Number density is a useful concept for thinking about macroscopic samples in a microscopic way. Number density can be thought of as the number of particles that are present in a particular volume.
The number density (symbol: n or ρN) is an intensive quantity used to describe the degree of concentration of countable objects (particles, molecules, phonons, cells, galaxies, etc.) in physical space: three-dimensional volumetric number density, two-dimensional areal number density, or one-dimensional linear number density.
Volume number density is the number of specified objects per unit volume: $$ n = \frac N V $$ where N is the total number of objects in a volume V.
Here it is assumed that N is large enough that rounding of the count to the nearest integer does not introduce much of an error, however V is chosen to be small enough that the resulting n does not depend much on the size or shape of the volume V because of large-scale features.
Area number density is the number of specified objects per unit area, A: $$ n’ = \frac N A $$
Similarly, linear number density is the number of specified objects per unit length, L: $$ n’’ = \frac N L $$
Column number density is a kind of areal density, the number or count of a substance per unit area, obtained integrating volumetric number density along a vertical path: $$ n_c = \int n \mathrm d s $$ It’s related to column mass density, with the volumetric number density replaced by the volume mass density.
