Z-Score to Percentile Calculator
The percentile of a z-score on the standard normal distribution.
Result
Percentile (below)
84.13
Percent above
15.87
How it works
A z-score locates a value inside a normal distribution: it counts how many standard deviations the value sits above (positive z) or below (negative z) the mean. This calculator converts that position into a percentile — the share of the population below it — using the standard normal cumulative function Φ(z). The landmarks are worth memorising: z = 0 is the 50th percentile (exactly average), z = 1 is about the 84th, z = 2 about the 97.7th, and z = 1.96 the 97.5th — the value behind the classic 95% confidence interval. Symmetry handles negatives: Φ(−z) = 1 − Φ(z), so z = −1 lands at the 16th percentile. Percentiles are how z-scores become meaningful in practice: standardized test results, children's growth charts and quality-control limits all report "you are here" as a percentage of the reference population.
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Frequently asked questions
What percentile is z = 1?
About the 84th percentile — 84% of values fall below it.
What does a negative z give?
A percentile below 50, since the value is below the mean.
How do I go back from a percentile to a z-score?
Use the inverse of Φ. Handy landmarks: the 90th percentile is z ≈ 1.28, the 95th z ≈ 1.645, the 97.5th z ≈ 1.96 and the 99th z ≈ 2.33.
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