Math & StatisticsFormula-based · Runs in your browser

Standard Deviation Calculator

Calculate population or sample standard deviation, variance, mean, sum, standard error, and margin of error.

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Inputs

Enter the values you know. Optional fields may be left empty.

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Result

Updates as valid inputs change.

Calculated locally
Standard deviation
Variance
Mean
Sum
Count
Standard error
Margin of error

Saved locally, explained clearly

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Calculation steps

Follow what happened from the selected formula to the displayed answer.

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  1. 1

    Formula selected

    The calculator uses the following formula or method.

    Population: σ = √[Σ(x − μ)²/n]; sample: s = √[Σ(x − x̄)²/(n − 1)]; margin = z·s/√n.

  2. 2

    Values entered

    Your values are placed into the calculation.

    Enter values to see what is used in this step.

  3. 3

    Result calculated

    The formula or method produces the following result values.

    Results will appear after a successful calculation.

  4. 4

    Answer formatted

    Displayed values are rounded and formatted using each output’s configured precision.

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Data and privacy

How it works

Calculate population or sample standard deviation, variance, mean, sum, standard error, and margin of error. Inputs are calculated locally in the browser, and valid values are retained in the page URL for bookmarking.

Input query strings and outputs

Use an input name in this page’s URL as ?name=value, and join additional inputs with &. Portable shared links may instead use the compact ?ac= state parameter.

Input query strings

3
  • ?values= Numbers

    Text · Required · Default: 10, 12, 23, 23, 16, 23, 21, 16

  • ?sample= Treat the values as a sample

    True or false · Optional · Default: false

  • ?confidenceLevel= Confidence level for margin of error

    Choice · Required · Default: 95 · Accepted values: 80, 90, 95, 98, 99

Outputs

7
  • standardDeviation Standard deviation

    Number · Primary output

  • variance Variance

    Number

  • mean Mean

    Number

  • sum Sum

    Number

  • count Count

    Whole number

  • standardError Standard error

    Number

  • marginOfError Margin of error

    Number

Formula notes

Population: σ = √[Σ(x − μ)²/n]; sample: s = √[Σ(x − x̄)²/(n − 1)]; margin = z·s/√n.

Input guidance

Use consistent units for every length or measurement in the same calculation. Results are educational mathematical estimates and should be checked before high-stakes use.

Sources
Limitations
  • Results depend on the selected method and input assumptions. Displayed decimals may be rounded; retain appropriate precision for later calculations.