Standard Deviation Calculator

Standard deviation measures how spread out a set of numbers is from its average. A small standard deviation means values cluster tightly around the mean; a large one means they're spread widely.

Population standard deviation is used when your numbers ARE the entire group you care about — divide the variance by N (the count). Sample standard deviation is used when your numbers are only a sample drawn from a larger group you're trying to draw conclusions about — divide by N-1 instead, which corrects for the fact that a sample tends to slightly underestimate the true spread of the full population.

This is known as Bessel's correction. A sample's own mean is calculated FROM that same sample, which makes the sample slightly less spread out around its own mean than the true population is around the true population mean. Dividing by N-1 instead of N slightly enlarges the result to correct for that bias.

Sample standard deviation divides by N-1, which is zero when there's only one value — a division that's mathematically undefined. Population standard deviation, on the other hand, works fine with one value (a single value has zero deviation from itself, so the result is exactly 0).

Variance is standard deviation squared — the average of each value's squared distance from the mean. It's an intermediate step in calculating standard deviation, shown here because it's useful in its own right for some statistical formulas.

Yes, both are fully supported.

No. Every calculation happens locally in your browser using JavaScript, with no intermediate rounding, so the result is as accurate as your browser's floating-point math allows. Nothing you enter here is sent to Brekzy or stored anywhere.