Finite Population Correction Calculator

The FPC factor is a multiplier used to reduce the standard error when sampling from a finite population without replacement. It accounts for the fact that as your sample covers a larger proportion of the population, there is less variability in the estimate. The formula is: FPC = √((N − n) / (N − 1)), where N is the population size and n is the sample size.

The standard error is reduced when you apply the FPC factor. Without correction, SE = σ / √n. With the FPC applied, the adjusted SE = (σ / √n) × √((N − n) / (N − 1)). The bigger your sample is relative to the population, the more the FPC shrinks the standard error, reflecting lower uncertainty.

You should apply the FPC when your sample size is more than about 5–10% of the total population. If the sampling fraction (n/N) is very small, the correction factor approaches 1 and has negligible effect, making it safe to use the standard infinite-population formula.

As n approaches N, the numerator (N − n) approaches 0, making the FPC factor approach 0 as well. This means the standard error also approaches 0 — which makes intuitive sense, because if you survey the entire population, there is no sampling uncertainty at all.

Sampling with replacement means each selected individual is returned before the next draw, so the same person can be selected more than once. Sampling without replacement — the more common real-world scenario — means each individual can only appear once in the sample. The FPC formula applies specifically to sampling without replacement from a finite population.

Yes. Since confidence intervals are built around the standard error (e.g., mean ± z × SE), a smaller adjusted SE from the FPC directly narrows your confidence interval. This means you get more precise estimates when sampling from a small, finite population.

The sampling fraction is simply n/N — the proportion of the population you have sampled. A higher sampling fraction means your sample captures more of the population, reducing uncertainty. Once the sampling fraction exceeds ~10%, the FPC correction becomes practically significant and should not be ignored.

The FPC factor itself (√((N − n) / (N − 1))) applies equally to standard errors of proportions and means. For proportions, the base standard error formula changes to √(p(1−p)/n), but you multiply the same FPC factor to get the adjusted value. This calculator uses the standard deviation σ input suited for means.