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Proportion · PROP-FPC

Sample Size for Estimation of a Single Proportion with FPC

Plan the sample size needed to estimate one proportion when the eligible target population is known and finite.

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%.

Enter the defined eligible target population size for this study question.

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

3. Results

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

Formula, assumptions, limitations, and methodological note

Example clinical scenario

A hospital with 800 healthcare workers wants to estimate influenza-vaccination coverage while accounting for the finite eligible workforce.

Formula and methodological note

The calculator first uses the standard large-sample normal-approximation formula n₀ = z²p(1 − p) / d². It then applies finite population correction using the unrounded initial value: nFPC = Nn₀ / (n₀ + N − 1).

The finite population size must be the complete, defined eligible population for the study question, with sampling without replacement. It should not be a general catchment or administrative population if those units are not eligible for recruitment or measurement.

The FPC-adjusted sample size is rounded upward. Non-response inflation is then applied to that rounded value and rounded upward again. Non-response inflation supports recruitment planning but does not correct non-response bias. A calculated recruitment target above the eligible population is retained for transparency and flagged as infeasible rather than silently capped.

The method assumes a binary outcome, independent observations, and a suitable normal approximation. It does not account for clustering, stratification, weighting, design effects, repeated measurements, or paired data. Rare or extreme proportions and small populations may require protocol-specific methodological review.

Method references

  1. Cochran WG. Sampling Techniques. 3rd ed. New York: John Wiley & Sons; 1977.
  2. Kish L. Survey Sampling. New York: John Wiley & Sons; 1965.
  3. Lwanga SK, Lemeshow S. Sample Size Determination in Health Studies: A Practical Manual. Geneva: World Health Organization; 1991.

Suggested citation

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