Standard Deviation Calculator

Standard deviation measures how spread out numbers are from the mean (average). A low standard deviation means values cluster close to the mean; a high standard deviation means values are widely dispersed. For example, test scores of [70, 72, 68, 71, 69] have a low SD (~1.6), while [50, 90, 60, 80, 70] have a high SD (~15.8).

Population SD (sigma) divides by N (total count) — use when your data includes every member of the group. Sample SD (s) divides by N-1 (Bessel's correction) — use when your data is a subset of a larger population. Sample SD is slightly larger, compensating for the underestimation that occurs with incomplete data.

Variance is the average of squared deviations from the mean. Standard deviation is the square root of variance. Variance is useful in statistical formulas, but standard deviation is more interpretable because it uses the same units as the original data. If heights are in cm, SD is in cm while variance is in cm squared.

Beyond standard deviation and variance, the calculator provides: mean (average), median (middle value), mode (most frequent value), range (max minus min), sum, count, minimum, maximum, quartiles (Q1, Q2, Q3), interquartile range (IQR), coefficient of variation, and standard error of the mean.

Enter numbers separated by commas, spaces, or newlines. The calculator accepts integers and decimals, including negative numbers. You can paste data directly from a spreadsheet — one column of numbers will be parsed automatically. The tool handles data sets from 2 to thousands of values.