Z-Score Calculator
Calculate the z-score (standard score) of a value given the mean and standard deviation.
How it works
- 1Enter the value (x), the mean (μ), and the standard deviation (σ).
- 2The z-score is (x − μ) ÷ σ.
- 3A positive z-score is above the mean; a negative one is below.
Use cases
- Standardise a test score against the class average.
- Compare values from different normal distributions.
- Spot outliers that are several standard deviations away.
Frequently asked questions
What is a z-score?
How many standard deviations a value is from the mean: z = (x − μ) ÷ σ. A z-score of 1.5 means the value is 1.5 standard deviations above the mean.
What does a negative z-score mean?
The value is below the mean. A z-score of 0 means the value equals the mean.
Why must the standard deviation be positive?
Dividing by zero is undefined, so a standard deviation of 0 yields no z-score.
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