Standard Deviation Calculator

Measure how widely values spread around their mean. Enter your own values below to see standard deviation and check the method behind it.

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Your inputs

Change the example values to match your situation.

Your result

Let’s work it out.

Fill in your inputs and select Calculate.
Your result and breakdown will appear here.

How this calculator works

Variance = sum of squared deviations from the mean ÷ N (population) or N−1 (sample). Standard deviation is its square root.

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What is Standard Deviation Calculator?

Standard Deviation Calculator helps you measure how widely values spread around their mean.

The main result is standard deviation, with a breakdown of mean, count and variance. The formula, example and assumptions below explain how to interpret it.

How to use Standard Deviation Calculator

Use the example to get familiar with the form, then enter your own figures. Any rates in the example are illustrative. Check the field labels and units before calculating.

  1. Gather data values and dataset type. Use values from the same situation or reporting period.
  2. Replace the example data values with your own value, then complete the other fields. Check the displayed units and each selected option.
  3. Select Calculate and read standard deviation with its result breakdown. Change one input and calculate again to compare a second scenario. Reset restores the original example.
  • Enter data values in the format shown by the example. Keep the same separators and row structure.
  • Choose dataset type from Whole population and Sample.

Standard Deviation Calculator: a worked example

With the inputs below, the result is 2 (standard deviation). Follow the example, then replace these illustrative values with your own.

Example inputs and output
Input or outputExample value
Data values2, 4, 4, 4, 5, 5, 7, 9
Dataset typeWhole population
Standard deviation2
Mean5
Count8
Variance4

Understanding the Standard Deviation result

Read standard deviation alongside mean, count and variance. These describe different parts of the same calculation.

Displayed results use a readable number of decimal places. When checking a result by hand, keep extra precision until the last step. To compare scenarios, change one input at a time and keep the others fixed.

  • Example Mean: 5
  • Example Count: 8
  • Example Variance: 4

Standard Deviation Calculator: assumptions and common mistakes

A useful estimate starts with the right inputs. Check the following assumptions and limits before applying the result to your situation.

  • Check the base value, sample definition and chosen operation. Display rounding should come after the calculation.

For wider guidance, visit NIST statistical handbook. The formula and scope of this specific tool are stated on this page.

Standard Deviation Calculator FAQs

What does Standard Deviation Calculator calculate?

Standard Deviation Calculator helps you measure how widely values spread around their mean. Its main output is standard deviation.

What inputs do I need for Standard Deviation Calculator?

You need data values and dataset type. Use the field labels and units to match your figures to the formula.

Which formula does Standard Deviation Calculator use?

Variance = sum of squared deviations from the mean ÷ N (population) or N−1 (sample). Standard deviation is its square root.

What is a worked example for Standard Deviation Calculator?

Example inputs: Data values: 2, 4, 4, 4, 5, 5, 7, 9; Dataset type: Whole population. The result is 2 (standard deviation).

How should I enter data values?

Enter data values in the format shown by the example. Keep the same separators and row structure.

How do I choose dataset type?

Choose dataset type from Whole population and Sample. The example uses Whole population; replace it if your circumstances differ.

How should I read standard deviation?

Read standard deviation alongside mean, count and variance. These describe different parts of the same calculation.

Why might my Standard Deviation Calculator result differ from my records?

Check the base value, sample definition and chosen operation. Display rounding should come after the calculation. Differences in entered values, units or rounding can also change the comparison.

Can I compare two scenarios in Standard Deviation Calculator?

Yes. Note your first standard deviation, change data values or another input, and select Calculate again. Editing a field clears the old result so it is not mistaken for a new calculation.

Is Standard Deviation Calculator free, and where are my inputs calculated?

This calculator is free to use without signing in. Its formula runs in your browser; calculator inputs are not sent to a calculation API. The inputs reset to the example values when you reset the form or start a fresh page.