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SurfaceArea[reg]

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

SurfaceArea[{x1,…,xn},{s,smin,ssmax},{t,tmin,tmax},{u,umin,umax}]

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

SurfaceArea[{x1,…,xn},{s,smin,ssmax},{t,tmin,tmax},{u,umin,umax},chart]

interprets the xi as coordinates in the specified coordinate chart.

Details and Options
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Special Regions  
Formula Regions  
Mesh Regions  
Derived Regions  
CSG Regions  
Subdivision Regions  
See Also
Related Guides
History
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SurfaceArea

SurfaceArea[reg]

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

SurfaceArea[{x1,…,xn},{s,smin,ssmax},{t,tmin,tmax},{u,umin,umax}]

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

SurfaceArea[{x1,…,xn},{s,smin,ssmax},{t,tmin,tmax},{u,umin,umax},chart]

interprets the xi as coordinates in the specified coordinate chart.

Details and Options

Examples

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Basic Examples  (2)

The surface area of a unit ball in 3D:

Wolfram Language code: SurfaceArea[Ball[]]
Wolfram Language code: Region[Ball[]]

The surface area of a standard simplex in 3D:

Wolfram Language code: SurfaceArea[Simplex[3]]
Wolfram Language code: Region[Simplex[3]]

Scope  (15)

Special Regions  (7)

Surface area of a Cuboid:

Wolfram Language code: SurfaceArea[Cuboid[{Subscript[l, x], Subscript[l, y], Subscript[l, z]}, {Subscript[u, x], Subscript[u, y], Subscript[u, z]}]]
Wolfram Language code: ℛ = Cuboid[{0, 0, 0}, {3, 2, 1}]; SurfaceArea[ℛ]
Wolfram Language code: Region[ℛ]

Parallelepiped:

Wolfram Language code: ℛ = Parallelepiped[{0, 0, 0}, {{1, 0, 0}, {1, 1, 0}, {0, 1, 1}}]; SurfaceArea[ℛ]
Wolfram Language code: Region[ℛ]

Simplex in 3D:

Wolfram Language code: SurfaceArea[Simplex[3]]
Wolfram Language code: Region[Simplex[3]]

Ball:

Wolfram Language code: SurfaceArea[Ball[{Subscript[c, x], Subscript[c, y], Subscript[c, z]}, r]]
Wolfram Language code: ℛ = Ball[{0, 0, 0}, 1]; SurfaceArea[ℛ]
Wolfram Language code: Region[ℛ]

Ellipsoid:

Wolfram Language code: SurfaceArea[Ellipsoid[{Subscript[c, x], Subscript[c, y], Subscript[c, z]}, {Subscript[r, x], Subscript[r, y], Subscript[r, z]}]]
Wolfram Language code: ℛ = Ellipsoid[{0, 0, 0}, {3, 2, 1}]; SurfaceArea[ℛ]
Wolfram Language code: Region[ℛ]

Cylinder:

Wolfram Language code: SurfaceArea[Cylinder[{{Subscript[x, 1], Subscript[y, 1], Subscript[z, 1]}, {Subscript[x, 2], Subscript[y, 2], Subscript[z, 2]}}, r]]
Wolfram Language code: ℛ = Cylinder[{{0, 0, 0}, {0, 0, 2}}, 1]; SurfaceArea[ℛ]
Wolfram Language code: Region[ℛ]

Cone:

Wolfram Language code: SurfaceArea[Cone[{{Subscript[x, 1], Subscript[y, 1], Subscript[z, 1]}, {Subscript[x, 2], Subscript[y, 2], Subscript[z, 2]}}, r]]
Wolfram Language code: ℛ = Cone[{{0, 0, 0}, {0, 0, 2}}, 1]; SurfaceArea[ℛ]
Wolfram Language code: Region[ℛ]

Formula Regions  (1)

The surface area of a ball represented as an ImplicitRegion:

Wolfram Language code: SurfaceArea[ImplicitRegion[x^2 + y^2 + z^2 ≤ 1, {x, y, z}]]

A cylinder:

Wolfram Language code: SurfaceArea[ImplicitRegion[x^2 + y^2 ≤ 1, {x, y, {z, 0, 2}}]]

Mesh Regions  (2)

The surface area of a MeshRegion:

Wolfram Language code: DelaunayMesh[RandomReal[1, {20, 3}]]
Wolfram Language code: SurfaceArea[%]

The surface area of a BoundaryMeshRegion:

Wolfram Language code: ConvexHullMesh[RandomReal[1, {20, 3}]]
Wolfram Language code: SurfaceArea[%]

Derived Regions  (2)

The surface area of a RegionIntersection:

Wolfram Language code: ℛ = RegionIntersection[Ball[{0, 0, 0}, 1], Ball[{0, 0, 1}, 1]];
Wolfram Language code: Region[ℛ]
Wolfram Language code: SurfaceArea[ℛ]

The surface area of a TransformedRegion:

Wolfram Language code: ℛ = TransformedRegion[Ball[{0, 0, 0}, 1], ScalingTransform[{a, b, c}]];
Wolfram Language code: Region[ℛ /. Thread[{a, b, c} -> {3, 2, 1}]]
Wolfram Language code: SurfaceArea[ℛ, Assumptions -> a > 0 && b > 0 && c > 0]

CSG Regions  (1)

Surface area of a linear CSGRegion:

Wolfram Language code: CSGRegion["Difference", {Cube[2], Cube[{1, 0, 1}, 3]}]
Wolfram Language code: SurfaceArea[%]

Nonlinear:

Wolfram Language code: CSGRegion["Intersection", {Ball[], Ball[{0, 0, 1}]}]
Wolfram Language code: SurfaceArea[%]

Subdivision Regions  (2)

The surface area of a SubdivisionRegion:

Wolfram Language code: SubdivisionRegion[Cube[]]
Wolfram Language code: SurfaceArea[%]

The surface area of successive subdivision levels converges to that of the limit region:

Wolfram Language code: levels = Table[SubdivisionRegion[Cube[], i], {i, 0, 3}]
Wolfram Language code: ListPlot[SurfaceArea /@ levels, ...]
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.html

BibTeX

@misc{reference.wolfram_2026_surfacearea, author="Wolfram Research", title="{SurfaceArea}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/SurfaceArea.html}", note=[Accessed: 13-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_surfacearea, organization={Wolfram Research}, title={SurfaceArea}, year={2019}, url={https://reference.wolfram.com/language/ref/SurfaceArea.html}, note=[Accessed: 13-June-2026]}