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Free Standard Deviation Calculator

Calculate mean, variance and standard deviation.

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What is the Standard Deviation Calculator?

An average alone hides a lot — two data sets can share the same mean while one is tightly clustered and the other wildly spread out. Standard deviation measures that spread, telling you how far values typically sit from the average.

This calculator finds the mean, variance and standard deviation of a data set, giving both the population and sample versions, right in your browser.

Last updated: Aug 12, 2026

What does this tool do?

You paste a list of numbers and the tool computes the mean, then how far the values deviate from it on average.

It reports both population standard deviation (when your data is the whole group) and sample standard deviation (when it's a subset), since the two use slightly different formulas.

Key features

Population and sample

Both standard deviations, side by side.

Mean and variance

The full set of spread statistics.

Flexible input

Commas, spaces or new lines all work.

Instant

Results update as you edit the data.

Private

Your numbers are calculated in the browser.

Example

Input
4, 8, 15, 16, 23, 42
Processing
The tool finds the mean, then the average squared deviation.
Output
Mean 18, with population and sample standard deviations.

Common use cases

  • StudentsSolve statistics coursework.
  • ResearchersSummarize the spread of results.
  • AnalystsMeasure variability in data.
  • TeachersCheck statistics answers.
  • Quality engineersTrack process consistency.
  • InvestorsGauge the volatility of returns.
  • ScientistsReport measurement uncertainty.
  • Sports analystsCompare consistency across players.

Benefits

  • It shows spread, which the mean alone can't.
  • It gives both population and sample versions.
  • It handles messy pasted data.
  • Your numbers stay on your device.

Tips

  • Use sample standard deviation when your data is a subset of a larger group.
  • Use population standard deviation when you have the entire group.
  • A larger standard deviation means more spread-out data.
  • Standard deviation is in the same units as your data; variance is squared.
  • Outliers inflate standard deviation, so check for them.
  • About two-thirds of normally distributed data falls within one standard deviation of the mean.
  • Separate values with commas, spaces or new lines.
  • Pair it with the average calculator for the full picture.

Common mistakes to avoid

Using population when you have a sample

Fix: For a subset of a larger group, use the sample standard deviation.

Comparing variance to raw data

Fix: Variance is in squared units — use standard deviation to compare with the data itself.

Ignoring outliers

Fix: A single extreme value can inflate the spread; check the data first.

Too few data points

Fix: Sample standard deviation needs at least two values.

How it works

  1. 1

    Enter data

    Paste your numbers.

  2. 2

    See the spread

    Mean, variance and deviation appear instantly.

Frequently asked questions

It shows both — use sample when your data is a subset, and population when it's the whole group.

Separate values with commas, spaces or new lines.

It shows both — use sample when your data is a subset, and population when it's the whole group.

Separate values with commas, spaces or new lines.

Standard deviation is the square root of variance, so it's in the same units as your data and easier to interpret.

The values are more spread out from the mean; a small one means they're tightly clustered.

Yes. Extreme values increase the standard deviation, so review your data for them.

No. Everything is calculated in your browser.

Conclusion

Standard deviation turns an average into a fuller story about your data's spread. Pair it with the average calculator to summarize any data set.

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