If a bike comes with 700x 28c tires what is the largest tire you could put on the wheel?

There's a chart on sheldonbrown.com for safe tire sizes. In any case, if you're sometimes lazy like me, you could cut a piece of cardboard to measure the outside width of the rim. Then you can deduct 4 or 5mm to estimate the inside width and look at the chart.

It all depends on how much clearence you have in your frame and fork and brake calipers(rim brakes).

On the wheel by itself, you could put up to a 700 x 60mm tire: https://www.universalcycles.com/shopp...s.php?id=16624 , but it would take a very special bike to accommodate a tire that big. As others said, the limitation is usually the clearance of the frame and fork.

Agreed. I just had some 38mm tires on a bike/wheel that originally had 23mm. That was as wide as I could go without running into a clearance problem with the chainstays. Check how much clearance you have with the 28 mm tires at the fork and chain/seat stays and at the brakes (if calipers). That should give an indication of about how wide a tire you can use without having it rub anywhere. Every extra 2 mm of tire width will reduce the clearance on each side by about 1 mm.