If I type in the dilution ratio and final volume it calculates the concentrate amount and water amount but I don't know how it does that and want to find out how it does that
Using simple numbers can help determine an unknown formula, sometimes. While there are easier formulas I am sure, I am just going to "reverse engineer" this one with the data I have.
In that example, I have a 2:1 ratio (3 parts total) with a final volume of 10fl/oz.
10floz / 3 parts is ~3.3 per part. 2 * 3.3 = 6.6, 1 * 3.3 = 3.3
6.6 + 3.3 = 9.9 (close enough..)
So, what we do is determine what is "one part" of the mixture, and then do some basic math on the given ratio.