Z-Score Calculator

How many standard deviations away from the mean? With percentile and tail probabilities.

Result

Z-score

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Percentile

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P(X < x)

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P(X > x)

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Two-tailed

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The formula

z = (x − μ) / σ

Z is the number of standard deviations between your value and the mean. Positive z means above the mean; negative below.

Standard z-score milestones

  • |z| < 1 — within one SD of the mean (≈68% of data live here)
  • |z| < 2 — within two SDs (≈95%)
  • |z| < 3 — within three SDs (≈99.7%)
  • |z| ≥ 3 — outlier territory, <0.3% chance