Standard Deviation Calculator

Standard deviation measures how spread out a set of numbers is around their mean (average). A small standard deviation means the values cluster close to the mean; a large one means they are widely scattered. It is the square root of the variance.

Population standard deviation divides the sum of squared deviations by n (the full count) and is used when you have every member of the group. Sample standard deviation divides by n−1 (Bessel’s correction) and is used when your data is a sample drawn from a larger population — it gives an unbiased estimate. When in doubt with real-world data, use sample.

First find the mean. Then subtract the mean from each value and square the result. Add up all those squared differences. Divide by n (population) or n−1 (sample) to get the variance. Finally, take the square root of the variance to get the standard deviation.

Variance is the average of the squared deviations from the mean. Standard deviation is the square root of the variance, which returns the measure to the original units of the data. Standard deviation is usually easier to interpret because it is in the same units as the values themselves.

A standard deviation of 0 means every value in the data set is identical — there is no spread at all. Standard deviation can never be negative.