Schwarzschild Radius Calculator
Bigger black holes are less dense, not more.
Work out Schwarzschild Radius. Bigger black holes are less dense, not more. Refuses out-of-range input instead of guessing.
Schwarzschild radius
29.5334 km
10 solar masses · mean density 1.8429 × 10^17 kg/m³
The Schwarzschild radius is 2GM/c² — the size a mass must be compressed to before nothing, not even light, can escape. The Sun's is about 3 km and the Earth's about 9 mm, which is a fair measure of how far ordinary matter is from collapsing. Because the radius scales linearly with mass while volume scales with its cube, the mean density inside the horizon falls as the black hole grows. A black hole of a billion solar masses has a mean density below that of water, which is one of the more startling facts in the subject. Hawking temperature runs the other way, inversely with mass. Stellar-mass black holes are far colder than the cosmic microwave background, so they absorb more than they radiate and are growing rather than evaporating — and their evaporation times run to 10^67 years, which is why none has ever been observed to do it.
How the Schwarzschild Radius Calculator works
The event horizon radius for any mass, with the mean density inside it, the Hawking temperature and the evaporation time. The density result is genuinely counterintuitive and follows directly from the linear scaling.
Also known as: how big would earth be as a black hole · event horizon size for a mass · black hole density calculator · hawking temperature of a black hole
Frequently asked questions
What is the Schwarzschild radius?
2GM/c² — the size a mass must be compressed to before light cannot escape. The Sun's is about 3 km and the Earth's about 9 mm.
Why are supermassive black holes less dense?
The radius scales linearly with mass while volume scales with its cube, so mean density falls as the square of the mass. A black hole of a billion solar masses has a mean density below that of water.
What is Hawking radiation?
A faint thermal glow predicted from quantum effects at the horizon, with a temperature inversely proportional to mass. Small black holes are hot; stellar-mass ones are far colder than the cosmic microwave background.
Do black holes evaporate?
In theory, over timescales scaling with the cube of the mass — around 10^67 years for a stellar-mass one. That is vastly longer than the current age of the universe, and none has ever been observed doing it.
What happens at the event horizon?
Nothing locally dramatic for someone falling in — it is not a surface. It is the boundary beyond which every future path leads inward, which is why nothing, including light, comes back out.
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