How to make a degree wheel

I have the two degree wheels, both are 7 inch. I am wondering if these small of wheels is going to give me the accuracy of readings that I am hoping to see.

I know that the larger the better. I see them 2 hundred plus wheels and I dont have an issue with buying a quality tool but I also am considering how often I would use it and that is in question still at this point.

Isnt there a way that a degree wheel can be made with a simple mathematical tool, I dont know what its called but I thought there was an in-expensive plastic see thru gimmick that we all had as kids and we carried in our bookbags never too be used. ( but it did look kinda cool sitting in there )

I thought a degree was a degree no matter the size but then my brain cant quite wrap its head around how a larger wheel would use the same size/spacing of lines to represent a degree.

Any input welcome, thanks

EDIT: Id like to make a larger degree wheel if possible, doing a search on-line dosent show much. I have plenty of metal and could clearcoat it too last so any suggestions on how to do this would be appreciated.