Standard Deviation Calculator

Find the mean of your data, subtract the mean from each value and square the result, average those squared differences to get the variance, then take the square root. The square root of the variance is the standard deviation.

When your numbers represent the entire group you care about, use the population formula, which divides the sum of squared differences by n. When your numbers are a sample drawn from a larger population, use the sample formula, which divides by n − 1 (Bessel's correction) to avoid underestimating the true spread.

Dividing by n − 1 corrects a bias: because the sample mean is itself estimated from the data, dividing by n would systematically underestimate the population variance. Using n − 1 gives an unbiased estimate. This is why most statistical software defaults to the sample formula.

Variance is the average squared distance from the mean, so its units are the square of the original data's units. Standard deviation is the square root of the variance, which puts it back into the same units as your data and makes it easier to interpret.

A high standard deviation means the values are spread out widely from the mean, while a low standard deviation means they cluster tightly around the mean. A standard deviation of zero means every value is identical.