How this calculator works
z = (x − mean) ÷ standard deviation. A z-score of 1.5 means 1.5 standard deviations above the mean.
For normally distributed data, z converts to a percentile using the standard normal distribution.
The share within ±|z| of the mean is also shown: about 68% within 1, 95% within 1.96 and 99.7% within 3.
Percentiles are accurate only if the data is roughly bell-shaped.
Worked example
A test score of 85 where the mean is 70 and SD is 10
- z = (85 − 70) ÷ 10 = 1.5.
- About 93.32% of scores fall below 85.
- So the score is around the 93rd percentile.
Questions people ask
What does a negative z-score mean?
The value is below the mean. z = −1 is one standard deviation below, around the 16th percentile.
What z-score is significant?
In many tests, |z| above 1.96 is significant at the 5% level, because only 5% of a normal distribution lies further out.
Can I compare scores from different tests?
Yes. Converting each to a z-score puts them on the same scale, showing which result was relatively better.
Where do I get the mean and standard deviation?
From your data set; the standard deviation and mean calculators work them out from a list of numbers.
Last reviewed October 2, 2026