Area density

For computer memory comparisons, see computer storage density. For other meanings, see Density (disambiguation)

The area density (also known as areal density, surface density, or superficial density) 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:

$\rho_A = \frac {M} {A}$

$\rho_A = \rho \cdot l$

where

ρ_A	= average area density
M	= total mass of the object
A	= total area of the object
ρ	= average density
l	= average thickness of the object

A special type of area density is called columnar density; it is obtained integrating volumetric density $\rho$ over a vertical column:^[1]

$\rho_A = \int \rho \; dz,$

where $z$ denotes the vertical coordinate (e.g., height or depth). An example is the Dobson unit for atmospheric ozone. Columnar density $\rho_A$ is closely related to the vertically averaged volumetric density $\bar{\rho}$ as

$\bar{\rho} = \rho_A / \Delta z,$

where $\Delta z = \int 1 \; dz$ ; notice that $\bar{\rho}$ , $\rho_A$ , and $\Delta z$ have units of, e.g., g/m³, g/m², and m, respectively.

Usage

The area density is often used to describe the thickness of paper, e.g. 80 g/m² is very common. It is also an important quantity for the absorption of radiation. When studying bodies falling through air, area density is important because resistance depends on area, and gravitational force is dependent on mass.

The Body mass index is in terms of area density.

References

^ Visconti, Guido (2001). Fundamentals of physics and chemistry of the atmosphere. Berlin: Springer. pp. 470. ISBN 978-3-540-67420-7.