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What equation determines when a black hole forms?

In other words, how much would I need to compress a certain amount of mass for it to form a black hole.

The simplest equation describing a black hole is the

Schwarzschild radius,

[math]r_s = \frac{2 M G}{c^2}[/math].

It applies to uncharged, non-rotating black holes. Other cases are more complicated, but this equation is good for first aproximations.

If the body’s physical radius is less than its Schwarzschild radius, it is a black hole. Otherwise, it isn’t.

You can calculate it for any body. For example, for the Earth, it's about 0.00887 m, about the size of you thumb. If the Earth’s mass were somehow compressed to fit within this radius, it would be a black hole.