So the rough breakdown you'll get should be documented in the terms of service of your bank, though they might not give the specific formula and talk about it in more general terms. Different banks will calculate break costs differently. Here's the link to the terms and conditions that describe it for kiwibank: https://www.kiwibank.co.nz/documents/home-loan-terms-and-conditions/

They'll take a bunch of different things in to account- like how much you can still currently repay without a breakage penalty, and how long you have left on the fixed rate. The general gist is that the breaking fee is typically proportional to how much profit the bank would have made had you continued paying the mortgage until the end of the current loan term limit, but a bit less in consideration that they get the money early.

So long story short, you breaking with two months left probably won't come with a high bill I wouldn't have thought. But whether or not it works out better financially is going to entirely depend on what happens with the floating rate.