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Standard Deviation Calculator

Calculate population standard deviation from a number list. See how the n denominator differs from sample standard deviation.

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Calculate population standard deviation from a number list. See how the n denominator differs from sample standard deviation.

This tool runs open-source code from CyberChef by GCHQ (Apache License 2.0). See open-source credits.

Standard Deviation Calculator measures spread around the mean using the population formula. It divides squared deviations by the accepted value count, then takes the square root. This differs from sample standard deviation, which divides by one fewer observation.

The result is population standard deviation, expressed in the same unit as the accepted input values. Processing runs in the browser.

  • Describe variability across all observations in a defined group.
  • Compare spread between complete datasets measured in the same units.
  • Check a population standard deviation calculation against a worked example.

Instructions

  1. Use Standard Deviation Calculator when your list represents the population you want to describe.
  2. Enter finite observations using one consistent measurement unit.
  3. Select the delimiter that separates your observations. Choose Space for the worked example.
  4. Read the population standard deviation. Use the separate sample calculator when the calculation requires n minus 1.

Example

Input: 2 4 4 4 5 5 7 9

Settings: Standard Deviation Calculator: Delimiter: space.

Result: The example returns 2. The mean is 5; squared deviations sum to 32; sqrt(32 / 8) = 2.

Standard Deviation Calculator: Using the sample denominator 7 would produce approximately 2.1381. This calculator uses the population denominator 8.

Limits

  • Standard Deviation Calculator: The parser excludes nonnumeric items, so check the full input before interpreting the spread.
  • Standard Deviation Calculator: This operation always uses the population denominator n. It has no sample-mode switch or confidence-interval calculation.
  • Standard Deviation Calculator: One finite observation or identical finite values produce zero. An empty accepted list has no standard deviation.

Questions

Does this calculate population or sample standard deviation?

This tool uses population standard deviation. It divides the sum of squared deviations by the accepted count n, then takes the square root. Use the separate sample standard deviation calculator when your formula requires n minus 1.

What is a worked population standard deviation example?

For 2, 4, 4, 4, 5, 5, 7, and 9, the mean is 5. Squared deviations sum to 32. Dividing by 8 gives 4, and its square root is 2.

Why can the result be zero?

Identical finite observations have no spread around their mean, so their population standard deviation is zero. One finite observation also produces zero under this formula. This does not establish that a larger population or future observations have no variation.

What should I check before interpreting the result?

Match the delimiter and use consistent units. Nonnumeric items are excluded, so inspect the source list for omissions. The result describes spread; it does not establish independence, normality, statistical significance, or a confidence interval.