# UnitConvert: the square of a dimensionless quantity is not dimensionless [closed]

This is pretty ridiculous. Look at the following code:

UnitConvert[Quantity["FineStructureConstant"], 1]^2


0.0000532513545

UnitConvert[Quantity["FineStructureConstant"]^2, 1]


Quantity::compat: DimensionlessUnit and (FineStructureConstant)^2 are incompatible units >>
UnitConvert[Quantity[1, ("FineStructureConstant")^2], 1]

UnitConvert[Quantity["FineStructureConstant"]^2, 1 1]


Quantity::compat: DimensionlessUnit and (FineStructureConstant)^2 are incompatible units >>
UnitConvert[Quantity[1, ("FineStructureConstant")^2], 1]

This reminded me of "Radians", which is not convertible to dimensionless. Isn't this behavior a kind of bug?

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Just drop the 1: UnitConvert[Quantity[1, ("FineStructureConstant")^2]]. –  swish May 10 at 4:19
@swish Wow, I never knew this syntax before. By the way, do you know if it's possible to convert radian to dimensionless? –  KevinSayHi May 10 at 4:40
The syntax given by Swiss is the second syntax form given in the UnitConvert doc page. Nothing special to it. As to your other question: MMA doesn't regard a radian as dimensionless. It has dimension "AngleUnit". But if you want to have its numerical value you could simply use QuantityMagnitude. –  Sjoerd C. de Vries May 11 at 0:26