I was looking on vexrobotics.com at some parts and saw that the gears have slightly different diameters then they should be. The pinion has a diameter of .58", the 36 tooth gear has a diameter of 1.58", and the 60 tooth gear has a diameter of 2.58". I havent measured them to check if these diameters are incorrect, but if you were to gear a 12 tooth gear to a 60 tooth gear, then the ratio would actually be 1:4.45 instead of 1:5. Is this correct?

The. 08 is the teeth. The ratio is exactly 5, 3,1. The ratio would be different if you made the edge of the teeth of 1 gear hit the edge of the teeth of the other, but that doesn’t happen. (you would have to fill in the holes to make it a perfect circle)

I think the difference you’re talking about is the difference between the gear’s “pitch diameter” and the physical outer diameter of the gear. The pitch diameter is the diameter at which the gear teeth effectively mesh and interact with each other, and this is the diameter that actually affects the gear ratio. When you zoom in on how gears actually work, the interactions of the teeth caused by their various shapes, angles, etc. can get fairly complex.