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If you are wondering how wide or skinny of a tire you can run on a particular rim size you can figure that out from those calculations too. Most tires can be stretched a little bit to fit on a slightly wider wheel than they were intended for.
To determine if a tire will fit on a specific rim you have to know the width of the rim. Then just take the width of the tire say a 155/80/13 again. Divide 155 / 25.4 = 6.1 inches of tread width. These should fit on 5.5 - 6.5 inch wide rims.
Also note that while the widths of rims generally go up with increased diameter, the diameter of every 12 inch wheel will be 12 inches, every 13 is 13 etc. The overall diameter of the wheel & tire combo is only changed by the tire.
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