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Proportion · PROP-1S

Sample Size for Test of One Proportion

Plan a one-sample test that compares an anticipated population proportion with a prespecified null value.

Enter percentage values, not decimals. For example, enter 20 for 20%, not 0.20.

1. Information obtained from previous studies or literature

Allowed range: 0.1% to 99.9%.

2. Information to be decided by the researcher

Enter the expected proportion under the alternative hypothesis.

Common planning value: 80%.

Common planning value: 5%.

Use 2 tails unless the protocol specifies a one-sided test.

Defaults to 10%. Enter 0 if no dropout adjustment is required.

3. Results

Enter the hypothesis-test assumptions and select Calculate to generate the sample size and suggested sample-size wording.

Formula, assumptions, limitations, and methodological note

Example clinical scenario

A health service tests whether influenza-vaccination uptake among older adults exceeds a target of 70%.

Formula and methodological note

The calculator preserves the established normal-approximation formula for a one-sample proportion test. It combines the null-proportion variance at the selected Type I error with the alternative-proportion variance at the selected power, then divides the squared sum by the squared difference between the two proportions.

The endpoint must be binary and observations should be independent. The null proportion is the prespecified reference value; the alternative proportion is the value the study is designed to detect. A two-sided alternative allows departures in either direction, while a one-sided alternative must be justified prospectively by the protocol.

The calculated sample size is rounded upward. If anticipated dropout is entered, the rounded sample size is divided by 1 − r and rounded upward again.

This normal approximation does not implement an exact binomial method or continuity correction and does not account for paired data, clustering, design effects, stratification, weighting, repeated measurements, or finite population correction. Rare or extreme proportions may require an alternative method and statistical review.

Method references

  1. Lemeshow S, Hosmer DW Jr, Klar J, Lwanga SK. Adequacy of Sample Size in Health Studies. Chichester: John Wiley & Sons; 1990.
  2. Chow SC, Shao J, Wang H, Lokhnygina Y. Sample Size Calculations in Clinical Research. 3rd ed. Boca Raton: Chapman and Hall/CRC; 2017.

Suggested citation

Yaacob, Najib Majdi. “Sample Size for Test of One Proportion (PROP-1S).” Web calculator. NajibMY, 2026. Accessed July 29, 2026. https://najibmy.netlify.app/tools/sample-size/proportion/one-proportion/.