Enter black hole size
Example data table
These examples use Schwarzschild radius as the “size”. Values are approximate.
| Example | Schwarzschild radius (km) | Mass (solar masses) | Mass (kg) |
|---|---|---|---|
| Earth-mass black hole | 8.8701e-6 | 3.00341e-6 | 5.9722e+24 |
| 1 solar-mass black hole | 2.95334 | 1.00000 | 1.98847e+30 |
| 10 solar-mass black hole | 29.5334 | 10.0000 | 1.98847e+31 |
| 1000 solar-mass black hole | 2,953.34 | 1,000.00 | 1.98847e+33 |
| Sgr A* (about 4.3M solar masses) | 1.26994e+7 | 4,300,000 | 8.55042e+36 |
| M87* (about 6.5B solar masses) | 1.91967e+10 | 6.5e+9 | 1.29251e+40 |
Formula used
For a non‑rotating, uncharged black hole, the event horizon radius is the Schwarzschild radius:
- rs = 2GM / c²
- M = rs c² / (2G)
Here, G is the gravitational constant and c is the speed of light. This calculator converts your chosen “size” into rs first.
How to use this calculator
- Enter the black hole size as a number.
- Select the unit that matches your measurement.
- Choose whether your size is radius, diameter, or circumference.
- Adjust significant figures if you want different rounding.
- Click Calculate to see results above the form.
- Use the export buttons to save CSV or PDF.
If your “size” came from imaging, confirm whether it represents radius, diameter, or circumference. That choice can change mass by factors of two or 2π.
Black hole size to mass guide
1) What “size” means here
This calculator treats “size” as an event-horizon measurement for a non‑rotating black hole. You can enter the Schwarzschild radius directly, or enter a diameter (twice the radius) or a circumference (2π times the radius). The interpretation matters because mass scales linearly with the radius you use.
2) The core relationship
For a Schwarzschild black hole, rs = 2GM/c², so M = rsc²/(2G). Rule of thumb: 1 km of Schwarzschild radius corresponds to about 0.339 solar masses (M☉) when using standard constants.
3) Stellar-mass reference points
A 1 M☉ black hole has rs ≈ 2.95 km, while a 10 M☉ black hole has rs ≈ 29.53 km. These values are handy for quick checks. If you enter diameter as radius, your computed mass will be about twice as large.
4) Planet-scale comparison
Tiny horizon sizes can still mean huge mass. An Earth‑mass black hole would have rs ≈ 8.87 mm—roughly a fingertip width. That contrast is why choosing mm, µm, or nm units is useful when exploring “micro” scenarios in education.
5) Supermassive examples
Scaling stays linear for supermassive objects. If Sgr A* is about 4.3 million solar masses, its Schwarzschild radius is ≈ 12,699,359 km. If M87* is about 6.5 billion solar masses, rs is ≈ 19,196,705,983 km. These are horizon radii, not the visible ring size.
6) Mean density insight
The calculator also reports an average density inside rs (mass divided by the volume of a sphere of radius rs). For 1 M☉, the average is about 1.84×1019 kg/m³. It drops sharply for larger holes: Sgr A* is ~9.97×105 kg/m³ and M87* is ~0.44 kg/m³.
7) Units and precision
Inputs are converted to meters internally, then results are shown in kilograms plus solar, Earth, and Jupiter masses. You can type scientific notation like 1.2e6. Larger units like light‑seconds, AU, Earth radii, and solar radii help match astronomy literature and imaging discussions without extra conversions. Significant figures only affect rounding of displayed values, not the underlying calculation.
8) Limits of the model
Astrophysical black holes often rotate, which shifts the horizon size for a given mass. This tool uses the Schwarzschild case so you can learn the scaling and compare magnitudes cleanly. For high‑spin objects, treat results as approximate, not definitive.
FAQs
1) What is the Schwarzschild radius?
It is the radius of the event horizon for a non‑rotating, uncharged black hole. In this model, the horizon radius is rₛ = 2GM/c², so it grows directly with mass.
2) Can I enter diameter or circumference instead of radius?
Yes. Choose the correct interpretation in the dropdown. The calculator will convert diameter (2rₛ) or circumference (2πrₛ) back to rₛ before computing mass.
3) Why does a tiny radius produce a very large mass?
Because gravity is extremely strong. Even millimeter‑scale Schwarzschild radii correspond to planetary masses. For example, an Earth‑mass black hole has rₛ near 8.87 mm.
4) Does black hole spin change the result?
Yes. Rotating (Kerr) black holes have a different horizon radius for the same mass, depending on spin. Use this tool as a clean Schwarzschild estimate when you want a simple baseline.
5) Is an imaged ‘ring size’ the same as horizon size?
Not necessarily. Images often show a photon ring or shadow feature whose apparent diameter depends on geometry, plasma, and lensing. Convert your measurement to a horizon radius only if your source defines it that way.
6) What does “mean density inside rₛ” mean?
It’s a geometric average: mass divided by the volume of a sphere with radius rₛ. It is not a real interior density profile, but it helps show why supermassive black holes can have low average densities.
7) How do CSV and PDF exports work?
After you calculate, use the buttons in the results box. The page stores the latest calculation in your session, then generates a downloadable CSV or a simple one‑page PDF report.