Formula
Infinite population: n₀ = z² × p × (1 − p) / E²
Finite-population correction: n = n₀ / ( 1 + (n₀ − 1) / N )
Use p = 0.5 for the most conservative (largest) sample when the true proportion is unknown.
FAQ
Why does p = 0.5 give the largest sample?
Because p(1 − p) peaks at 0.25 when p = 0.5. Any other value gives a smaller required sample.
What about A/B tests?
For comparing two proportions (control vs variant) and detecting a specific lift with given power, use a power-analysis approach — this calculator handles single-proportion surveys.