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Statistics — Dispersion
Standard Deviation Calculator
Paste any list of numbers to get the sample and population standard deviation, variance and mean — the full measure of how spread out your data is.
Sample standard deviation (s)
—
Spread of a sample around its mean.
| Count how many values (n) | — |
|---|---|
| Mean the average | — |
| Sum | — |
| Sample variance s², divides by n−1 | — |
| Population variance σ², divides by n | — |
| Population std. deviation σ | — |
Show our math
Enter your figures above to see the step-by-step working.
Paste comma, space or line-separated numbers — sample and population both shownEverything computed client-side — nothing leaves this page
How the Standard Deviation Calculator Works
Standard deviation measures how far a set of numbers typically sits from their mean. A small standard deviation means the values cluster tightly around the average; a large one means they are spread out. Paste your data set and the desk returns both the sample and population figures, along with the mean, variance and count.
Use the sample standard deviation (which divides by n−1) when your numbers are a sample drawn from a larger group — the most common case. Use the population standard deviation (which divides by n) only when your data covers the entire population. The difference shrinks as the sample grows.
s = √( Σ(x − x̄)² ÷ (n − 1) ) · σ = √( Σ(x − x̄)² ÷ n )
Frequently Asked Questions
What is the difference between sample and population standard deviation?
The sample version divides the summed squared deviations by n−1 (Bessel’s correction) and is used when your data is a sample of a larger group. The population version divides by n and is used only when you have every member of the population. This tool shows both.
Should I use standard deviation or variance?
Variance is the average squared deviation from the mean; standard deviation is its square root. Standard deviation is usually more useful because it is in the same units as your data, while variance is in squared units.
What counts as a high standard deviation?
It depends entirely on your data’s scale — there is no universal threshold. Compare it to the mean: a standard deviation that is a large fraction of the mean indicates high relative variability.
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