Compress any mass inside its Schwarzschild radius and it becomes a black hole. For the Sun that is about 3 km; for Earth, just 9 mm. Supermassive black holes are so large that their average density can be lower than water’s.
How to use the Schwarzschild Radius Calculator
- Mass M
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Enter the mass.
What each result means
- Schwarzschild radius r_s = 2×6.6743e-11×[Mass M]÷299792458^2
- Surface gravity κ = 299792458^4÷(4×6.6743e-11×[Mass M])
- Average density inside the horizon = [Mass M]÷(4÷3×pi×[Schwarzschild radius r_s]^3)
Example values
How the main result changes when Mass M changes and everything else stays at the example values above:
| Mass M (M☉) | Schwarzschild radius r_s (km) |
|---|---|
| 0.5 | 1.4767 |
| 0.75 | 2.215 |
| 1 | 2.9533 |
| 1.25 | 3.6917 |
| 1.5 | 4.43 |
| 2 | 5.9067 |
Formula
r_s = 2GM/c², κ = c⁴/(4GM), ρ = M / (4/3·π·r_s³)
Worked example
Inputs — Mass M: 1 M☉.
Results — Schwarzschild radius r_s = 2.953339 km; Surface gravity κ = 15,215,914,300,168.049 m/s²; Average density inside the horizon = 1.8429e19 kg/m³.
Key terms
- Event horizon
- Boundary beyond which nothing can escape.
Frequently asked questions
What is the Schwarzschild radius of the Sun?
About 2.95 km.
What about Earth?
About 8.9 mm.
Can a black hole have low density?
Yes – density falls as 1/M², so huge black holes are "light".
Does this apply to spinning black holes?
No – rotating (Kerr) black holes have smaller horizons.