Calculated result
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Proportion-planning formula
The initial estimate is n₀ = z²p(1 − p) / e². Confidence is converted to a two-sided z score with a deterministic inverse-normal calculation. The final result always rounds up.
Worked example
At 95% confidence, 5% margin, and p = 50%, n₀ is about 384.15, so the required whole sample is 385.
Finite population and assumptions
When N is entered, n = n₀ / (1 + (n₀ − 1)/N). This basic simple-random-sampling model does not include design effects, nonresponse, clustering, weighting, rare-event needs, or medical-study power.