Deriving formulas for the expected sample size needed in A/B tests

I'm not qualified to comment on Cam's math, but Evan Miller's tools [1] are my go-to source for calculating sample sizes and significance. How does this differ? (If it does.)

http://www.evanmiller.org/ab-testing/sample-size.html

That looks right to me. This is a very important calculation to do in order to avoid getting 100x the number of samples that you really need.

Essentially the same calculation applies to classification error.