Finite Population Correction Calculator
When a sample is drawn without replacement from a known finite population, sampling variability can be reduced compared with an effectively infinite population.
How to use this calculator
- Enter integer population and sample sizes, with sample size no greater than population size.
- Check that every input uses the stated units and covers the same period, population or project scope.
- Change one assumption at a time when comparing scenarios.
Formula used by finite population correction calculator
FPC = √((N−n)/(N−1))
- FPC = √((N−n)/(N−1))
- It does not replace adjustments for clustering, stratification, non-response or other complex survey design.
- Inputs are validated against the tool-specific constraints; displayed results are rounded for readability.
Worked examples
Worked example
For a population of 1,000 and a sample of 100, the correction factor is less than one and reduces the uncorrected standard error.
The factor is calculated from population size and sample size and can be applied to an otherwise appropriate standard error.
The factor is calculated from population size and sample size and can be applied to an otherwise appropriate standard error.
Understanding the result
When a sample is drawn without replacement from a known finite population, sampling variability can be reduced compared with an effectively infinite population.
It does not replace adjustments for clustering, stratification, non-response or other complex survey design.
Important notes
It does not replace adjustments for clustering, stratification, non-response or other complex survey design.
Treat the result as an estimate for the assumptions entered; verify important specifications against the relevant source or professional guidance.
Frequently asked questions
When is the correction useful?
It is useful for simple random sampling without replacement when the sampling fraction is material.
Can I apply it to every survey?
No. Check the sampling design and the standard error formula before applying the factor.
How should I use this result?
Enter integer population and sample sizes, with sample size no greater than population size.
Related calculators
- Standard Error Calculator — Estimate the standard error of a sample mean from sample standard deviation and sample size.
- Standard Deviation Calculator — Calculate population or sample standard deviation, variance, mean, sum, and count.
- Percent Error Calculator — Calculate percentage error and absolute error between observed and reference values.
- Margin of Error Calculator — Estimate a simple proportion margin of error from sample size, assumed proportion, and a critical z value.
- Root Mean Square Error Calculator — Compare observed and predicted numeric sequences using root mean square error, mean squared error and count of observations.
- Mean Absolute Percentage Error Calculator — Calculate mean absolute percentage error from aligned observed and predicted values.
Related explanations
Learn the method behind the number or compare the terminology before using the calculator.
- How to Calculate Standard Deviation — Learn what standard deviation measures, the population and sample formulas, and how to interpret the result.
- How to Calculate Percent Error — Learn the percent error formula and how to compare an experimental value with a reference or accepted value.
- Standard Deviation — Understand standard deviation as a measure of spread and the difference between population and sample standard deviation.
This page provides a calculation tool plus explanatory information so you can understand what the result means and when the underlying method may not fit your situation.