What density does something have to have to be considered a black hole?

[klite]

"Any amount of mass at all can in principle be made to form a black hole if you compress it to a high enough density."

What is the high enough density?

 

[Nabeshin]

This high enough density is the density at which the schwarzchild radius of the object is less than the actual radius of the object.

Mathematically,
$$r_s=\frac{2Gm}{c^2}=r$$
If you assume the object to be a uniform sphere, we can write its mass as the product of density and volume:
$$m=\rho V=\frac{4/3}\rho\pi r^3$$

And substituting into the first equation,
$$r=\frac{2G(\frac{4/3}\rho\pi r^3){c^2}$$
$$\rho=\frac{3}{8}\frac{c^2}{G\pi r^2}$$

In a completely classical universe.