US: S to United Kingdom Size 7 1/8
Cross-market women’s hat conversion mapping S specifications into 7 1/8.

Analyzing Hat Size Equivalence Across Markets
US: S: Features a head circumference of 54.5 (21.5 ) measured just above the brow and ears.
United Kingdom Size 7 1/8: Features a head circumference of 58.5 (23 ) measured just above the brow and ears.