Several problems...
Metric and imperial. Those tyre descriptions are different in how they all work.
Tyre sizes are NOMINAL and not exact.
An imperial tyre such as a typical rear tyre on a chair will be 3.00 x 8. Its REAL description in full is 14 x 300-8 Or 14 (OUTER DIAMETER) X 3.00 (WIDTH) - 8 (RIM DIAMETER) Where did 14 come from? Sidewall is 3, + rim is 8, + sidewall other side it 3...
So if you see a caster tyre that is say, 3 x 4, or 3.00 x 4, it really means its TEN (10") outer diameter, and 3 inches wide, and fits a 4 inch diameter rim. It SHOULD be called in full, a 10x300-4 tyre. It would need a 2 inch WIDE rim.
A low profile imperial tyre is usually described as say 300 x 260 x 4 for an example. That just means its: 3 inches wide. Has a 2.6 inch sidewall. And fits a 4 inch rim. It SHOULD be described as a 9 x 300/260 - 4. All sizes here are NOMINAL and approximate. Except the rim size and thats exact.
If its a METRIC tyre, it will be sized in Millimeters wide, and % sidewall and inch diameter!
So a 120/70 - 8 tyres such as I use on my Salsa chair, is 120mm wide (about 4.6 inches? Has a sidewall that is 70% of that 120... So an 84mm sidewall. Its total diameter is the 8 inch rim, (200mm) + 84 + 84 - 368mm (or 14.5 inches.)
Does that help?
When I see a tyre advertised all that goes through my head.
