# Surface area of ellipsoid

I think this is a bug

Area @ Ellipsoid[{0, 0, 0}, {1, 2, 3}]

returns Infinity in Mathematica 11.

Is there a way I can compute the surface area of an ellipsoid in Mathematica?

• 1. This is not a question, and as such not fit for a QA site (unless you rephrase appropriately). 2. Please do not use the bugs tag when posting new question. This is in the tag description. 3. Reporting bugs is good, but they must be reported to Wolfram directly. This is not a Wolfram site. – Szabolcs Aug 28 '17 at 16:39
• @Szabolcs Sorry, actually I wanted a way to compute the surface area, a workaround. I'll edit. – becko Aug 28 '17 at 18:30

In the documentation of Area:

The area of a region of dimension three or higher is $\infty$:

For the surface area you can do:

Area @ RegionBoundary @ Ellipsoid[{0, 0, 0}, {1, 2, 3}]


π (2 + 8 Sqrt[2] EllipticE[ArcCos[1/3], 27/32] + Sqrt[2] EllipticF[ArcCos[1/3], 27/32])

• Also, the "Properties & Relations" section of the documentation for Area states "To get the surface area of a 3D region, use RegionBoundary" – Bob Hanlon Aug 28 '17 at 17:50
• However, Area@Sphere[{0, 0, 0}, 1] gives the correct surface area. Seems inconsistent, @BobHanlon. – becko Aug 28 '17 at 18:31
• @becko That's because RegionDimension[Sphere[{0, 0, 0}, 1]] is 2, not 3. Ball is the equivalent of Ellipsoid. – Carl Woll Aug 28 '17 at 18:46
• @CarlWoll Oh, I see. – becko Aug 28 '17 at 20:52