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Mean · MEAN-FPC

Sample Size for Estimation of a Mean with FPC

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

1. Information obtained from previous studies or literature

Enter the planning SD in the same outcome units as the margin of error.

2. Information decided by the researcher

Enter the desired confidence-interval half-width in outcome units.

Use the total number of eligible people from whom the sample can be drawn.

3. Results

Enter the planning assumptions and select Calculate.

Formula, assumptions, limitations, and methodological note

Example clinical scenario

A clinic registry contains 600 adults with diabetes, and the clinic wants to estimate their mean HbA1c while accounting for the large sampling fraction.

Formula and methodological note

The calculator first estimates the unrestricted sample size using n = (z × SD / d)², then applies the finite population correction nFPC = n × N / (n + N − 1). Both planning values are rounded up before the dropout/non-response recruitment adjustment.

Use this calculator only when the full eligible population size is known, finite, and relevant to the intended sampling frame. The SD and margin of error must use the same outcome units.

It does not account for clustering, design effects, stratification, weighting, repeated measurements, or markedly non-normal outcomes. The finite population correction may be inappropriate when the stated population is not the actual sampling frame.

Method references

  1. Cochran WG. Sampling Techniques. 3rd ed. John Wiley & Sons; 1977.
  2. Chow SC, Shao J, Wang H, Lokhnygina Y. Sample Size Calculations in Clinical Research. 3rd ed. Chapman and Hall/CRC; 2017.

Suggested citation

Yaacob, Najib Majdi. “Sample Size for Estimation of a Mean with FPC (MEAN-FPC).” Web calculator. NajibMY, 2026. Accessed July 29, 2026. https://najibmy.netlify.app/tools/sample-size/mean/finite-population-correction/.