Choosing a useful naval railgun caliber

If suitable materials made a naval railgun workable, what projectile caliber would be most useful?

About five inches for general-purpose use, smaller for air defense, and roughly 9.2 inches for a dedicated land-attack weapon.

The question assumes that suitable materials have made a naval railgun workable. A general-purpose weapon would probably use a projectile of roughly five inches. Dual-purpose or air-defence applications could favor roughly three inches or 40 mm, depending on the job. Land attack could justify about 9.2 inches. These are proposed choices by role, without a detailed gun or mounting design.