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Aspect Ratio and Rim Width
Aspect ratio is the ratio of the tyre's section height to its section width. The aspect ratio is sometimes referred to as the tyre 'series'. So a 50-series tyre means one with an aspect ratio of 50%. The maths is pretty simple and the resulting figure is stamped on all tyres as part of the sizing information: aspect ratio = section height / section width
The actual dimensions of a tyre depend on the rim on which it is mounted. The biggest variable is the tyre's section width; a change of about 0.2" for every 0.5" change in rim width.
The ratio between the section width and the rim width is pretty important. If the rim width is too narrow, you pinch the tyre in and cause it to balloon more in cross-section. If the rim width is too wide, you run the risk of the tyre ripping away at high speed.
For 50-series tyres and above, the rim width is 70% of the tyre's section width, rounded off to the nearest 0.5.
For example, a 255/50R16 tyre has a design section width of 10.04" (255mm = 10.04 inches). 70% of 10.04" is 7.028", which, rounded to the nearest half inch, is 7". Ideally then, a 255/50R16 tyre should be mounted on a 7x16 rim.
For 45-series tyres and below, the rim width is 85% of the tyre's section width, rounded off to the nearest 0.5.
For example, a 255/45R17 tyre also has a design section width of 10.04" (255mm = 10.04 inches), but 85% of 10.04" is 8.534", which, rounded to the nearest half inch, is 8.5". Ideally then, a 255/45R17 tyre should be mounted on an 8½x17 rim.
Source: ETRTO Design manual. Yokohama Tyres