Standard Deviation Calculator

Population standard deviation (σ) divides by n — use it when your numbers are the entire population you care about. Sample standard deviation (s) divides by n − 1 (Bessel's correction) — use it when your numbers are a sample drawn from a larger population. For most everyday data analysis, sample std dev is what you want; statistical software defaults to it.

When in doubt, report the sample standard deviation. It's the unbiased estimator of the underlying population's spread when you only have a sample. We show both so you can pick the one that matches your context.

Variance is the average squared distance from the mean. Standard deviation is the square root of variance — it brings the figure back into the same units as your data. So std dev = √variance.

Population standard deviation will be 0 (a single value has no spread). Sample standard deviation is undefined when n = 1, because dividing by n − 1 means dividing by zero — we report it as undefined rather than 0.