I went to http://www.dickssportinggoods.com/sm...g-2715028.html
It says that a size 11 shoe is about 10.3-10.5 inches. That sounds about right; my foot is a size 10 and it is just less than 10 inches.
Your friend will appreciate these socks very much! You have no idea how frustrating it is for ladies with larger feet to find socks that fit comfortably. I wear men's socks, otherwise my toes poke holes in them within a month.