Population & Sample Variance Calculator

About this calculator

Population variance divides the sum of squared deviations from the mean by N: σ² = Σ(x−μ)²/N. Sample variance instead divides by n−1 — s² = Σ(x−x̄)²/(n−1), known as Bessel's correction — which corrects the downward bias that would otherwise result when estimating a population's variance from a limited sample.

This calculator returns both figures along with the mean and count, since which one applies depends entirely on whether your numbers are the entire group of interest or just a sample of it. It's used throughout statistics coursework, quality-control process monitoring, financial return-volatility analysis, and any research setting where the spread of the data — not just its average — needs to be reported correctly.