Boo and Cliff, I think you want c=2piR. The other is area. A shortcut is 6.28x radius=c or 3.14xdiameter=c. But be sure to allow for thickness fo material of hat, and any overlap required.
Also, a straight piece of band will pucker if the crown tapers any at all, and without making a complicated pattern for each one, I would recommend using bias cut fabric to make the band. It has some stretchability.