Power analysis for a one- or two-sample proportion test is parameterised by Cohen's h, the arcsine difference.
Cohen's h = 2·arcsin(√p₁) − 2·arcsin(√p₂) makes the variance approximately constant across the (0, 1) range. Anchors: 0.2 small, 0.5 medium, 0.8 large.
Design (one- vs two-sample) + three of {n, h, α, power}.
Fourth quantity.
For unequal arm sizes, the harmonic-mean n approximation is used; very lopsided allocations lose power vs balanced — favour 1:1 unless you have a reason.