Z-score calculator
Z-score of a value, and the probability to the left or right of it.
About this calculator
This z-score calculator works out how many standard deviations a value is from the mean. Enter the value, the mean and the standard deviation, or start from a z-score.
You also get the probability below and above the value, the two-tailed probability and the percentile, from the standard normal distribution.
How it works
A z-score is (x − μ) ÷ σ: how many standard deviations a value is from the mean. Probabilities come from the standard normal distribution.
Last reviewed:
Worked example
- Start from: A value, mean and standard deviation
- Value (x): 85
- Mean (μ): 70
- Standard deviation (σ): 10
Z-score: 1.5 (above the mean)
Common questions
What does a z-score tell you?
How unusual a value is. A z-score of 0 is exactly average, 1 is one standard deviation above, and −2 is two below. About 95% of values lie between −1.96 and 1.96.
How do I turn a z-score into a percentile?
Find the probability below the z-score and multiply by 100. A z-score of 1 is about the 84th percentile.
What is a two-tailed probability?
The chance of a value at least this far from the mean in either direction. It's used in hypothesis tests, where it equals the p-value for a z-test.
Sources and further reading
The story behind it
Where the idea came from: Carl Friedrich Gauss used the normal distribution in 1809 to describe errors in astronomical measurements, which is why it is also called the Gaussian distribution.
Abraham de Moivre had found the bell curve earlier, in 1733, while studying games of chance. Gauss and Pierre-Simon Laplace showed how widely it applies, from measurement errors to heights and test scores. Z-scores put any normal distribution on the same scale, so one table, or this calculator, serves them all.
Why you can trust this calculator
- It runs in your browser. Nothing you type into it is sent anywhere.
- The method is explained on this page, so you can check it yourself.
- Free to use, with no sign-up.
- Results are estimates, so please double-check anything important.
- Spotted a mistake? Tell us and we'll look into it.
After 15 years as a mathematics educator, I built CalculStore to give students, teachers, professionals and anyone working with numbers simple, reliable tools.
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