# 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. Aug 28, 2017 at 16:39
• @Szabolcs Sorry, actually I wanted a way to compute the surface area, a workaround. I'll edit.
– a06e
Aug 28, 2017 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" Aug 28, 2017 at 17:50
• However, Area@Sphere[{0, 0, 0}, 1] gives the correct surface area. Seems inconsistent, @BobHanlon.
– a06e
Aug 28, 2017 at 18:31
• @becko That's because RegionDimension[Sphere[{0, 0, 0}, 1]] is 2, not 3. Ball is the equivalent of Ellipsoid. Aug 28, 2017 at 18:46
• @CarlWoll Oh, I see.
– a06e
Aug 28, 2017 at 20:52