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href="#Fabric"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.5</span> <span>Fabric</span> </div> </a> <ul id="toc-Fabric-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Other" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Other"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.6</span> <span>Other</span> </div> </a> <ul id="toc-Other-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-See_also" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#See_also"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>See also</span> </div> </a> <ul id="toc-See_also-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-References" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#References"> <div class="vector-toc-text"> <span 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href="https://de.wikipedia.org/wiki/Massenbelegung" title="Massenbelegung – German" lang="de" hreflang="de" data-title="Massenbelegung" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Densidad_superficial" title="Densidad superficial – Spanish" lang="es" hreflang="es" data-title="Densidad superficial" data-language-autonym="Español" data-language-local-name="Spanish" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%DA%86%DA%AF%D8%A7%D9%84%DB%8C_%D8%B3%D8%B7%D8%AD" title="چگالی سطح – Persian" lang="fa" hreflang="fa" data-title="چگالی سطح" data-language-autonym="فارسی" data-language-local-name="Persian" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Masse_surfacique" title="Masse surfacique – French" lang="fr" hreflang="fr" data-title="Masse surfacique" data-language-autonym="Français" data-language-local-name="French" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Oppervlaktemassa" title="Oppervlaktemassa – Dutch" lang="nl" hreflang="nl" data-title="Oppervlaktemassa" data-language-autonym="Nederlands" data-language-local-name="Dutch" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Arealvekt" title="Arealvekt – Norwegian Bokmål" lang="nb" hreflang="nb" data-title="Arealvekt" data-language-autonym="Norsk bokmål" data-language-local-name="Norwegian Bokmål" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Maydon_zichligi" title="Maydon zichligi – Uzbek" lang="uz" hreflang="uz" data-title="Maydon zichligi" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="Uzbek" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Gramatura" title="Gramatura – Polish" lang="pl" hreflang="pl" data-title="Gramatura" data-language-autonym="Polski" data-language-local-name="Polish" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Densidade_de_%C3%A1rea" title="Densidade de área – Portuguese" lang="pt" hreflang="pt" data-title="Densidade de área" data-language-autonym="Português" data-language-local-name="Portuguese" class="interlanguage-link-target"><span>Português</span></a></li><li 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.hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">This article is about the property of two-dimensional objects. For other uses, see <a href="/wiki/Density_(disambiguation)" class="mw-disambig" title="Density (disambiguation)">Density (disambiguation)</a>.</div> <style data-mw-deduplicate="TemplateStyles:r1257001546">.mw-parser-output .infobox-subbox{padding:0;border:none;margin:-3px;width:auto;min-width:100%;font-size:100%;clear:none;float:none;background-color:transparent}.mw-parser-output .infobox-3cols-child{margin:auto}.mw-parser-output .infobox .navbar{font-size:100%}@media screen{html.skin-theme-clientpref-night .mw-parser-output .infobox-full-data:not(.notheme)>div:not(.notheme)[style]{background:#1f1f23!important;color:#f8f9fa}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .infobox-full-data:not(.notheme) div:not(.notheme){background:#1f1f23!important;color:#f8f9fa}}@media(min-width:640px){body.skin--responsive .mw-parser-output .infobox-table{display:table!important}body.skin--responsive .mw-parser-output .infobox-table>caption{display:table-caption!important}body.skin--responsive .mw-parser-output .infobox-table>tbody{display:table-row-group}body.skin--responsive .mw-parser-output .infobox-table tr{display:table-row!important}body.skin--responsive .mw-parser-output .infobox-table th,body.skin--responsive .mw-parser-output .infobox-table td{padding-left:inherit;padding-right:inherit}}</style><table class="infobox"><tbody><tr><th colspan="2" class="infobox-above">Area density</th></tr><tr><th scope="row" class="infobox-label"><div style="display: inline-block; line-height: 1.2em; padding: .1em 0;">Common symbols</div></th><td class="infobox-data"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rho _{A}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho _{A}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/32af5b17c837d7a6b93c13248569c555327e5542" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:2.667ex; height:2.176ex;" alt="{\displaystyle \rho _{A}}"></span></td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/SI_unit" class="mw-redirect" title="SI unit">SI unit</a></th><td class="infobox-data">kg/m<sup>2</sup></td></tr><tr><th scope="row" class="infobox-label">In <a href="/wiki/SI_base_unit" title="SI base unit"><span class="wrap">SI base units</span></a></th><td class="infobox-data">m<sup>−2</sup>⋅kg</td></tr><tr><th scope="row" class="infobox-label"><div style="display: inline-block; line-height: 1.2em; padding: .1em 0;">Derivations from<br />other quantities</div></th><td class="infobox-data"><style data-mw-deduplicate="TemplateStyles:r1126788409">.mw-parser-output .plainlist ol,.mw-parser-output .plainlist ul{line-height:inherit;list-style:none;margin:0;padding:0}.mw-parser-output .plainlist ol li,.mw-parser-output .plainlist ul li{margin-bottom:0}</style><div class="plainlist"><ul><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rho _{A}={\frac {m}{A}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>m</mi> <mi>A</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho _{A}={\frac {m}{A}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a6a41cb07e027a7020b5d7897d3c4af77c0a145c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:8.642ex; height:4.843ex;" alt="{\displaystyle \rho _{A}={\frac {m}{A}}}"></span></li><li><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rho _{A}=\rho l}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> <mo>=</mo> <mi>ρ</mi> <mi>l</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho _{A}=\rho l}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6bfd3ae32aa6594773d943d8627ea756a6c088e1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.66ex; height:2.676ex;" alt="{\displaystyle \rho _{A}=\rho l}"></span></li></ul></div></td></tr><tr><th scope="row" class="infobox-label"><a href="/wiki/Dimensional_analysis#Formulation" title="Dimensional analysis">Dimension</a></th><td class="infobox-data"><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\mathsf {L}}^{-2}{\mathsf {M}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="sans-serif">L</mi> </mrow> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mo>−</mo> <mn>2</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="sans-serif">M</mi> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\mathsf {L}}^{-2}{\mathsf {M}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/50a5d1127c8d9ca20a8d93a983ebe64cca3586da" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.626ex; height:2.676ex;" alt="{\displaystyle {\mathsf {L}}^{-2}{\mathsf {M}}}"></span></td></tr></tbody></table> <p>The <b>area density</b> (also known as <b>areal density</b>, <b>surface density</b>, <b>superficial density</b>, <b>areic density</b>, <b>mass thickness</b>, <b>column density</b>, or <b>density thickness</b>) of a two-dimensional object is calculated as the <a href="/wiki/Mass" title="Mass">mass</a> per unit <a href="/wiki/Area" title="Area">area</a>. The <a href="/wiki/SI_derived_unit" title="SI derived unit">SI derived unit</a> is the "<a href="/wiki/Kilogram" title="Kilogram">kilogram</a> per <a href="/wiki/Square_metre" title="Square metre">square metre</a>" (kg·m<sup>−2</sup>). </p><p>In the paper and fabric industries, it is called <a href="/wiki/Grammage" title="Grammage">grammage</a> and is expressed in grams per square meter (g/m<sup>2</sup>); for paper in particular, it may be expressed as pounds per <a href="/wiki/Paper_ream" class="mw-redirect" title="Paper ream">ream</a> of standard sizes ("basis ream"). </p><p>A related <i><a href="/wiki/Area_number_density" class="mw-redirect" title="Area number density">area number density</a></i> can be defined by replacing mass by <a href="/wiki/Number_of_particles" class="mw-redirect" title="Number of particles">number of particles</a> or other <a href="/wiki/Countable_quantity" class="mw-redirect" title="Countable quantity">countable quantity</a>, with resulting units of m<sup>−2</sup>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Formulation">Formulation</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Area_density&action=edit&section=1" title="Edit section: Formulation"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Area density can be calculated as: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rho _{A}={\frac {m}{A}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>m</mi> <mi>A</mi> </mfrac> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho _{A}={\frac {m}{A}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a6a41cb07e027a7020b5d7897d3c4af77c0a145c" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:8.642ex; height:4.843ex;" alt="{\displaystyle \rho _{A}={\frac {m}{A}}}"></span> or <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rho _{A}=\rho \cdot l,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> <mo>=</mo> <mi>ρ</mi> <mo>⋅</mo> <mi>l</mi> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho _{A}=\rho \cdot l,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/78bac1ce0271256135a11ad742c14727019cded1" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:9.986ex; height:2.676ex;" alt="{\displaystyle \rho _{A}=\rho \cdot l,}"></span> where <i><span class="texhtml">ρ<sub>A</sub></span></i> is the average area density, <i><span class="texhtml">m</span></i> is the total mass of the object, <i><span class="texhtml">A</span></i> is the total area of the object, <i><span class="texhtml">ρ</span></i> is the average <a href="/wiki/Density" title="Density">density</a>, and <i><span class="texhtml">l</span></i> is the average thickness of the object. </p> <div class="mw-heading mw-heading2"><h2 id="Column_density">Column density</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Area_density&action=edit&section=2" title="Edit section: Column density"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A special type of area density is called <i>column density</i> (also <i>columnar mass density</i> or simply <i>column density</i>), denoted <i>ρ</i><sub>A</sub> or <i>σ</i>. It is the <a href="/wiki/Mass" title="Mass">mass</a> of <a href="/wiki/Chemical_substance" title="Chemical substance">substance</a> per unit <a href="/wiki/Area" title="Area">area</a> <a href="/wiki/Integral" title="Integral">integrated</a> along a path;<sup id="cite_ref-Boeker_vanGrondelle2000_1-0" class="reference"><a href="#cite_note-Boeker_vanGrondelle2000-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> It is obtained integrating <a href="/wiki/Density" title="Density">volumetric density</a> <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rho }"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>ρ</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho }</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1f7d439671d1289b6a816e6af7a304be40608d64" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.202ex; height:2.176ex;" alt="{\displaystyle \rho }"></span> over a column:<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sigma =\int \rho \,\mathrm {d} s.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>σ</mi> <mo>=</mo> <mo>∫</mo> <mi>ρ</mi> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>s</mi> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sigma =\int \rho \,\mathrm {d} s.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f6f680f66dc30093926f20cb729ff082152389ad" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:11.628ex; height:5.676ex;" alt="{\displaystyle \sigma =\int \rho \,\mathrm {d} s.}"></span> </p><p>In general the integration path can be slant or oblique incidence (as in, for example, <a href="/wiki/Line_of_sight_propagation" class="mw-redirect" title="Line of sight propagation">line of sight propagation</a> in <a href="/wiki/Atmospheric_physics" title="Atmospheric physics">atmospheric physics</a>). A common special case is a vertical path, from the bottom to the top of the medium: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sigma =\int \rho \,\mathrm {d} z,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>σ</mi> <mo>=</mo> <mo>∫</mo> <mi>ρ</mi> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>z</mi> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sigma =\int \rho \,\mathrm {d} z,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f87baed1e40faba270ebe5cb10697369593b47da" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:11.625ex; height:5.676ex;" alt="{\displaystyle \sigma =\int \rho \,\mathrm {d} z,}"></span> where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle z}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>z</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle z}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bf368e72c009decd9b6686ee84a375632e11de98" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.088ex; height:1.676ex;" alt="{\displaystyle z}"></span> denotes the vertical coordinate (e.g., height or depth). </p><p>Columnar density <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rho _{A}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho _{A}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/32af5b17c837d7a6b93c13248569c555327e5542" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:2.667ex; height:2.176ex;" alt="{\displaystyle \rho _{A}}"></span> is closely related to the vertically averaged volumetric density <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\bar {\rho }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>ρ</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\bar {\rho }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f84e8286bd1f258e03bf38271584df9cd8575a93" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.376ex; height:2.509ex;" alt="{\displaystyle {\bar {\rho }}}"></span> as <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\bar {\rho }}={\frac {\rho _{A}}{\Delta z}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>ρ</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> <mrow> <mi mathvariant="normal">Δ</mi> <mi>z</mi> </mrow> </mfrac> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\bar {\rho }}={\frac {\rho _{A}}{\Delta z}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/68370af8d583cc181123a0a147afb2ee83ed9d64" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.005ex; width:8.981ex; height:5.009ex;" alt="{\displaystyle {\bar {\rho }}={\frac {\rho _{A}}{\Delta z}},}"></span> where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\textstyle \Delta z=\int 1\,\mathrm {d} z}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="false" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>z</mi> <mo>=</mo> <mo>∫</mo> <mn>1</mn> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>z</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\textstyle \Delta z=\int 1\,\mathrm {d} z}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/087ce45770ea88adc192ad08e3a80759a41834da" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:11.858ex; height:3.176ex;" alt="{\textstyle \Delta z=\int 1\,\mathrm {d} z}"></span>; <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\bar {\rho }}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mrow class="MJX-TeXAtom-ORD"> <mover> <mi>ρ</mi> <mo stretchy="false">¯</mo> </mover> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\bar {\rho }}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f84e8286bd1f258e03bf38271584df9cd8575a93" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:1.376ex; height:2.509ex;" alt="{\displaystyle {\bar {\rho }}}"></span>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \rho _{A}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>A</mi> </mrow> </msub> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \rho _{A}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/32af5b17c837d7a6b93c13248569c555327e5542" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:2.667ex; height:2.176ex;" alt="{\displaystyle \rho _{A}}"></span>, and <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \Delta z}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">Δ</mi> <mi>z</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \Delta z}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/cf59b5e4dc02e6b2b89b426a27e02c84861c0caa" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:3.024ex; height:2.176ex;" alt="{\displaystyle \Delta z}"></span> have units of, for example, grams per cubic metre, grams per square metre, and metres, respectively. </p> <div class="mw-heading mw-heading2"><h2 id="Usage">Usage</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Area_density&action=edit&section=3" title="Edit section: Usage"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Atmospheric_physics">Atmospheric physics</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Area_density&action=edit&section=4" title="Edit section: Atmospheric physics"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>It is a quantity commonly retrieved by <a href="/wiki/Remote_sensing" title="Remote sensing">remote sensing</a> instruments, for instance the <a href="/wiki/Total_Ozone_Mapping_Spectrometer" title="Total Ozone Mapping Spectrometer">Total Ozone Mapping Spectrometer</a> (TOMS) which retrieves ozone columns around the globe. Columns are also returned by the <a href="/wiki/Differential_absorption_spectroscopy" class="mw-redirect" title="Differential absorption spectroscopy">differential optical absorption spectroscopy (DOAS)</a> method<sup id="cite_ref-Sinreich_etal2008_3-0" class="reference"><a href="#cite_note-Sinreich_etal2008-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup> and are a common retrieval product from <a href="/wiki/Nadir" title="Nadir">nadir</a>-looking <a href="/wiki/Microwave" title="Microwave">microwave</a> <a href="/wiki/Radiometers" class="mw-redirect" title="Radiometers">radiometers</a>.<sup id="cite_ref-Melseimer_Heygster2008_4-0" class="reference"><a href="#cite_note-Melseimer_Heygster2008-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-Melseimer_etal2009_5-0" class="reference"><a href="#cite_note-Melseimer_etal2009-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> </p><p>A closely related concept is that of ice or <a href="/wiki/Liquid_water_path" title="Liquid water path">liquid water path</a>, which specifies the volume per unit area or depth instead of mass per unit area, thus the two are related: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle P={\frac {\sigma }{\rho _{0}}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>P</mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mi>σ</mi> <msub> <mi>ρ</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>0</mn> </mrow> </msub> </mfrac> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle P={\frac {\sigma }{\rho _{0}}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/49301f14d3a2c99d3367b39bc89e6b5a0f725397" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:8.583ex; height:5.176ex;" alt="{\displaystyle P={\frac {\sigma }{\rho _{0}}}.}"></span> </p><p>Another closely related concept is <a href="/wiki/Optical_depth" title="Optical depth">optical depth</a>. </p> <div class="mw-heading mw-heading3"><h3 id="Astronomy">Astronomy</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Area_density&action=edit&section=5" title="Edit section: Astronomy"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1251242444">.mw-parser-output .ambox{border:1px solid #a2a9b1;border-left:10px solid #36c;background-color:#fbfbfb;box-sizing:border-box}.mw-parser-output .ambox+link+.ambox,.mw-parser-output .ambox+link+style+.ambox,.mw-parser-output .ambox+link+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+style+.ambox,.mw-parser-output .ambox+.mw-empty-elt+link+link+.ambox{margin-top:-1px}html body.mediawiki .mw-parser-output .ambox.mbox-small-left{margin:4px 1em 4px 0;overflow:hidden;width:238px;border-collapse:collapse;font-size:88%;line-height:1.25em}.mw-parser-output .ambox-speedy{border-left:10px solid #b32424;background-color:#fee7e6}.mw-parser-output .ambox-delete{border-left:10px solid #b32424}.mw-parser-output .ambox-content{border-left:10px solid #f28500}.mw-parser-output .ambox-style{border-left:10px solid #fc3}.mw-parser-output .ambox-move{border-left:10px solid #9932cc}.mw-parser-output .ambox-protection{border-left:10px solid #a2a9b1}.mw-parser-output .ambox .mbox-text{border:none;padding:0.25em 0.5em;width:100%}.mw-parser-output .ambox .mbox-image{border:none;padding:2px 0 2px 0.5em;text-align:center}.mw-parser-output .ambox .mbox-imageright{border:none;padding:2px 0.5em 2px 0;text-align:center}.mw-parser-output .ambox .mbox-empty-cell{border:none;padding:0;width:1px}.mw-parser-output .ambox .mbox-image-div{width:52px}@media(min-width:720px){.mw-parser-output .ambox{margin:0 10%}}@media print{body.ns-0 .mw-parser-output .ambox{display:none!important}}</style><table class="box-Expand_section plainlinks metadata ambox mbox-small-left ambox-content" role="presentation"><tbody><tr><td class="mbox-image"><span typeof="mw:File"><a href="/wiki/File:Wiki_letter_w_cropped.svg" class="mw-file-description"><img alt="[icon]" src="//upload.wikimedia.org/wikipedia/commons/thumb/1/1c/Wiki_letter_w_cropped.svg/20px-Wiki_letter_w_cropped.svg.png" decoding="async" width="20" height="14" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/1c/Wiki_letter_w_cropped.svg/30px-Wiki_letter_w_cropped.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/1c/Wiki_letter_w_cropped.svg/40px-Wiki_letter_w_cropped.svg.png 2x" data-file-width="44" data-file-height="31" /></a></span></td><td class="mbox-text"><div class="mbox-text-span">This section <b>needs expansion</b>. You can help by <a class="external text" href="https://en.wikipedia.org/w/index.php?title=Area_density&action=edit&section=">adding to it</a>. <span class="date-container"><i>(<span class="date">August 2015</span>)</i></span></div></td></tr></tbody></table> <p>In astronomy, the column density is generally used to indicate the number of atoms or molecules per square cm (cm<sup>2</sup>) along the line of sight in a particular direction, as derived from observations of e.g. the 21-cm <a href="/wiki/Hydrogen_line" title="Hydrogen line">hydrogen line</a> or from observations of a certain molecular species. Also the <a href="/wiki/Extinction_(astronomy)" title="Extinction (astronomy)">interstellar extinction</a> can be related to the column density of H or H<sub>2</sub>.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> </p><p>The concept of area density can be useful when analysing <a href="/wiki/Accretion_disk" title="Accretion disk">accretion disks</a>. 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 <a href="/wiki/Mass" title="Mass">mass</a> of <a href="/wiki/Chemical_substance" title="Chemical substance">substance</a> per unit <a href="/wiki/Area" title="Area">area</a> <a href="/wiki/Integral" title="Integral">integrated</a> along the vertical path that goes through the disk <a href="/wiki/Sightline" class="mw-redirect" title="Sightline">(line-of-sight)</a>, from the bottom to the top of the medium: </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \sigma =\int \rho \,\mathrm {d} z,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>σ</mi> <mo>=</mo> <mo>∫</mo> <mi>ρ</mi> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>z</mi> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \sigma =\int \rho \,\mathrm {d} z,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f87baed1e40faba270ebe5cb10697369593b47da" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:11.625ex; height:5.676ex;" alt="{\displaystyle \sigma =\int \rho \,\mathrm {d} z,}"></span> </p><p>where <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle z}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>z</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle z}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bf368e72c009decd9b6686ee84a375632e11de98" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.088ex; height:1.676ex;" alt="{\displaystyle z}"></span> 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): </p><p><span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle N=\int n\,\mathrm {d} z.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>N</mi> <mo>=</mo> <mo>∫</mo> <mi>n</mi> <mspace width="thinmathspace" /> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">d</mi> </mrow> <mi>z</mi> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle N=\int n\,\mathrm {d} z.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/897454211355806eb1a6288a17d01a08cef8bc6e" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.338ex; width:12.552ex; height:5.676ex;" alt="{\displaystyle N=\int n\,\mathrm {d} z.}"></span> </p> <div class="mw-heading mw-heading3"><h3 id="Data_storage_media">Data storage media</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Area_density&action=edit&section=6" title="Edit section: Data storage media"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Areal_density_(computer_storage)" class="mw-redirect" title="Areal density (computer storage)">Areal density (computer storage)</a></div> <p>Areal density is used to quantify and compare different types media used in data storage devices such as <a href="/wiki/Hard_disk_drives" class="mw-redirect" title="Hard disk drives">hard disk drives</a>, <a href="/wiki/Optical_disc" title="Optical disc">optical disc drives</a> and <a href="/wiki/Tape_drives" class="mw-redirect" title="Tape drives">tape drives</a>. The current unit of measure is typically gigabits per square inch.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading3"><h3 id="Paper">Paper</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Area_density&action=edit&section=7" title="Edit section: Paper"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Grammage" title="Grammage">grammage</a></div> <p>The area density is often used to describe the thickness of paper; e.g., 80 g/m<sup>2</sup> is very common. </p> <div class="mw-heading mw-heading3"><h3 id="Fabric">Fabric</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Area_density&action=edit&section=8" title="Edit section: Fabric"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/Grammage" title="Grammage">grammage</a></div> <p>Fabric "weight" is often specified as mass per unit area, grams per square meter (gsm) or <a href="/wiki/Ounce" title="Ounce">ounces</a> 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. </p> <div class="mw-heading mw-heading3"><h3 id="Other">Other</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Area_density&action=edit&section=9" title="Edit section: Other"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>It is also an important quantity for the <a href="/wiki/Absorption_(electromagnetic_radiation)" title="Absorption (electromagnetic radiation)">absorption of radiation</a>. </p><p>When studying bodies falling through air, area density is important because resistance depends on area, and gravitational force is dependent on mass. </p><p><a href="/wiki/Bone_density" title="Bone density">Bone density</a> is often expressed in grams per square centimeter (g·cm<sup>−2</sup>) as measured by x-ray absorptiometry, as a proxy for the actual density. </p><p>The <a href="/wiki/Body_mass_index" title="Body mass index">body mass index</a> is expressed in units of kilograms per square meter, though the area figure is nominal, being the square of the height. </p><p>The <a href="/wiki/Total_electron_content" title="Total electron content">total electron content</a> in the ionosphere is a quantity of type columnar number density. </p><p><a href="/wiki/Snow_water_equivalent" class="mw-redirect" title="Snow water equivalent">Snow water equivalent</a> is a quantity of type columnar mass density. </p> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Area_density&action=edit&section=10" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Areic_quantity" class="mw-redirect" title="Areic quantity">Areic quantity</a></li> <li><a href="/wiki/Linear_density" title="Linear density">Linear density</a></li> <li><a href="/wiki/Paper_density" title="Paper density">Paper density</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Area_density&action=edit&section=11" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-Boeker_vanGrondelle2000-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-Boeker_vanGrondelle2000_1-0">^</a></b></span> <span class="reference-text"> <style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite id="CITEREFEgbert_BoekerRienk_van_Grondelle2000" class="citation book cs1">Egbert Boeker; Rienk van Grondelle (2000). <i>Environmental Physics</i> (2nd ed.). Wiley.</cite><span title="ctx_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&rft.genre=book&rft.btitle=Environmental+Physics&rft.edition=2nd&rft.pub=Wiley&rft.date=2000&rft.au=Egbert+Boeker&rft.au=Rienk+van+Grondelle&rfr_id=info%3Asid%2Fen.wikipedia.org%3AArea+density" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFVisconti2001" class="citation book cs1">Visconti, Guido (2001). <i>Fundamentals of physics and chemistry of the atmosphere</i>. 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