Area density

This article is about the property of two-dimensional objects. For other uses, seeDensity (disambiguation).

Thearea density(also known asareal density,surface density,superficial density,areic density,mass thickness,column density,ordensity thickness) of a two-dimensional object is calculated as themassper unitarea.TheSI derived unitis the "kilogrampersquare metre"(kg·m⁻²).

Area density
Common symbols	$\rho _{A}$
SI unit	kg/m2
InSI base units	m−2⋅kg
Derivations from other quantities	$\rho _{A}={\frac {m}{A}}$ $\rho _{A}=\rho l$
Dimension	${\mathsf {L}}^{-2}{\mathsf {M}}$

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

A relatedarea number densitycan be defined by replacing mass bynumber of particlesor othercountable quantity,with resulting units of m⁻².

Formulation

Area density can be calculated as: $$\rho _{A}={\frac {m}{A}}$$ or $$\rho _{A}=\rho \cdot l,$$ whereρ_Ais the average area density,mis the total mass of the object,Ais the total area of the object,ρis the averagedensity,andlis the average thickness of the object.

Column density

A special type of area density is calledcolumn density(alsocolumnar mass densityor simplycolumn density), denotedρ_Aorσ.It is themassofsubstanceper unitareaintegratedalong a path;It is obtained integratingvolumetric density$\rho$over a column: $$\sigma =\int \rho \,\mathrm {d} s.$$

In general the integration path can be slant or oblique incidence (as in, for example,line of sight propagationinatmospheric physics). A common special case is a vertical path, from the bottom to the top of the medium: $$\sigma =\int \rho \,\mathrm {d} z,$$ 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 $${\bar {\rho }}={\frac {\rho _{A}}{\Delta z}},$$ where${\textstyle \Delta z=\int 1\,\mathrm {d} z}$;${\bar {\rho }}$,$\rho _{A}$,and$\Delta z$have units of, for example, grams per cubic metre, grams per square metre, and metres, respectively.

Usage

Atmospheric physics

It is a quantity commonly retrieved byremote sensinginstruments, for instance theTotal Ozone Mapping Spectrometer(TOMS) which retrieves ozone columns around the globe. Columns are also returned by thedifferential optical absorption spectroscopy (DOAS)methodand are a common retrieval product fromnadir-lookingmicrowaveradiometers.

A closely related concept is that of ice orliquid 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 isoptical depth.

Astronomy

In astronomy, the column density is generally used to indicate the number of atoms or molecules per square cm (cm²) along the line of sight in a particular direction, as derived from observations of e.g. the 21-cmhydrogen lineor from observations of a certain molecular species. Also theinterstellar extinctioncan be related to the column density of H or H₂.

The concept of area density can be useful when analysingaccretion disks.In the case of a disk seen face-on, area density for a given area of the disk is defined as column density: that is, either as themassofsubstanceper unitareaintegratedalong the vertical path that goes through the disk(line-of-sight),from the bottom to the top of the medium:

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

where$z$denotes the vertical coordinate (e.g., height or depth), or as the number or count of a substance—rather than the mass—per unit area integrated along a path (column number density):

$$N=\int n\,\mathrm {d} z.$$

Data storage media

Main article:Areal density (computer storage)

Areal density is used to quantify and compare different types media used in data storage devices such ashard disk drives,optical disc drivesandtape drives.The current unit of measure is typically gigabits per square inch.

Paper

Main article:grammage

The area density is often used to describe the thickness of paper; e.g., 80 g/m²is very common.

Fabric

Main article:grammage

Fabric "weight" is often specified as mass per unit area, grams per square meter (gsm) orouncesper square yard. It is also sometimes specified in ounces per yard in a standard width for the particular cloth. One gram per square meter equals 0.0295 ounces per square yard; one ounce per square yard equals 33.9 grams per square meter.

Other

It is also an important quantity for theabsorption 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 densityis often expressed in grams per square centimeter (g·cm⁻²) as measured by x-ray absorptiometry, as a proxy for the actual density.

Thebody mass indexis expressed in units of kilograms per square meter, though the area figure is nominal, being the square of the height.

Thetotal electron contentin the ionosphere is a quantity of type columnar number density.

Snow water equivalentis a quantity of type columnar mass density.

See also

• Areic quantity
• Linear density
• Paper density