Math & StatisticsFormula-based · Runs in your browser

Confidence Interval Calculator

Calculate a two-sided normal confidence interval and margin of error for a population mean.

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Inputs

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Result

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Calculated locally
Lower bound
Upper bound
Confidence interval
Margin of error
Standard error
Critical z-score

Saved locally, explained clearly

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Calculation steps

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  1. 1

    Formula selected

    The calculator uses the following formula or method.

    CI=x̄±z*·σ/√n; margin of error=z*·σ/√n.

  2. 2

    Values entered

    Your values are placed into the calculation.

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  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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How it works

Calculate a two-sided normal confidence interval and margin of error for a population mean. 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

4
  • ?sampleSize= Sample size (n)

    Number · Required · Default: 100

  • ?sampleMean= Sample mean (x̄)

    Number · Required · Default: 50

  • ?standardDeviation= Standard deviation (σ or s)

    Number · Required · Default: 10

  • ?confidenceLevel= Confidence level

    Choice · Required · Default: 95 · Accepted values: 80, 85, 90, 95, 98, 99, 99.9

Outputs

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  • lowerBound Lower bound

    Number · Primary output

  • upperBound Upper bound

    Number · Primary output

  • interval Confidence interval

    Text

  • marginOfError Margin of error

    Number

  • standardError Standard error

    Number

  • criticalZ Critical z-score

    Number

Formula notes

CI=x̄±z*·σ/√n; margin of error=z*·σ/√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.

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