Calculate sample size

Estimate a simple-random-sample size for a population proportion and chosen margin of error.

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ToolSample Size Calculator
Input
Output
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How it works

The initial size is z²p(1−p) ÷ e², where e is absolute margin and z comes from the confidence level. A supplied finite population reduces it to n ÷ (1 + (n−1)/N), after which the result rounds upward.

  • Expected proportion begins at 0.5 because p(1−p) is largest there.
  • The initial 95% confidence choice still assumes simple random sampling and a suitable normal approximation.

Worked example

A general public survey
5% margin of error at 95% confidence, no assumption about the answer split
Input
											Margin of error percent: 5
Confidence level: 95
Output
												Sample size: 385
Z value: 1.96
Population proportion: 0.5

When to use this

Survey plans size respondent targets, quality audits choose defect samples, and prevalence studies compare the conservative 50% assumption with prior evidence.

Edge cases

  • Rare expected proportions can leave too few successes or failures for the normal approximation.
  • Clustered, stratified, weighted, or nonresponse-prone samples need design effects or other adjustments absent here.
  • A finite population correction reduces size only for a valid population count; it does not repair convenience sampling.

References