Schwarzschild Radius Calculator
The Schwarzschild radius of any mass — how small it would have to be compressed to become a black hole — with the density inside the horizon, the tidal stretch at it, and the Hawking temperature.
Every mass has a Schwarzschild radius: 2GM over c².
How the schwarzschild radius calculator works
Every mass has a Schwarzschild radius: 2GM over c². Compress the mass inside it and nothing, including light, gets out. The Sun's is three kilometres; the Earth's is nine millimetres. The radius grows in proportion to mass, so the mean density inside it falls with the square of the mass — a galaxy-mass black hole is less dense than air.
The tidal force at the horizon also falls with mass: a stellar black hole would shred you long before you crossed; a supermassive one would let you through without noticing.
Formula: R_s = 2GM / c²; T_H = ħc³ / (8πGMk)
Worked examples
| Inputs | Schwarzschild radius (km) | Note |
|---|---|---|
| The Sun | 2.954 | 2.95 km |
| The Earth | 8.8709e-6 | 8.9 millimetres |
| Sagittarius A* | 1.2702e+7 | 12.7 million km |
FAQFrequently asked questions
What is the Schwarzschild radius?
The radius of the event horizon for a non-rotating mass: 2GM over c². Compress anything inside its own Schwarzschild radius and it becomes a black hole.
Does everything have one?
Yes — it is a property of mass, not of black holes. Yours is about 10⁻²⁵ metres. The point is whether the mass fits inside it, and for ordinary objects it never does.
Why are big black holes less dense?
Radius grows with mass while volume grows with radius cubed, so density falls as one over mass squared. A billion-solar-mass hole has the density of water.
What is the tidal stretch?
The difference in gravity between your head and feet. At a stellar-mass horizon it is billions of g and you are spaghettified; at a supermassive one it is gentler than Earth's.
What is Hawking temperature?
The temperature at which a black hole radiates by quantum effects — inversely proportional to mass. A solar-mass hole is 60 billionths of a kelvin, far colder than the microwave background, so it grows rather than evaporates.
Where these figures come from
- NIST — CODATA 2018 fundamental physical constants — G and the speed of light
- IAU 2015 Resolution B3 — nominal solar and planetary conversion constants — the astronomical unit, solar mass and planetary radii
- Royal Observatory Greenwich — the historic home of the prime meridian
Last checked: September 2026. Constants are CODATA 2018 (G, c) and IAU 2015 nominal values (solar and planetary parameters).