If the collets are 3AT or 3C, 1/2" is the largest size that either of those types come in, and is the largest size that will fit a 9", 10" or 12" Atlas or Atlas-Craftsman lathe, because that's about the limit on the draw tube diameter, which has to be somewhat larger OD and ID than the collet capacity. And the collet closer adapter must also fit into a 3MT taper.
If the collets are ER type, there is an upper and a lower limit for each ER size.