Schwarzschild Radius Calculator
Find the event-horizon radius of a black hole from its mass with r_s = 2GM ÷ c².
That is 2,954 m (1.000e+0 M☉). r_s = 2GM ÷ c², with G = 6.674×10⁻¹¹ N·m²/kg² and c = 2.99792458×10⁸ m/s.
The Schwarzschild radius is how small a mass must be squeezed to become a black hole: r_s = 2GM ÷ c². Compress the Sun (1 M☉) inside a radius of about 2.95 km and it forms an event horizon; the Earth would need to shrink to roughly 8.9 mm, smaller than a marble.
What the Schwarzschild radius is
The Schwarzschild radius r_s marks the event horizon of a non-rotating black hole — the surface at which the escape velocity equals the speed of light, so nothing, not even light, can get out. Karl Schwarzschild derived it in 1916 from Einstein’s field equations. Any mass compressed within its own Schwarzschild radius collapses into a black hole; a mass spread over a larger radius stays an ordinary star, planet, or lump of matter.
G = 6.674×10⁻¹¹ N·m²/kg², c = 2.99792458×10⁸ m/s, M is the mass in kg, r_s the radius in metres
Worked example
What is the Sun’s Schwarzschild radius? Use M = 1.989×10³⁰ kg (one solar mass).
- 1 Write the formula. r_s = 2GM ÷ c², with G = 6.674×10⁻¹¹ N·m²/kg² and c = 2.99792458×10⁸ m/s.
- 2 Put the mass in kilograms. One solar mass is 1.989×10³⁰ kg, so M = 1.989×10³⁰ kg.
- 3 Substitute the values. r_s = 2 × 6.674×10⁻¹¹ × 1.989×10³⁰ ÷ (2.99792458×10⁸)².
- 4 Evaluate. The numerator is ≈ 2.655×10²⁰ and c² ≈ 8.988×10¹⁶, giving r_s ≈ 2,954 m ≈ 2.95 km.
Schwarzschild radius of some masses
Event-horizon radius computed with r_s = 2GM ÷ c².
| Object | Mass | Schwarzschild radius |
|---|---|---|
| Earth | 5.972×10²⁴ kg | 8.9 mm |
| The Sun | 1.989×10³⁰ kg (1 M☉) | 2.95 km |
| Sagittarius A* | ≈ 4.3×10⁶ M☉ | ≈ 1.3×10⁷ km |
Reading the result
The Schwarzschild radius is directly proportional to mass: double the mass and you double r_s. That is why the answer scales so cleanly — every solar mass adds about 2.95 km to the horizon. Sagittarius A*, the supermassive black hole at the centre of the Milky Way, holds roughly 4.3 million solar masses, so its horizon spans about 1.3×10⁷ km — larger than the orbit of Mercury.
Crossing inside r_s does not mean hitting a solid surface; the event horizon is a boundary in spacetime, not a wall. It simply marks the point of no return, where escaping would require travelling faster than light. Anything — a star, a planet, or you — compressed to a radius smaller than its own r_s becomes a black hole.