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SurfaceArea—Wolfram Language Documentation

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BUILT-IN SYMBOL

SurfaceArea[reg]

gives the surface area of the three-dimensional region reg.

SurfaceArea[{x₁,…,x_n},{s,s_min,s_smax},{t,t_min,t_max},{u,u_min,u_max}]

gives the surface area of the parametrized region whose Cartesian coordinates x_i are functions of s, t, u.

SurfaceArea[{x₁,…,x_n},{s,s_min,s_smax},{t,t_min,t_max},{u,u_min,u_max},chart]

interprets the x_i as coordinates in the specified coordinate chart.

Details and Options

A three-dimensional region can be embedded in any dimension greater than or equal to three.
In SurfaceArea[x,{s,s_min,s_smax},{t,t_min,t_max},{u,u_min,u_max}], if x is a scalar, SurfaceArea returns the surface area of the parametric three-region {s,t,u,x}.
Coordinate charts in the fifth argument of SurfaceArea can be specified as triples {coordsys,metric,dim} in the same way as in the first argument of CoordinateChartData. The short form in which dim is omitted may be used.
The following options can be given:

Examplesopen allclose all Basic Examples (2)

The surface area of a unit ball in 3D:

The surface area of a standard simplex in 3D:

Scope (12) Formula Regions (1)

The surface area of a ball represented as an ImplicitRegion:

A cylinder:

Wolfram Research (2019), SurfaceArea, Wolfram Language function, https://reference.wolfram.com/language/ref/SurfaceArea.html. Text Wolfram Research (2019), SurfaceArea, Wolfram Language function, https://reference.wolfram.com/language/ref/SurfaceArea.html.CMS Wolfram Language. 2019. "SurfaceArea." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/SurfaceArea.html.APA Wolfram Language. (2019). SurfaceArea. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/SurfaceArea.htmlBibTeX @misc{reference.wolfram_2025_surfacearea, author="Wolfram Research", title="{SurfaceArea}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/SurfaceArea.html}", note=[Accessed: 11-July-2025 ]}BibLaTeX @online{reference.wolfram_2025_surfacearea, organization={Wolfram Research}, title={SurfaceArea}, year={2019}, url={https://reference.wolfram.com/language/ref/SurfaceArea.html}, note=[Accessed: 11-July-2025 ]}

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