I am wanting to make a bainter notch filter but I don't understand some of the formula such as angular frequency and s and s^2...

Here's a link with some info, it doesn't have w in the eq shown..

http://www.changpuak.ch/electronics/Bainter_Notch_Filter.php

 

What center frequency?
What Q? (width of notch)?

The calculator on your linked page avoids having to understand the transfer function...

 

Notch of 50hz
A q high enough so that the 3rd harmonic(150hz) is not effected any. So around 8 or so.

I want to use it to see only 3rd harmonic distortion...I'd like to attenuate the notch freq as much as possible, no less then -80db but preferably 100db