Well, I didn't have an empty toilet roll to hand but did have a kitchen towel roll which I measured as 55mm across - which, if my maths is right means it is a circumference of 6.8 inches...

Well, I managed to get the head in just about but I got wedged after a couple of inches and there was no going any further. Which surprised me because I'd always thought my girth was about 5.75. Maybe I miscalculated the thickest part!