How dense is matter inside a black hole?

First, the simplest definition of density: it is how heavy something is relative to its size. A pound of rocks weighs the same as a pound of ping pong balls. But the ping pong balls take up a lot more space. Hence, the rocks are much more dense. Another way to look at density is to think of it as a measure of the “compactness” of matter.

More background… at the center of an atom is a very dense core called the nucleus. It’s composed of protons and neutrons (held very tightly together). Surrounding this nucleus in somewhat of a cloud are the electrons. Atomically speaking, the electrons are very far apart and far from the nucleus. Consider this: the entire atom composed of an electron cloud surrounding the nucleus is about 99.9% empty space.

The electrons are negatively charged and repel anything else negatively charged with a very strong electromagnetic force, or EMF. Now imagine a force strong enough to overcome this EMF and compress atoms to a much greater density. This is what happens in old and dying stars– the compressing force of gravity starts to overcome this electromagnetic force. The atoms start squeezing together resulting in what’s called degenerate matter. Stars involved in this process are called white dwarfs and the matter in them can reach a density of one million times that of water.

While this is very dense, it is not the densest state that matter can reach. If the dying star is massive enough, its gravitational force can be powerful enough to overcome the repelling force in the degenerate matter. The center of this body is now called neutronic fluid and these stars are now called neutron stars or pulsars. Now we’re getting pretty dense. A 1cm cube of neutron star material would weigh 100 million tons and if dropped would fall straight through to the center of the earth.

Now for even bigger stars (more than three times the mass of our sun), it can have a gravitational force strong enough to break down even this neutronic matter. After this, there will be no barrier left. The matter can not compress any further and it is basically a single point called a singularity. A star that has collapsed into itself to this point is called a black hole.

Since there is no way to measure anything of this magnitude, estimates are made by estimating the matter outside and near this singularity. If we use matter on Earth as a first order of magnitude, degenerate matter (inside white dwarfs) is about one million times as dense. Neutronium (inside neutron stars) is about one trillion times as dense. And finally, black holes, which are about ten trillion times as dense.

Source: Why Nothing Can Travel Faster than Light. Contemporary Books, 1993.