This z-score calculator shows how many standard deviations a value is above or below the mean, and converts it to a percentile assuming a normal distribution.
Z-score formula
z = (x − μ) ÷ σ
x is the value, μ is the mean and σ is the standard deviation. A z-score of 0 is exactly average; positive values are above the mean and negative values are below it.
Worked example
A test has a mean of 70 and a standard deviation of 10. A score of 85 has z = (85 − 70) ÷ 10 = 1.5. In a normal distribution, about 93.32% of scores fall below it.
Frequently asked questions
What counts as an unusual z-score?
About 95% of values in a normal distribution lie within z = ±1.96, and about 99.7% within ±3. Values beyond ±2 or ±3 are often treated as unusual.
Where do I get the mean and standard deviation?
From your data set. The standard deviation calculator finds both.