Boaters are often worn higher on head due to shallow crown height or at can be worn a slanted angle. Likewise Berets are worn higher ( some say 2 finger above eyebrow - though depends on ones fingers size!). The diagram show this cross section of the head is smaller than the standard "hat" position. So as a rule a Beret or Boater is one size SMALLER than standard HAT size as heads tend to taper in further up to smaller a cross-section.
A. Carding (combing the fibers), Bowing (cleaning and fluffing) B. Matting (various layers of the fiber into felt) C. Basoning (manipulated the batt of felt into a triangular shape called a capade or gore that will become the crown of the Hat) D. Flanging (attaching the brim) E. Blocking (forcing the hat body onto a wood form and stamping the moisture from it)