How the sample size is calculated
A test has to be big enough that an effect worth having would show up, and small enough to finish. Those two pull against each other, and four numbers settle the argument: the rate you convert at today, the smallest lift worth detecting, how often you accept a false positive, and how often you are willing to miss a real effect.
The sample per variant is the standard two-sided test of two proportions, with the pooled variance under the null hypothesis:
n equals the square of z at one minus alpha over two, times the square root of twice the average rate times one minus that average, plus z at the power, times the square root of each rate times one minus itself, all divided by the square of the difference between the rates.
The difference enters squared, which is the fact everything else follows from. Halving the effect you want to catch quadruples the test.
Above two variants the significance level is divided across the comparisons against control. That is the blunt correction, and it is the right default: it never understates what a test needs, and running three variants at the significance level of one is how teams find effects that are not there.
Why runtime is in days
A sample size on its own tells you nothing about whether to start. The question a team actually asks is when the result arrives, and that depends on traffic, on how much of it you allocate, and on how many variants are splitting it. All three are inputs here.
The runtime rounds up to whole weeks. Weekday and weekend traffic convert differently, so a test stopped on a Wednesday has weighted part of the week more heavily than the rest.
The split check
If a fifty-fifty assignment did not arrive fifty-fifty, the difference between the arms is measuring whatever broke the assignment. A redirect that drops people, a bot filter applied to one side, a tag that fires late on slow connections: each of them produces an effect size, and none of them is the change you shipped.
The check is a chi-square test on the counts against the split you configured. The threshold is strict, a p-value below 0.001, because a mismatch costs an hour to investigate and a wrong decision costs a quarter.
Why reading early is not free
A fixed-horizon test spends its whole false positive budget on one look. Every extra look at a dashboard is another chance for noise to cross the line, so a result read before the planned sample arrives was never tested at the level anybody is about to quote in a meeting.
This page does not try to tell you how much your significance level inflated, because that depends on how many times the dashboard was opened and nobody records it. It tells you how much sample is still missing. If you need to stop early on purpose, that is a different design with its own mathematics, and a fixed-horizon calculator is the wrong tool for it.