Standard Deviation Calculator

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Enter a data set to compute the sample and population standard deviation, variance and mean. Robust parsing handles commas, spaces and new lines. Free and instant.

Separate values with commas, spaces or new lines.
Sample std. deviation (s) –
Population std. deviation (σ) –
Sample variance (s²) –
Population variance (σ²) –
Mean –
Count –
Sample statistics divide by n−1 (Bessel's correction); population statistics divide by n. Sample values need at least two data points.

About Standard Deviation Calculator

The standard deviation calculator computes the sample and population standard deviation, both variances, the mean and the count from any data set you paste in. Its parser is forgiving — separate values with commas, spaces or new lines and it reads them all.

The two flavors differ by one detail: sample statistics divide the squared deviations by n − 1 (Bessel’s correction), which corrects the bias when your data is only a sample of a larger population, while population statistics divide by n. Variance is simply the standard deviation squared.

Standard deviation measures spread — how far values typically sit from the mean — making this a quick free tool for statistics homework, lab reports, quality control and analyzing survey or test results.

How to use Standard Deviation Calculator

  1. Paste or type your data set into the input, e.g. 10, 12, 23, 23, 16, 23, 21, 16.
  2. Separate values with commas, spaces or new lines — the parser handles all three.
  3. Read the sample standard deviation (s) and population standard deviation (σ).
  4. Check the variances, the mean and the count to complete your write-up.

Frequently asked questions

Use sample (s) when your data is a subset drawn from a larger group — the usual case in surveys and experiments. Use population (σ) only when your data covers every member of the group.

Bessel's correction. Deviations are measured from the sample mean, which sits closer to your data than the true mean, understating spread. Dividing by n − 1 instead of n compensates for that bias.

Variance is the average squared deviation from the mean; standard deviation is its square root. The calculator reports both (s², σ², s, σ), since variance suits further math while standard deviation reads in the data's own units.

More spread: values sit further from the mean on average. Two classes can share the same average score while one has far more variation — standard deviation is what captures that difference.

The sample formula divides by n − 1, which is zero for a single value, so sample statistics are undefined. Deviation also has no meaning until there is more than one value to differ.
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