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
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?sampleSize=Sample size (n)Number · Required · Default: 100
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?sampleMean=Sample mean (x̄)Number · Required · Default: 50
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?standardDeviation=Standard deviation (σ or s)Number · Required · Default: 10
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?confidenceLevel=Confidence levelChoice · Required · Default: 95 · Accepted values: 80, 85, 90, 95, 98, 99, 99.9
Outputs
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lowerBoundLower boundNumber · Primary output
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upperBoundUpper boundNumber · Primary output
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intervalConfidence intervalText
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marginOfErrorMargin of errorNumber
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standardErrorStandard errorNumber
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criticalZCritical z-scoreNumber
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.