Standard Deviation Calculator

How it works

Standard deviation measures how spread out a set of numbers is from the mean. A small standard deviation means values cluster tightly around the average; a large standard deviation means they vary widely. It is one of the most useful descriptive statistics in any quantitative field.

There are two versions: population standard deviation (σ, divides by N) and sample standard deviation (s, divides by N−1). Use the population version when you have data on every member of the group you care about; use the sample version when you have a subset and want to estimate the standard deviation of the larger population. The N−1 in the sample formula is "Bessel's correction" and corrects for the bias that arises from estimating the population mean from the sample.

In practice, most data is sampled — survey results, lab measurements, manufacturing tolerances — so the sample standard deviation is what you usually want. Spreadsheet functions like STDEV() typically compute the sample version; STDEVP() is the population version.

Standard deviation has the same units as the data, which makes it easier to interpret than variance (which is in squared units). For normally distributed data, ~68% of values fall within 1 standard deviation of the mean, ~95% within 2, and ~99.7% within 3. Many real-world distributions are not normal, so use this rule with care.

This calculator also outputs the median (the middle value when sorted), which is more robust than the mean to outliers, and the min/max/range. For small datasets the median is often a more honest summary than the mean. Look at both, and consider plotting the data — summary statistics can hide bimodal or skewed distributions that you'd miss without a visualization.