This question has many variables but here is a starting guide for some of the most common rotary tumbler barrel sizes:
1.5lb barrel — Up to 1″
3lb Barrel — Up to 1.5″
4lb Barrel — Up to 2.5″
6lb Barrel — Up to 3″
12lb Barrel — Up to 4″
15lb Barrel — Up to 4 1/2″
Now, for some of those variables….. mixed sizes or smaller sizes will generally yield best results when tumbling. When I say a 4lb barrel can take stones up to 2.5″, we mean maybe one or two 2.5″ stones and then add a mixture of smaller material, preferably down to 1/2″ in size.
If you want to do more 2.5″ material, then moving up to a 6lb barrel would be best.
The most critical variables are the other 2 dimensions of the stone. While a 3″ rock can be a slender 3″ X 1″ X 1″ stick, it could also
be the size of a baseball. The sizes I mention above are common sense sizes. Maybe not sticks, but definitely not baseballs. However, if you want to do a special 3″ baseball size stone, it could be done by just doing that stone and filling the rest of the barrel with either small stones or small ceramics but mainly concentrating on the one stone. Keep in mind that the larger the stones are, the more coarse grinds you may have to do to get them ready to move to the 2nd stage due to the circumfrence of the stone. Coarse grinding a batch of 1″ stones will likely take a week in a rotary tumbler. Coarse grinding a batch of 2.5″ stones could take 3 or even 4 weeks.