These buttons measure around 3 1/4" or 80mm and I have a number for sale in a range of different types of wood. Being handmade, sizes may vary by a few millimetres.
I've seen them used as a feature on a scarf or bag and they'd be just great as a feature on a woollen hat. See the November 14th blog entry here: http://www.woollywormhead.com/blog/ for a superb knitted hat pattern by Woolly Wormhead!