US: M to United Kingdom Size 6 3/4
Cross-market women’s hat conversion mapping M specifications into 6 3/4.

Analyzing Hat Size Equivalence Across Markets
US: M: Features a head circumference of 56.5 (22.2 ) measured just above the brow and ears.
United Kingdom Size 6 3/4: Features a head circumference of 55.5 (21.9 ) measured just above the brow and ears.