Deriving formulas for the expected sample size needed in A/B tests (camdp.com)

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.

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