# Area density

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Mass per unit area

This article is about the property of two-dimensional objects. For other uses, see [Density (disambiguation)](/source/Density_(disambiguation)).

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

The **area density** (also known as **areal density**, **surface density**, **superficial density**, **column density**, or **density thickness**) of a [two-dimensional](/source/Two-dimensional) object is defined as the [quotient](/source/Quotient) of [mass](/source/Mass) by [area](/source/Area). The [SI derived unit](/source/SI_derived_unit) is the "[kilogram](/source/Kilogram) per [square metre](/source/Square_metre)" ([unit symbol](/source/Unit_symbol) kg·m−2).

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

A generalized **areic quantity** is defined as the quotient of a generic [physical quantity](/source/Physical_quantity) by area,[1] such as [surface charge density](/source/Surface_charge_density) or areic electric charge.[2] A related *[area number density](/source/Area_number_density)* can be defined by replacing mass by [number of particles](/source/Number_of_particles) or other [countable quantity](/source/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](/source/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 *ρ*A or *σ*. It is the [mass](/source/Mass) of [substance](/source/Chemical_substance) per unit [area](/source/Area) [integrated](/source/Integral) along a path;[3] It is obtained integrating [volumetric density](/source/Density) ρ {\displaystyle \rho } over a column:[4] 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](/source/Line_of_sight_propagation) in [atmospheric physics](/source/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).

Columnar density ρ A {\displaystyle \rho _{A}} is closely related to the vertically averaged volumetric density ρ ¯ {\displaystyle {\bar {\rho }}} as ρ ¯ = ρ A Δ z , {\displaystyle {\bar {\rho }}={\frac {\rho _{A}}{\Delta z}},} where Δ z = ∫ 1 d z {\textstyle \Delta z=\int 1\,\mathrm {d} z} ; ρ ¯ {\displaystyle {\bar {\rho }}} , ρ A {\displaystyle \rho _{A}} , and Δ z {\displaystyle \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 by [remote sensing](/source/Remote_sensing) instruments, such as the [Total Ozone Mapping Spectrometer](/source/Total_Ozone_Mapping_Spectrometer) (TOMS), which retrieves ozone columns around the globe. Columns are also returned by the [differential optical absorption spectroscopy (DOAS)](/source/Differential_absorption_spectroscopy) method[5] and are a common retrieval product from [nadir](/source/Nadir)-looking [microwave](/source/Microwave) [radiometers](/source/Radiometers).[6][7]

A closely related concept is that of ice or [liquid water path](/source/Liquid_water_path), which specifies the volume per unit area or depth instead of mass per unit area, so the two are related: P = σ ρ 0 . {\displaystyle P={\frac {\sigma }{\rho _{0}}}.}

Another closely related concept is [optical depth](/source/Optical_depth).

### Astronomy

This section needs expansion. You can help by adding missing information. (August 2015)

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 cm [hydrogen line](/source/Hydrogen_line) or from observations of a certain molecular species. Also the [interstellar extinction](/source/Extinction_(astronomy)) can be related to the column density of H or H2.[8]

The concept of area density can be useful when analysing [accretion disks](/source/Accretion_disk). 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 the [mass](/source/Mass) of [substance](/source/Chemical_substance) per unit [area](/source/Area) [integrated](/source/Integral) along the vertical path that goes through the disk [(line-of-sight)](/source/Sightline), 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), or as the number or count of a substance—rather than the mass—per unit area integrated along a path (column number density):

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

### Data storage media

Main article: [Areal density (computer storage)](/source/Areal_density_(computer_storage))

Areal density is used to quantify and compare different types media used in data storage devices such as [hard disk drives](/source/Hard_disk_drives), [optical disc drives](/source/Optical_disc) and [tape drives](/source/Tape_drives). The current unit of measure is typically gigabits per square inch.[9]

### Paper

Main article: [grammage](/source/Grammage)

The area density is often used to describe the thickness of paper; e.g., 80 g/m2 is very common.

### Fabric

Main article: [grammage](/source/Grammage)

Fabric "weight" is often specified as mass per unit area, grams per square meter (gsm) or [ounces](/source/Ounce) per 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 the [absorption of radiation](/source/Absorption_(electromagnetic_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](/source/Bone_density) is often expressed in grams per square centimeter (g·cm−2) as measured by x-ray absorptiometry, as a proxy for the actual density.

The [body mass index](/source/Body_mass_index) is expressed in units of kilograms per square meter, though the area figure is nominal, being the square of the height.

The [total electron content](/source/Total_electron_content) in the ionosphere is a quantity of type columnar number density.

[Snow water equivalent](/source/Snow_water_equivalent) is a quantity of type columnar mass density.

## Generalization: areic quantities

The qualifier ***areic*** is recommended in the [International System of Quantities](/source/International_System_of_Quantities) ([ISO 80000-1](/source/ISO_80000-1)) to denote the quotient of any [physical quantity](/source/Physical_quantity) by area.[1] The expressions "per unit area" or "surface ... density" (or simply "density") are also often used, with resulting units involving [reciprocal](/source/Multiplicative_inverse) square metre (m−2), for example:

- surface mass density or areic mass[1][10]

- volume per area or areic volume, as in [rainfall](/source/Rainfall)[1]

- [surface charge density](/source/Surface_charge_density) or areic electric charge, electric charge per unit area[1][2]

- [surface current density](/source/Surface_current_density) or areic electric current, the quotient of [electric current](/source/Electric_current) to area[2]

- surface [magnetic flux density](/source/Magnetic_flux_density) or areic magnetic flux[1]

- surface [activity](/source/Total_activity) density or areic activity[11]

- [heat flow rate](/source/Heat_flow_rate) density or areic heat flow rate[12]

- [surface power density](/source/Surface_power_density), power per unit area

- [specific surface energy](/source/Specific_surface_energy), free energy per unit surface are

## See also

- [Linear density](/source/Linear_density)

- [Paper density](/source/Paper_density)

## References

1. ^ [***a***](#cite_ref-ISO80000-1_1-0) [***b***](#cite_ref-ISO80000-1_1-1) [***c***](#cite_ref-ISO80000-1_1-2) [***d***](#cite_ref-ISO80000-1_1-3) [***e***](#cite_ref-ISO80000-1_1-4) [***f***](#cite_ref-ISO80000-1_1-5) ["ISO 80000-1: Quantities and units — Part 1: General"](https://www.iso.org/obp/ui/#iso:std:iso:80000:-1:ed-2:v1:en). *iso.org*. Retrieved 2023-10-16.

1. ^ [***a***](#cite_ref-ISO80000-6_2-0) [***b***](#cite_ref-ISO80000-6_2-1) [***c***](#cite_ref-ISO80000-6_2-2) ["IEC 80000-6:2022 Quantities and units — Part 6: Electromagnetism"](https://www.iso.org/standard/77846.html). [International Organization for Standardization](/source/International_Organization_for_Standardization). Retrieved 2022-11-20.

1. **[^](#cite_ref-Boeker_vanGrondelle2000_3-0)** Egbert Boeker; Rienk van Grondelle (2000). *Environmental Physics* (2nd ed.). Wiley.

1. **[^](#cite_ref-4)** Visconti, Guido (2001). *Fundamentals of physics and chemistry of the atmosphere*. Berlin: Springer. p. 470. [ISBN](/source/ISBN_(identifier)) [978-3-540-67420-7](https://en.wikipedia.org/wiki/Special:BookSources/978-3-540-67420-7).

1. **[^](#cite_ref-Sinreich_etal2008_5-0)** R. Sinreich; U. Frieß; T. Wagner; S. Yilmaz; U. Platt (2008). "Retrieval of Aerosol Distributions by Multi-Axis Differential Absorption Spectroscopy (MAX-DOAS)". *Nucleation and Atmospheric Aerosols*. pp. 1145–1149. [doi](/source/Doi_(identifier)):[10.1007/978-1-4020-6475-3_227](https://doi.org/10.1007%2F978-1-4020-6475-3_227). [ISBN](/source/ISBN_(identifier)) [978-1-4020-6474-6](https://en.wikipedia.org/wiki/Special:BookSources/978-1-4020-6474-6).

1. **[^](#cite_ref-Melseimer_Heygster2008_6-0)** C. Melsheimer; G. Heygster (2008). "Improved retrieval of total water vapor over polar regions from [AMSU](/source/Advanced_Microwave_Sounding_Unit)-B microwave radiometer data". *IEEE Trans. Geosci. Remote Sens*. **46** (8): 2307–2322. [Bibcode](/source/Bibcode_(identifier)):[2008ITGRS..46.2307M](https://ui.adsabs.harvard.edu/abs/2008ITGRS..46.2307M). [doi](/source/Doi_(identifier)):[10.1109/TGRS.2008.918013](https://doi.org/10.1109%2FTGRS.2008.918013). [S2CID](/source/S2CID_(identifier)) [20910677](https://api.semanticscholar.org/CorpusID:20910677).

1. **[^](#cite_ref-Melseimer_etal2009_7-0)** C. Melsheimer; G. Heygster; N. Mathew; L. Toudal Pedersen (2009). "Retrieval of Sea Ice Emissivity and Integrated Retrieval of Surface and Atmospheric Parameters over the Arctic from [AMSR](/source/AMSR)-E data". *Journal of the Remote Sensing Society of Japan*. Vol. 29, no. 1. pp. 236–241.

1. **[^](#cite_ref-8)** ["Column Density | COSMOS"](http://astronomy.swin.edu.au/cosmos/C/Column+Density).

1. **[^](#cite_ref-9)** ["Areal Density"](http://www.webopedia.com/TERM/A/areal_density.html). Webopedia. 3 March 1997. Retrieved April 9, 2014.

1. **[^](#cite_ref-80000-4:2019_10-0)** ["ISO 80000-4:2019 Quantities and units — Part 4: Mechanics"](https://www.iso.org/standard/64975.html). [International Organization for Standardization](/source/International_Organization_for_Standardization). Retrieved 2019-09-15.

1. **[^](#cite_ref-ISO80000-10_11-0)** ["ISO 80000-10:2019 Quantities and units — Part 10: Atomic and nuclear physics"](https://www.iso.org/standard/64980.html). [International Organization for Standardization](/source/International_Organization_for_Standardization). Retrieved 2019-09-15.

1. **[^](#cite_ref-ISO80000-14_12-0)** ["IEC 80000-14:2008 Quantities and units — Part 14: Telebiometrics related to human physiology"](https://www.iso.org/standard/43012.html). [International Organization for Standardization](/source/International_Organization_for_Standardization). Retrieved 2019-09-15.

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Adapted from the Wikipedia article [Area density](https://en.wikipedia.org/wiki/Area_density) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Area_density?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.