Z-Score Calculator
Enter a value, mean, and standard deviation below to instantly get the z-score.
What Is a Z-Score?
A z-score standardizes a value by measuring how many standard deviations it sits from the mean. It's built directly on the mean and standard deviation from the standard deviation calculator.
Worked example
A test score of 85, with a class mean of 75 and standard deviation of 5.
z = (85 − 75) / 5 = 10 / 5 = 2
This score is 2 standard deviations above the mean.
Frequently Asked Questions
What is a z-score?
A z-score tells you how many standard deviations a value is from the mean. A z-score of 2 means the value sits two standard deviations above the average; a z-score of −1 means one standard deviation below.
What is the z-score formula?
z = (x − μ) / σ, where x is the value, μ is the population mean, and σ is the population standard deviation.
What does a z-score of 0 mean?
A z-score of 0 means the value is exactly equal to the mean — no distance above or below it at all.
Why convert values to z-scores?
Z-scores put values from different scales on the same footing, since they all measure distance from the mean in standard-deviation units. That makes it possible to compare, say, a test score and a height on the same terms, and it's the basis for looking up probabilities in a standard normal table.
Related Calculators
- Standard Deviation Calculator — Statistics
- Percentile Calculator — Statistics
- Mean, Median, Mode Calculator — Statistics
- Variance Calculator — Statistics