Z-Score Calculator
Find z-scores, percentiles and convert z-scores back to values.
All calculations happen locally in your browser — nothing is uploaded, stored or tracked.
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Find the z-score of a value, or the value for a z-score.
Enter mean and standard deviation
Plus x or z.
Read the result
Z-score, percentile and interpretation.
What Is a Z-Score?
A z-score (standard score) tells you how many standard deviations a value is above or below the mean of a distribution. A z-score of 1.5 means the value sits 1.5 standard deviations above the mean.
Z-scores let you compare values from different distributions and find percentiles using the normal distribution. The calculator includes the cumulative probability (percentile) via a high-accuracy approximation of the normal CDF.
The Formula
Where x is the raw value, μ the mean and σ the standard deviation. The percentile is the area under the standard normal curve to the left of z.
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Frequently Asked Questions
How do I calculate a z-score?
Subtract the mean from the value and divide by the standard deviation: z = (x − μ) ÷ σ.
What does a z-score of 2 mean?
The value is two standard deviations above the mean — above about 97.7% of the data in a normal distribution.
Can z-scores be negative?
Yes — a negative z-score means the value is below the mean.
What is a good z-score?
There is no universally "good" score; it depends on the context. For standardized tests, higher z-scores mean better-than-average performance.
How is the percentile calculated?
From the cumulative standard normal distribution, using a numerical approximation accurate to several decimal places.