A z-score says how many standard deviations a value is above or below the mean. It lets you compare results from different scales and, for normally distributed data, find the percentile a value sits at.
Formula
z = (x - mu) / sigma
Where z is the z-score, x is the raw value, mu is the mean (μ), sigma is the standard deviation (σ).
Choose any value to calculate — the calculator rearranges the formula for you.
Worked example
A test score of 85 where the mean is 70 and the standard deviation is 10 has z = (85 − 70) ÷ 10 = 1.5. About 93.32% of scores fall below it, so it is roughly the 93rd percentile.
Reading z-scores
z = 0 is exactly average. About 68% of values have |z| < 1, 95% have |z| < 1.96 and 99.7% have |z| < 3. Values beyond ±3 are often treated as outliers.
Frequently asked questions
Can a z-score be negative?
Yes — a negative z-score means the value is below the mean. z = −2 is two standard deviations below average.
How is the percentile calculated?
From the standard normal distribution: the percentile is the area under the bell curve to the left of the z-score. This assumes your data is roughly normally distributed.
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