Sample standard deviation

Sample standard deviation is the square root of sample variance:

s = √(Σ(xᵢ − x̄)² / (n − 1))

Where x̄ is the sample mean, n is the sample size, and the sum runs over all values. The n − 1 divisor is Bessel’s correction — it compensates for the fact that the sample mean is closer to the data than the (unknown) true population mean would be, which makes the raw sum of squared deviations under-estimate the true population variance.

Use sample SD when your dataset is drawn from a larger group you can’t measure exhaustively (which is almost always). Use population SD (divide by n) only when the dataset literally is the entire population — every employee in your company, every transaction in March.

At large sample sizes the difference is negligible (n vs n-1 is rounding noise). At small sample sizes — say, n < 30 — the correction matters meaningfully and you should prefer the sample form.

Our statistics calculator defaults to the sample form with a toggle to switch to population.