mass black holes: extremely high density. For supermassive black holes: surprisingly low, because r_s grows linearly with mass while the volume inside it grows as the cube. Sgr A* (4 million solar masses) averages about 1,150× the density of water, and the truly giant M87* (6.5 billion solar masses) comes out at roughly 0.44 kg/m³, which is a third the density of the air in this room.

What the event horizon actually is

The event horizon is not a physical surface. It is a mathematical boundary where the escape velocity equals the speed of light. A falling observer crosses the event horizon without feeling anything special at the moment of crossing. Only later, when they cannot communicate back to the outside universe, is the crossing significant. Locally, the laws of physics still work as expected inside the horizon. The boundary is a one-way membrane in spacetime, not a wall.