Z-score calculator
A z-score tells you how many standard deviations a value sits from the mean, which lets you compare results from different tests.
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How to use it
- Enter value (x), mean (μ) and standard deviation (σ).
- The result appears straight away and updates as you edit.
- Copy the result, or copy a link that keeps the same values to share it.
How it is calculated
z = (x - μ) ÷ σ. Share below = Φ(z), where Φ is the standard normal cumulative distribution function.
Example
Inputs: Value (x) = 85, Mean (μ) = 70, Standard deviation (σ) = 10. Result: Z-score: 1.5; Share of values below x: 93.3193%; Share of values above x: 6.6807%.
Limits and caveats
- The percentages hold only when the data is roughly normally distributed.
- The z-score itself is valid for any distribution.
Questions about this tool
What does a negative z-score mean?
The value is below the mean. For example, z = -1 is one standard deviation below it.
Which z-scores count as unusual?
Many fields treat values beyond 2 or 3 in absolute terms as unusual, but the cutoff depends on the field.
How do I compare scores from two different tests?
Work out z for each score using its own test mean and standard deviation, then compare the two z values directly.