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Proportion · PROP-CI

Sample Size for Estimation of a Single Proportion

Plan the sample size needed to estimate one population proportion with a chosen confidence level and absolute margin of error.

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 percentage-point half-width, such as 5 for 5 percentage points.

Enter a value greater than 0% and less than 100%.

Defaults to 10%. Enter 0 if no non-response adjustment is required.

3. Results

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

Formula, assumptions, limitations, and methodological note

Example clinical scenario

A community survey aims to estimate the prevalence of hypertension among adults with a specified confidence level and absolute margin of error.

Formula and methodological note

The calculator uses the standard large-sample normal-approximation formula n = z²p(1 − p) / d², where p is the anticipated proportion, d is the absolute margin of error, and z is the two-sided normal critical value for the selected confidence level. The calculated sample size is rounded upward.

If anticipated non-response is entered, the rounded initial sample size is divided by 1 − r and rounded upward again. This inflation supports recruitment planning but does not correct non-response bias.

The method assumes a binary outcome, independent observations, and a normal approximation suitable for the intended setting. The anticipated proportion should come from relevant literature, pilot data, surveillance, or another defensible planning source. When no credible estimate exists, 50% gives the largest sample size under this formula and may be used as a conservative assumption.

This calculator does not apply a finite population correction or account for cluster sampling, stratification, weighting, design effects, repeated measurements, or paired data. Rare or extreme proportions and small expected counts may require an alternative interval method and protocol-specific statistical review.

Method references

  1. Cochran WG. Sampling Techniques. 3rd ed. New York: John Wiley & Sons; 1977.
  2. Lwanga SK, Lemeshow S. Sample Size Determination in Health Studies: A Practical Manual. Geneva: World Health Organization; 1991.
  3. Lemeshow S, Hosmer DW Jr, Klar J, Lwanga SK. Adequacy of Sample Size in Health Studies. Chichester: John Wiley & Sons; 1990.

Suggested citation

Yaacob, Najib Majdi. “Sample Size for Estimation of a Single Proportion (PROP-CI).” Web calculator. NajibMY, 2026. Accessed July 29, 2026. https://najibmy.netlify.app/tools/sample-size/proportion/estimate-proportion/.