Relationship between given width of a tire and actual height I've spent some time digging around and can't quite find a satisfactory answer here. I have an older (80's) road frame that currently has 622x23 tires. I would like to upgrade to 28mm or even 32mm tires. Generally the issue with larger tires is clearance between the brake calipers. In my case this is not the issue. The calipers themselves are plenty wide to accommodate much larger tires. The problem at hand is the clearance between the top of the tire and the cross beam between the seat stays where the brakes are mounted. It's quite small (3-5) mm. So... Is the diameter of a tire affected in three dimensions, or will a wider tire (28mm vs 23mm) also be "taller" aka vertically higher from the rim. I've seen a few comparisons and tire reviews that imply width and height are separate, but that seems logically impossible based on the inner tube expanding equally in all directions. Any clarification on this would be wonderfully appreciated. Thanks and smooth roads ahead ; )
In bicycle tires the height and width are directly related. This is because unlike unlike car and motorcycle tires, the cords that hold the tire together are aligned diagonal and the resulting fabric stretches to round shape when inflated. The tube does not have anything to do with it, because it expands to fill all available space. If you have a piece of non stretchy fabric like a flannel shirt at hand, you can try stretching different directions to see how it works.

Tires that have thick tread are taller than fully round tube shape would be, because tread is outside of the fabric.