How it works
Calculate a required survey sample size or the margin of error for a proportion, including finite-population correction. 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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?calculation=CalculateChoice · Required · Default: sample-size · Accepted values: sample-size, margin-error
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?confidenceLevel=Confidence levelChoice · Required · Default: 95 · Accepted values: 80, 85, 90, 92, 95, 96, 98, 99, 99.9
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?populationProportion=Population proportionPercentage · Required · Default: 50
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?populationSize=Population size (optional)Number · Optional
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?marginOfError=Desired margin of errorPercentage · Required · Default: 5 · Used when calculation = sample-size
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?sampleSize=Observed sample sizeNumber · Required · Default: 385 · Used when calculation = margin-error
Outputs
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requiredSampleSizeRequired sample sizeWhole number · Primary output
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marginOfErrorResultMargin of errorPercentage
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confidenceIntervalConfidence intervalText
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criticalZCritical z-scoreNumber
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finiteCorrectionFinite-population correctionNumber
Formula notes
n₀=z²p(1−p)/e²; finite n=n₀/[1+(n₀−1)/N]; e=z√[p(1−p)/n] with finite correction.
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.