Sample Size for Proportion Calculator
Two-sided sample size for estimating a proportion: n = p*(1-p)*(z/E)^2 with z defaulting to 1.96.
Description
Estimate sample size for a proportion from expected prevalence, margin of error, and z critical value.
This calculator applies the normal-approximation planning formula for a two-sided confidence interval around a population proportion.
When to use Sample Size for Proportion Calculator
- Plan a survey proportion estimate
- Compare precision at different expected proportions
- Use p = 0.5 for the largest variance when no estimate is available
How the calculation works
The requirement is p(1−p)(z/E)² and is rounded up. For fixed z and margin, p = 0.5 maximizes p(1−p) and therefore produces the conservative largest size.
n = p(1 − p)(z / E)² Interpreting the result
Margin of error is entered as a proportion, so five percentage points is 0.05. The ceiling—not the displayed unrounded value—is the planning count.
Important limitations
- Independent simple-random sampling and normal-approximation conditions are assumed.
- Finite populations, nonresponse, clustering, weighting, design effects, and rare-event methods are not included.