If a particular hat says for example “7 1/8” inside the brim, what is that referring to? I thought it might be diameter, but a lot of hats are longer than they are wide, so what dimension do they use?
IIRC, it’s the circumference of the head divided by three.
When come back, bring [symbol]p[/symbol].
FWIW, the size is the computationally-derived diameter of the head. As the OP notes, heads aren’t perfectly round.
If you’re making a hat, measure the head, add half an inch for comfort (most sized hats can be adjusted down in size by placing filler materal in the hatband - 1/16" thick sponge exists for just this purpose) and cut the hatband to that size. Otherwise, divide that number by pi, convert the decimal to fraction and look for that size.