Area density

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

In the paper and fabric industries, it is called grammage and is expressed in grams per square meter (g/m2); for paper in particular, it may be expressed as pounds per ream of standard sizes ("basis ream").

A generalized areic quantity is defined as the quotient of a generic physical quantity by area, such as surface charge density or areic electric charge.

A related area number density can be defined by replacing mass by number of particles or other countable quantity.

Formulation

Area density can be calculated as:

ρ

A

=

m

A

{\displaystyle \rho _{A}={\frac {m}{A}}}

or

ρ

A

=

ρ

⋅

l

,

{\displaystyle \rho _{A}=\rho \cdot l,}

where ρA is the average area density, m is the total mass of the object, A is the total area of the object, ρ is the average density, and l is the average thickness of the object.

Column density

A special type of area density is called column density (also columnar mass density or simply column density), denoted ρA or σ. It is the mass of substance per unit area integrated along a path; It is obtained integrating volumetric density

ρ

{\displaystyle \rho }

over a column:

σ

=

∫

ρ

d

s

.

{\displaystyle \sigma =\int \rho \,\mathrm {d} s.}

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:

σ

=

∫

ρ

d

z

,

{\displaystyle \sigma =\int \rho \,\mathrm {d} z,}

where

z

{\displaystyle z}

denotes the vertical coordinate (e.g., height or depth).