Physics

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Black Hole Calculator.

Calculate Schwarzschild radius from black-hole mass.

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schwarzschildRadius: 2,954.126555

schwarzschildRadius

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Use Cases

Astrophysics Education

Helps students and educators visualize the size of a black hole's event horizon for a given mass, making abstract concepts more tangible.

Example: Calculate the Schwarzschild radius for a black hole with 10 solar masses (about 2×10^31 kg).

Science Communication

Enables science writers and communicators to provide accurate comparisons of black hole sizes in articles, videos, or presentations.

Example: Show that a black hole with Earth's mass (5.97×10^24 kg) would have a radius of about 9 mm.

Frequently Asked Questions

What is the Schwarzschild radius?
The Schwarzschild radius is the distance from the center of a non-rotating black hole to its event horizon. It is the radius at which the escape velocity equals the speed of light. For a given mass, it is calculated using the formula r_s = 2GM/c^2.
How do I use this calculator?
Simply enter the mass of the black hole in kilograms into the 'Black-hole mass' field. The calculator will then compute the corresponding Schwarzschild radius using the standard formula. The result is the radius in meters.
What is the formula used?
The calculator uses the Schwarzschild radius formula: r_s = 2GM/c^2, where G is the gravitational constant (6.674×10^-11 m^3 kg^-1 s^-2), M is the mass in kilograms, and c is the speed of light (299,792,458 m/s).

Tips & Common Mistakes

Tips

  • Ensure the mass is entered in kilograms. If you have mass in solar masses, multiply by 1.989×10^30 kg to convert.
  • The result is the Schwarzschild radius in meters. To convert to kilometers, divide by 1000.
  • This calculator assumes a non-rotating, uncharged black hole (Schwarzschild black hole). For rotating black holes, the radius differs.
  • Use scientific notation for very large or small masses to avoid errors.

Common Mistakes to Avoid

  • Forgetting to convert mass to kilograms before entering it, leading to incorrect results.
  • Confusing the Schwarzschild radius with the radius of the black hole's singularity, which is zero.
  • Assuming the calculator works for any object; it only applies to objects with mass, but the radius is only physically meaningful for black holes.

Last updated: August 13, 2026