I agree, it could/should be so much simpler.
The width is in millimeters. It's not the tread width, it's the section width, which is the width of the tire at it's widest point.
The aspect ratio is the sidewall height expressed as a percentage of the width. for example, the sidewall height on a 50 series tire is 50% of the width.
As an example, my daily driver takes a 205/50-16 tire.
The section width is 205 mm. Divide by 25.4 to convert MM to inches = 8.07"
the aspect ratio is 50%. 50% of 8.07" is 4.035"
And, of course 16 is the rim size in inches.
So to figure the tire diameter, you add the rim diameter to twice the sidewall height: 16 + 4.035 + 4.035 = 24.07"
Hope this helps....