How To 

How To Calculate a Black Hole’s Event Horizon



Black holes are stunning, mysterious, and oh so intriguing. We know a surprising amount about them (or have at least theorized a lot), but research is ongoing and will be for quite some time. One of the most interesting aspects of a black hole that we have been able to calculate is what’s known as the event horizon. This is the point past which no light can escape. Every black hole has a different event horizon. Here’s how to calculate it.



1. Use the Schwarzschild Radius formula.
The more precise name for the event horizon is the Schwarzschild Radius, named after Karl Schwarzschild. The formula for the Schwarzschild Radius is Rs = 2GM/c^2. “G” represents the gravitational constant (6.67 x 10^-11 m^3/(kg x s^2), “M” is the mass of the black hole, and “c” is the speed of light (3 x 10^8 m/s).

2. Ensure you have the mass of the black hole.
As you can see from the formula, aside from the constants all you really need to know is the mass of the black hole. When you have the mass of the black hole, simply plug it into the formula and you have your answer!



3. Calculating the Schwarzschild Radius in terms of the mass of the sun.
Occasionally, you will be given the mass of the black hole in terms of the mass of the sun. These are called solar units. For example, the black hole’s mass could be 10MSun, which means the black hole is 10 times the mass of our sun. When you have solar units, you can use a slightly modified version of the Schwarzschild Radius formula:
Rs = 3 x M/MSun in kg.
 

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