Math equation implemented in crochet

Never come across into my mind that learning the math equation in the past might actually useful now in crocheting.
I have been receiving some crochet hat order for the past few weeks from a friend of mine.

one of the design ordered

another ordered design

At first looking at the pattern, i actually thought everything actually gonna be easy to do.
However i got myself totally wrong when there are actually few different type sizes i have to do and been scratching my head for few day, wanted to find the best way to make sure my crocheted hat will turn as requested.

I searched around for assistance on the actual way on making sure the crochet hat will fit accordingly to the measurement given.
I was told that in order to make the hat, i have to start with the hat base. When the base has come to the needed measurement then i can continue with the repeating stitches and that's how a hat should be done.

Then again i scratch my head, what if during measuring, the size turns out to be wrong as i just have to measure the base circularly.
That's when all of sudden i remember there's an equation to calculate a circle overall sizes, and it comes to a relieve that it's actually work out.

Since then i keep on having this sort of mesmerize thought on my head that math equation is actually can be useful too sometime :)
Now just finger cross that the order can be finish on time...