I knew that I had to increase the size of the crocheted circle until it was the right circumference, but how could I figure the circumference when the top of the hat was still in pancake form?
My sister, Linda, reminded me about pi, which I'd encountered so long ago in high school geometry. Just multiply the diameter -- the width across the middle of the circle -- by pi, or 3.142, and you get the circumference.
Pi and a calculator can tell you when your hat is big enough around.
Or you can use this circumference chart.