Black Hole Mass Calculator
The Schwarzschild radius is one of the cleanest ideas in physics: compress any mass inside a small enough sphere and it becomes a black hole, and the radius of that sphere depends on nothing but the mass. The Sun would need squeezing to 3 kilometers. The Earth would fit inside a marble. The formula is high-school algebra wrapped around two of nature’s constants.
The Black Hole Mass Calculator below works in both directions: enter a Schwarzschild radius to get the mass in kilograms, solar masses, and Earth masses, or enter a mass to get the event-horizon radius. It also includes one-click presets for famous black holes, from Cygnus X-1 to TON 618, so you can feel the scale.
Quick Answer
Key takeaways
- The Schwarzschild radius is directly proportional to mass: double the mass, double the radius.
- Memorize 2.95 km per solar mass and you can estimate any black hole in your head.
- The formula assumes a non-rotating, uncharged black hole; real rotating (Kerr) black holes are slightly different.
- Compressing the Earth to a black hole gives an 8.9 mm marble; the Sun becomes a 2.95 km sphere.
Where the formula comes from
In 1916, Karl Schwarzschild solved Einstein's field equations for the simplest possible case: a perfectly spherical, non-rotating mass sitting alone in empty space. The solution contains a critical radius where the escape velocity reaches the speed of light. Set the Newtonian escape velocity formula's v to c and solve for r, and you get r = 2GM/c^2. Rearranged, that gives mass from radius.
The Newtonian derivation is technically a coincidence that gives the right answer for the wrong reasons, but the full general-relativity treatment lands on the same radius, which is why the simple formula survives in textbooks.
Worked example: radius of 2,953 meters
Enter the pre-filled default (2,953 m) in radius-to-mass mode and click Calculate:
| Figure | Value |
|---|---|
| Mass in kilograms | 1.988 x 10^30 kg |
| Mass in solar masses | 1.000 solar masses (one Sun) |
| Classification | Stellar-mass black hole |
Flip to mass-to-radius mode and enter 4,300,000 solar masses (Sagittarius A*): the radius comes out to about 12.7 million km, roughly 8% of the Earth-Sun distance. That is the scale jump between stellar and supermassive: the same linear formula, seven orders of magnitude apart.
Famous black holes, by the numbers
| Object | Mass | Schwarzschild radius | Type |
|---|---|---|---|
| Cygnus X-1 | 21 solar masses | 62 km | Stellar |
| Sagittarius A* (Milky Way center) | 4.3 million solar masses | 12.7 million km | Supermassive |
| M87* (first imaged) | 6.5 billion solar masses | 19.2 billion km | Supermassive |
| TON 618 | 66 billion solar masses | 195 billion km | Ultramassive |
Try each one with the preset dropdown. TON 618's event horizon is wider than the orbit of Neptune by a factor of forty, yet its average density is thinner than air: supermassive black holes are diffuse because radius grows linearly with mass while volume grows with the cube.
The marble, the city, and the solar system
These comparisons do more than impress. They show why stellar-mass black holes are insanely dense (a mountain range per sugar cube) while supermassive ones are not: density falls as mass rises, because the radius only grows in direct proportion.
What competing calculators miss
One direction only. The top-ranking black hole calculators convert radius to mass and stop. Mass-to-radius is the direction students and hobbyists actually need when they read that some galaxy hosts a 10-billion-solar-mass beast, so this tool does both.
No presets. Competitors make you look up the mass of Sagittarius A* elsewhere and type nine digits by hand. The preset dropdown loads the famous objects in one click.
No classification. A raw kilogram figure means nothing without context. The verdict badge classifies the result as stellar, intermediate, or supermassive automatically.
Kilograms only. Scientific notation in kilograms is unreadable at these scales. Solar masses and Earth masses are the units astronomers actually think in, so they lead the output.
Frequently asked questions
Use M = (r x c^2) / (2 x G), where r is the Schwarzschild radius in meters, c is 299,792,458 m/s, and G is 6.67430 x 10^-11 m^3/kg/s^2. Divide the kilogram result by 1.98847 x 10^30 to get solar masses. A 2,953 m radius gives almost exactly one solar mass.
It is the radius of the event horizon: the boundary inside which nothing, not even light, can escape. For a non-rotating, uncharged black hole it equals 2GM/c^2. Anything compressed inside its own Schwarzschild radius becomes a black hole.
Sagittarius A* has a mass of about 4.3 million Suns, giving a Schwarzschild radius of roughly 12.7 million km, about 8% of the Earth-Sun distance. Select it in the preset dropdown to see the full calculation.
In theory there is no minimum from the formula alone, but astrophysical black holes form from collapsed stars, so the smallest observed are around 3-5 solar masses. Hypothetical primordial black holes could be far smaller; one with Earth's mass would be 8.9 mm across.
Not exactly. The Schwarzschild formula assumes no rotation and no charge. Real astrophysical black holes spin, and rotating (Kerr) black holes have a more complex horizon structure. For mass estimates the Schwarzschild value remains the standard reference number.
Because r = 2GM/c^2 is linear in M: G and c are constants, so doubling the mass doubles the radius. This is unusual; most objects grow in volume with the cube of their radius. It is why supermassive black holes have such low average densities.
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References
- Brave Calculator, "Black Hole Mass Calculator" - M = (r x c^2)/(2G) formula with solar-mass conversion and worked example. Brave Calculator: Black Hole Mass Calculator. Accessed October 19, 2026.
- Calculator.now, "Schwarzschild Radius Calculator" - r = 2GM/c^2 formula, 2.95 km per solar mass simplification, and size comparisons. Calculator.now: Schwarzschild Radius Calculator. Accessed October 19, 2026.
- TrueGeometry, "Schwarzschild Radius Calculation" - worked examples for Earth, Sun, and solar-mass black holes with Kerr and Reissner-Nordstrom caveats. TrueGeometry: Schwarzschild Radius Calculation. Accessed October 19, 2026.
- OnlyCalculators, "Black Hole Temperature Calculator" - Hawking temperature, evaporation time, and Schwarzschild radius for a 10 solar mass black hole. OnlyCalculators: Black Hole Temperature Calculator. Accessed October 19, 2026.
- Vaia, "Estimate the Schwarzschild radius for a supermassive black hole" - step-by-step 26-billion-solar-mass worked solution. Vaia: Schwarzschild Radius Problem Solution. Accessed October 19, 2026.