It is somewhat counterintuitive to note that the average density of a SMBH within its event horizon (defined as the mass of the black hole divided by the volume of space within its Schwarzschild radius) can be smaller than the density of water. This is because the Schwarzschild radius ( r s ) is directly proportional to its mass. Since the volume of a spherical object (such as the event horizon of a non-rotating black hole) is directly proportional to the cube of the radius, the density of a black hole is inversely proportional to the square of the mass, and thus higher mass black holes have a lower average density.