I'm not sure if this is the answer you're looking for, but degrees/radians are considered dimensionless in that they're defined by the ratio of two lengths. Th

I'm not sure if this is the answer you're looking for, but degrees/radians are considered dimensionless in that they're defined by the ratio of two lengths. There's no way for the value of 1 radian to magically 'double' without causing π radians to magically amount to a full circle, which would seriously warp Euclidean geometry as we know it.