Schwarzschild Radius (Black Hole) Calculator
Calculate the Schwarzschild radius — the event horizon — of any mass.
From asteroids to supermassive black holes.
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.
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 (actual radius 695,700 km — 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 black hole (~6.5 billion M☉): r_s ≈ 19.2 billion km (2.7× the orbit of Pluto!)
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 — the average density inside the Sgr A* event horizon is only a few times the density of water! This is because r_s scales with mass while volume scales with r_s³.