4
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UnitConvert[Quantity[360, "Degrees^2"], "Steradians"]

AngularDegrees^2 and Steradians are incompatible units

What am I doing wrong in not getting 4$\pi$?

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    $\begingroup$ By any chance, are you using "Degrees"^2, with the ^2 outside of the string, rather than "Degrees^2" ? That's the only way I can get something similar to your error. Alternatively, "AngularDegrees"^2 and "AngularDegrees^2" both work fine. $\endgroup$ – MarcoB Dec 28 '20 at 15:26
  • $\begingroup$ No that doesn't seem to be the problem.I even get the error with UnitConvert[Quantity[1, "Steradians"], "Radians^2"] $\endgroup$ – Nickpick Dec 28 '20 at 17:10
  • $\begingroup$ Have tried the below answers with a fresh kernel? $\endgroup$ – CA Trevillian Dec 28 '20 at 17:38
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    $\begingroup$ restarting the kernel after upgrading to Mathematica 12 solved the problem $\endgroup$ – Nickpick Dec 28 '20 at 18:33
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It seems you have misspelled "Degrees". When I correct your misspelling, I get

UnitConvert[Quantity[360, "Degrees^2"], "Steradians"]

Quantity[Pi^2/90, "Steradians"]

It quite a bit less than $4 \pi$. To find the angular measure of a complete sphere in angular degrees we can do the following:

UnitConvert[Quantity[4 π, "Steradians"], "Degrees^2"]
Quantity[129600/π, ("AngularDegrees")^2]

Also, note that a steradian is the same as a square radian.

UnitConvert[Quantity[1, "Steradians"], "Radians^2"]
Quantity[1, "Radians"^2]
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  • $\begingroup$ Corrected the spelling, but sill getting Quantity::compat: (AngularDegrees)^2 and Steradians are incompatible units $\endgroup$ – Nickpick Dec 28 '20 at 15:02
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    $\begingroup$ @Nickpick I can reproduce the result in this answer on MMA cloud. What’s your version and OS? $\endgroup$ – MarcoB Dec 28 '20 at 15:09
  • $\begingroup$ I'm still on Mathematica 11, maybe need to upgrade to 12 $\endgroup$ – Nickpick Dec 28 '20 at 15:35
  • $\begingroup$ @Nickpick I can't seem to reproduce your problem on MMA 12.0.0, see my answer below $\endgroup$ – MarcoB Dec 28 '20 at 17:35
  • $\begingroup$ Mathematica 12 solves the problem. Seems to have been a bug in Mathematica 11 $\endgroup$ – Nickpick Dec 28 '20 at 19:38
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We can't seem to reproduce your problem.

Here are the results of your simpler question from comments, first on my laptop:

$Version
UnitConvert[Quantity[1, "Steradians"], "Radians^2"]

(* Out: 
"12.0.0 for Microsoft Windows (64-bit) (April 6, 2019)"
Quantity[1, "Radians"^2] 
*)

... and on the cloud version:

$Version
UnitConvert[Quantity[1, "Steradians"], "Radians^2"]

(* Out: 
"12.2.0 for Linux x86 (64-bit) (November 16, 2020)"
Quantity[1, "Radians"^2]
*)
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