Columnar number density

The area density (also known as areal density, surface density, superficial density, or density thickness) of a two-dimensional object is calculated as the mass per unit area. The SI derived unit is: kilogram per square metre (kg·m⁻²).

It can be calculated as:

or

where,

A special type of area density is called column (mass) density (also columnar mass density), denoted ρ_A or σ. It is the mass of substance per unit area integrated along a path; It is obtained integrating volumetric density ${\displaystyle \rho }$ over a column:

In general the integration path can be slant or oblique incidence (as in, for example, line of sight propagation in atmospheric physics). A common special case is a vertical path, from the bottom to the top of the medium:

where ${\displaystyle z}$ denotes the vertical coordinate (e.g., height or depth).

Columnar density ${\displaystyle \rho _{A}}$ is closely related to the vertically averaged volumetric density ${\displaystyle {\bar {\rho }}}$ as

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