A top-down beanie starts as a flat circle, then stops increasing and works straight down. Fit comes from one number: the stitch count at the end of the increases.
Measure the head
Wrap a tape measure around the head just above the ears. Hats are normally made a little smaller than the head so they stay on. The pattern maker uses about 8% less.
Work the crown
Start with a magic ring and increase evenly in each round. Keep the circle flat. If it cups like a bowl, you need more stitches. If it ruffles, you need fewer.
Stop at the right size
Try the circle against the head once the increases are done, or measure around it. The hat should stretch comfortably without feeling tight.
Work the sides
Work without increasing until the hat reaches the height you want. About 21 cm is a common adult height, but folded brims need more.
Finish
Fasten off and weave in the ends through the stitches, so they stay hidden when the hat stretches.
Enter a head size in the beanie maker to get each round for your yarn.