How it works
Calculate a z-score, convert between z and normal probability, or find probability between two z-scores. 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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?mode=CalculationChoice · Required · Default: raw-score · Accepted values: raw-score, z-to-probability, probability-to-z, between
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?rawScore=Raw score (x)Number · Required · Default: 85 · Used when mode = raw-score
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?mean=Population mean (μ)Number · Required · Default: 75 · Used when mode = raw-score
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?standardDeviation=Standard deviation (σ)Number · Required · Default: 10 · Used when mode = raw-score
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?zValue=Z-scoreNumber · Required · Default: 1 · Used when mode = z-to-probability
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?leftProbability=Left-tail probability P(X<z)Number · Required · Default: 0.841344746 · Used when mode = probability-to-z
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?leftZ=Left z-scoreNumber · Required · Default: -1 · Used when mode = between
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?rightZ=Right z-scoreNumber · Required · Default: 1 · Used when mode = between
Outputs
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zScoreZ-scoreNumber · Primary output
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probabilityLessP(X < z)Percentage
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probabilityGreaterP(X > z)Percentage
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probabilityMeanToZArea between mean and zPercentage
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probabilityCentralP(−|z| < X < |z|)Percentage
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probabilityTwoTailOutside ±|z|Percentage
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betweenProbabilityProbability between boundsPercentage
Formula notes
z=(x−μ)/σ; probabilities use the standard-normal CDF Φ(z); inverse conversion uses z=Φ⁻¹(p).
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.