A lot of the early Regency hats I was looking at are labelled Chapeau de Velours (Velvet Hat), and I conveniently had some leftover red velveteen, so that's what I'm making my hat out of. I drafted a pattern based on measurements from a baseball cap and some trial-and-error for the brim. This is the pattern I came up with:
The long strip/band is 23 inches long and 2 inches wide. The crown (circle) is 14 inches in diameter. You can tell from my try-on that this is too small. All pieces have a 1/2 inch seam allowance.
Aside from the too small crown, which should be poufier, I'm really pleased with how it's turning out. I think it's pretty cute. :)