Z-Score Calculator
Calculate z-scores from raw scores, find raw scores from z-scores, and convert between z-scores and percentiles. Free online z-score calculator.
Common Z-Scores
z = -3→ 0.13%
z = -2→ 2.28%
z = -1→ 15.87%
z = 0→ 50%
z = 1→ 84.13%
z = 2→ 97.72%
z = 3→ 99.87%
z = 1.96→ 97.5%
Z-Score Formulas
Z-Score: z = (x - μ) / σ
Raw Score: x = μ + zσ
Where: x = raw score, μ = mean, σ = standard deviation
Standard Normal Distribution
About 68% of values fall within ±1 standard deviation
About 95% of values fall within ±2 standard deviations
About 99.7% of values fall within ±3 standard deviations
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