What this calculator does
The Schwarzschild radius is the size to which a mass must be compressed for its escape velocity to reach the speed of light. Compress anything below it and nothing, not even light, can get back out.
For ordinary objects the figure is absurdly small, which is why nothing in daily life is remotely close. Earth's entire mass would have to be squeezed into a sphere under a centimetre across.
The formula
Multiply twice the gravitational constant by the mass and divide by the speed of light squared. The result is the event horizon radius for a non-rotating, uncharged black hole.
| Term | Meaning |
|---|---|
| Event horizon | The boundary at the Schwarzschild radius, past which no signal can escape outward. |
| Schwarzschild solution | The exact solution of general relativity for the spacetime around a spherical non-rotating mass. |
| Singularity | The point of infinite density predicted at the centre, generally taken as a sign that the theory is incomplete rather than a literal description. |
The inputs explained
| Field | What to enter |
|---|---|
| Mass (kg) | The mass in kilograms. The Sun is about 1.989 × 10³⁰; Earth about 5.972 × 10²⁴. |
When to use it
Finding a black hole's size
The event horizon radius follows directly from mass, and it is the only property that determines it for a simple black hole.
Seeing why compression matters more than mass
Any mass can in principle become a black hole if compressed far enough, which the density figure makes vivid.
Comparing stellar and supermassive holes
Radius scales linearly with mass, so a hole a million times heavier is a million times wider.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How large would different masses have to be compressed?
A range of masses from planetary to stellar.
| Mass | Schwarzschild radius | Average density inside |
|---|---|---|
| 5.97e+24 kg | 8.8698e-3 m | 2.0431e+30 kg/m³ |
| 1.99e+30 kg | 2.9540e+3 m | 1.8420e+19 kg/m³ |
| 1.99e+31 kg | 2.9540e+4 m | 1.8420e+17 kg/m³ |
Questions
Does radius scale with mass?
Linearly, yes. Double the mass and the event horizon doubles in radius. That makes density fall with the square of mass, which is why the largest black holes have average densities lower than water.
Is the Sun going to become a black hole?
No. It is nowhere near massive enough. Stars need considerably more mass than the Sun for their cores to collapse that far, and the Sun will end as a white dwarf.
What happens at the event horizon?
Nothing locally dramatic for a large black hole; an infalling observer would not notice crossing it. What changes is that all future paths lead inward, so escape becomes geometrically impossible rather than merely difficult.
Does this account for rotation?
No. The Schwarzschild solution describes a non-rotating, uncharged black hole. Real black holes spin, which is described by the Kerr solution and gives a more complicated horizon structure.
For the escape speed at ordinary scales, see the escape velocity calculator. For the gravitational force involved, see the Newton's law of gravitation calculator.