Enter the mass of a black hole in solar masses into the calculator to determine the Schwarzschild radius, which is the radius of the event horizon.

Black Hole Radius Formula

The following formula is used to calculate the Schwarzschild radius of a black hole:

R = \frac{2GM}{c^2}

Variables:

  • R is the Schwarzschild radius (kilometers)
  • G is the gravitational constant (6.67430 × 10^-11 m^3 kg^-1 s^-2)
  • M is the mass of the black hole (solar masses)
  • c is the speed of light (299,792,458 meters/second)

To calculate the Schwarzschild radius, multiply twice the gravitational constant by the mass of the black hole in kilograms, and then divide by the square of the speed of light. The result is the radius of the event horizon in meters, which can be converted to kilometers.

What is a Black Hole Radius?

The Schwarzschild radius, also known as the black hole radius, is the distance from the center of a black hole to its event horizon, the point beyond which nothing, not even light, can escape its gravitational pull. It is a critical measure in astrophysics for understanding the size and boundary of a black hole.

How to Calculate Black Hole Radius?

The following steps outline how to calculate the Schwarzschild radius of a black hole:


  1. First, determine the mass of the black hole (M) in solar masses.
  2. Next, use the gravitational constant (G) and the speed of light (c) in the formula.
  3. Apply the formula R = (2GM) / c^2 to calculate the Schwarzschild radius.
  4. Finally, convert the radius from meters to kilometers if necessary.
  5. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem:

Use the following variables as an example problem to test your knowledge.

Mass of the black hole (M) = 10 solar masses

Using the formula, the Schwarzschild radius (R) is calculated as follows:

R = (2 * 6.67430 × 10^-11 m^3 kg^-1 s^-2 * 10 * 1.98847 × 10^30 kg) / (299,792,458 m/s)^2

R = 29.53 kilometeres