Standard Deviation Calculator

The standard deviation calculator takes one pasted list of numbers and reports how spread out they are: the standard deviation itself, the variance, the mean, the standard error of the mean (SEM) and the coefficient of variation (CV%). Separators are flexible — commas, spaces, semicolons or one value per line — and locale decimal commas such as 3,14 are read correctly.

The math is the exact two-pass definition, not an approximation. First pass: the mean x̄ = Σxᵢ ÷ n. Second pass: the sum of squared deviations Σ(xᵢ − x̄)². The variance divides that sum by n − 1 for a sample or by n for a full population, and the standard deviation is its square root. For the classic list 2, 4, 4, 4, 5, 5, 7, 9 the population SD is exactly 2 and the sample SD is about 2.1381.

Choosing between sample and population matters. Use population (÷ n) when your numbers are the complete set you care about — every student in one class, every server in one rack. Use sample (÷ n − 1, Bessel's correction) when the numbers are a subset standing in for something larger — a poll, a batch of measurements — because dividing by n would systematically underestimate the spread.

The step-by-step table prints xᵢ, xᵢ − x̄ and (xᵢ − x̄)² for each value, so you can hand-check any row — for long lists it shows the first 50 rows and says so honestly, while the sums underneath always include every value. Everything runs locally in your browser: no upload, no account, instant results.