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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2 Answers
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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]
answered Dec 28, 2020 at 14:35
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$\begingroup$ Corrected the spelling, but sill getting Quantity::compat: (AngularDegrees)^2 and Steradians are incompatible units $\endgroup$– NickpickCommented Dec 28, 2020 at 15:02
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1$\begingroup$ @Nickpick I can reproduce the result in this answer on MMA cloud. What’s your version and OS? $\endgroup$– MarcoBCommented Dec 28, 2020 at 15:09
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$\begingroup$ I'm still on Mathematica 11, maybe need to upgrade to 12 $\endgroup$– NickpickCommented Dec 28, 2020 at 15:35
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$\begingroup$ @Nickpick I can't seem to reproduce your problem on MMA 12.0.0, see my answer below $\endgroup$– MarcoBCommented Dec 28, 2020 at 17:35
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$\begingroup$ Mathematica 12 solves the problem. Seems to have been a bug in Mathematica 11 $\endgroup$– NickpickCommented Dec 28, 2020 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]
*)
"Degrees"^2, with the^2outside of the string, rather than"Degrees^2"? That's the only way I can get something similar to your error. Alternatively,"AngularDegrees"^2and"AngularDegrees^2"both work fine. $\endgroup$UnitConvert[Quantity[1, "Steradians"], "Radians^2"]$\endgroup$