Z-Score Calculator
Calculate the z-score (standard score) for a value in a distribution.
Tip: Z = (value − mean) ÷ standard deviation. Z = 0 is the mean; Z = ±2 is far out.
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About this digital tool
The z-score calculator shows how many standard deviations a value is away from the population mean. Enter the value x, the mean (μ) and the standard deviation (σ) and get the z-score as well as the interpretation: above average, below average or at the average. The standard deviation must be greater than zero.
The formula is z = (x − μ) ÷ σ. If a student scores 85, the class mean is 70 and the standard deviation 10, then z = (85 − 70) ÷ 10 = 1.5, so the score is 1.5 deviations above the mean. The z-score allows comparison of values from different distributions and is used in statistics, in education, in quality control and for detecting outliers.
How to use
- Enter the value x you want to evaluate.
- Enter the population mean (μ).
- Enter the standard deviation (σ), which must be greater than zero.
- Read the z-score and the interpretation: above, below or at the mean.
Frequently asked questions
What does the z-score show?
How many standard deviations from the mean the value lies. Z = 1.96 means 97.5% of values are below this level (in a normal distribution).
What does a negative z-score mean?
It means the value is below the mean. E.g. x = 55, μ = 70, σ = 10 gives z = −1.5, so 1.5 deviations below the mean.
How do I compare two scores from different tests with the z-score?
Calculate z for each. If A has 80 (μ = 70, σ = 10) and B has 88 (μ = 70, σ = 12), z_A = 1 and z_B = 1.5, so B is relatively better.
What is the 68-95-99.7 rule?
In a normal distribution about 68% of values fall within z = ±1, 95% within ±2 and 99.7% within ±3. A z-score above 3 is considered very rare.