Areal 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


ρA = average area density
m = total mass of the object
A = total area of the object
ρ = average density
l = average thickness of the object

Column density

A special type of area density is called column (mass) density (also columnar mass density), denoted ρA or σ. It is the mass of substance per unit area integrated along a path; [1] It is obtained integrating volumetric density \rho over a column:[2]

\sigma=\int \rho \; \mathrm d s.

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

\sigma = \int \rho \; dz

where z denotes the vertical coordinate (e.g., height or depth). 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., grams per cubic metre, grams per square metre, and metres, respectively.

Column number density

Column number density refers instead to a number density type of quantity: the number or count of a substance -- rather than the mass -- per unit area integrated along a path:

N=\int n \; \mathrm d s.


Atmospheric physics

It is a quantity commonly retrieved by remote sensing instruments, for instance the Total Ozone Mapping Spectrometer (TOMS) which retrieves ozone columns around the globe. Columns are also returned by the differential optical absorption spectroscopy (DOAS) method [3] and are a common retrieval product from nadir-looking microwave radiometers. [4] [5]

A closely related concept is that of ice or liquid water path, which specifies the volume per unit area or depth instead of mass per unit area, thus the two are related:

P = \frac{\sigma}{\rho_0} ,

Another closely related concept is optical depth.



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.

Bone density may be measured in grams per square centimetre (g·cm−2).

The body mass index is in terms of area density.

The total electron content in the ionosphere is a quantity of type columnar number density.

Snow water equivalent is a quantity of type columnar mass density.

See also


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