Z-Score Calculator
Formula
Z = (X - μ) / σ
Standard deviations from the mean
About This Calculator
This z-score calculator helps you move from raw inputs to a decision-ready output in seconds.
Standardize values against a distribution to measure how far an observation sits from the mean in standard deviations.
If your workflow expands, pair this calculator with Standard Deviation Calculator and Mean, Median, Mode Calculator to cross-check assumptions and build a stronger analysis chain.
Formula
z = (x - mu) / sigma
Example Calculation
The worked example below demonstrates how the input fields translate into the final output. Use it as a quick validation pass before entering your own numbers.
- valueX: 78
- mean: 65
- standardDeviation: 5
Explanation of Results
Result Interpretation
A z-score of 2.6 means the observation is 2.6 standard deviations above the distribution mean.
FAQ
What z-score is considered unusual?
In many contexts, absolute z-scores above 2 are uncommon and above 3 are rare under normal assumptions.
Can z-score be negative?
Yes. Negative values indicate observations below the mean.
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See Also
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