Conversion between semicircles and latitude units

Question

I've recently come across the semicircle unit that is used to describe a latitude and longitude using the maximum precision allowed by a 32-bit number. The conversion here is given as degrees = semicircles * ( 180 / 2^31 ), semicircles = degrees * ( 2^31 / 180 ).

However it doesn't explain if this should be used differently for latitude since the maximum allowed number of semicircles is 2^31, and if you substitute this into the equation you get the answer 180 degrees, but latitude only goes up to 90. Would a different conversion between latitude be used instead? Such as, degrees = semicircles * ( 90 / 2^31 ), semicircles = degrees * ( 2^31 / 90 )?

If so then you wouldn't be using the 'semicircle' as a unit for latitude, more like a quarter circle in this case.

Has anybody else come across this issue?

Answer 1

The constant 180 would still be used for latitude because the relationship is 1 degree to a half circle. The Max and Min semicircles for latitude will be different (.5 to -.5) vs. Max and Min semicircles for longitude (1.0 to -1.0).