Do you want to take the mystery out of making hats? I struggled with this when I first started to crochet. While making hats, I did some research into how to correctly size your flat circle and height of the hat. The formula I found most helpful to figure out the correct size of the diameter of your flat circle is you need to know the circumference of the head.
An adult woman's head averages about 22 inches. The formula is to divide your circumference by 3.14
Head circumference 22 divided by 3.14 = 7.00 inches. Now you know your circle needs to be 7 inches. To get the correct height (from top of crown to bottom of the ear) you divide your circumference by 10 and multiply this number times 4.
Head circumference 22 divided by 10 = 2.2 x 4 = 8.8. So the hat height should be 8.8 inches. Hats are made about an inch smaller in circumference than the circumference of the head. This keeps the hat fitting tightly and to keep it from falling off.
Below is a chart for the sizes that you may find helpful.
I hope that this helps all of you that are struggling with making hats!