I have seen revolvers from 1" to 14" barrels. What do you need to get a caliber to perform?
What do you mean by perform?
If you mean,"Hit what your're shooting at," your barrel length only needs to be long enough to stabilize the bullet. I carry a K-Frame .38 with a 1 7/8" barrel..I can make good hits at 20 yards.
If you mean "Maximize bullet energy when it leaves the barrel," it depends on your caliber, bullet weight, powder charge, barrel length," etc.