Z-Score Calculator
Convert a raw value to a z-score and percentile: how many standard deviations from the mean, and what share of a normal population falls below it.
Z-score
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Percentile —
Interpretation —
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How it works
z = (x − μ) ÷ σ; percentile = Φ(z)Frequently Asked Questions
What does a z-score tell you?
How unusual a value is: z = 0 is exactly average, z = +1 beats about 84% of a normal population, z = +2 beats about 97.7%. Negative scores mirror below the mean.
How do I convert a z-score to a percentile?
Look up (or compute) the standard normal cumulative probability Φ(z). This calculator does it with a high-accuracy approximation of the error function.
Where are z-scores used?
Standardized testing, quality control, medical growth charts, finance risk models — anywhere values from different scales must be compared on one footing.