## What is the size of a black hole? (Intermediate)

I have read that a black hole has very strong gravitation force and nothing can escape from the gravitational force of a black hole not even light. Now my question is what is the size of the black hole?

When you read about black holes, you would have read about something called the event horizon. That is the point from which light can no longer escape from the black hole. Nobody knows as to what really happens inside the event horizon. One needs to have a theory on quantum gravity to explain that. Classically, matter collapses to a point, called a singularity (infinite density), but what really happens is not known.

When astronomers refer to the "size" of the black hole, they are talking about the event horizon. The event horizon is refers to the location from the black hole where the escape velocity equals the speed of light. In other words, no particle (even light) can escape from within the event horizon.

Mathematically, the size of the black hole is given by 2GM/c2 where G is the gravitational constant, M is the mass of the black hole and c is the speed of light. So, when one says that the black hole has a size of 5 km, it means that the event horizon is at a distance of 5 km from the center of the black hole. If the Sun were to become a black hole, then its size would be about 3 km.