Z-Score Calculator

Calculate z-score, percentile rank, and probability for any value in a normal distribution.

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How it works

Enter a raw score, the population mean, and the standard deviation. The tool computes the z-score (how many standard deviations the score is from the mean), then uses the cumulative normal distribution function to find the percentile rank — the percentage of values below this score. The complementary probability (values above) is also shown. All math runs locally in your browser.


              z = (x − μ) / σ

Common use cases

  • Finding where a test score falls relative to the class average.
  • Determining the percentile rank of a measurement in a normal population.
  • Checking whether an outlier is statistically unusual (z > 2 or z < −2).

Frequently asked questions

What does a z-score of 2 mean?

It means the value is 2 standard deviations above the mean. In a normal distribution, about 97.7% of values fall below z = 2.

Does this assume a normal distribution?

Yes. Z-scores and the percentile conversions assume the data follows a normal (Gaussian) distribution. For non-normal data, the percentile interpretation may not be accurate.