# AngularDegrees^2 and Steradians are incompatible units

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

AngularDegrees^2 and Steradians are incompatible units


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

• 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. – MarcoB Dec 28 '20 at 15:26
• No that doesn't seem to be the problem.I even get the error with UnitConvert[Quantity[1, "Steradians"], "Radians^2"] – Nickpick Dec 28 '20 at 17:10
• Have tried the below answers with a fresh kernel? – CA Trevillian Dec 28 '20 at 17:38
• restarting the kernel after upgrading to Mathematica 12 solved the problem – Nickpick Dec 28 '20 at 18:33

It seems you have misspelled "Degrees". When I correct your misspelling, I get

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

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

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