I designed this helpful chart to determine how large to make the increase circle when crocheting a hat from the top down. Just lay your circle on the bottom of the chart and press flat. Your circle needs to match (approximately) the circle size matching the hat size you wish to make.

These are AVERAGE sizes.

I also have available a Customize-A-Hat pattern which includes directions to make a basic beanie fit even more accurately - along with the pattern for a basic beanie and 5 different options to finish the hat.