Exact distributions, not approximations
Each calculator here solves for whichever quantity you don't already know — sample size, given a target power, or achieved power, given a planned sample — from the actual sampling distribution the test uses: noncentral t, noncentral F, noncentral chi-square, or Fisher's z for correlations. That matches what dedicated power-analysis software (like G*Power) reports, rather than a rule-of-thumb table.
Effect-size conventions throughout follow Cohen (1988): small, medium, and large benchmarks exist for convenience, but a defensible effect size for a real study should come from prior research, a pilot, or the smallest effect that would matter substantively — not a default. Power below the conventional .80 minimum means a real effect of the assumed size has a meaningful chance of being missed entirely, not found and misreported.