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A z-score standardizes a value by expressing it in terms of standard deviations from the mean — a way to compare values from different distributions on the same scale.
This calculator finds a value's z-score and its corresponding percentile in a normal distribution.
How it works
Enter a value, the mean of its distribution, and the standard deviation. The calculator subtracts the mean from the value and divides by the standard deviation to find the z-score, then converts it to a percentile using the standard normal distribution.
- Enter value (x).
- Enter mean (μ).
- Enter standard deviation (σ).
- Click Calculate to see your results.
Examples
A test score
A score of 85 from a distribution with mean 75 and standard deviation 10 gives a z-score of 1.0 — higher than about 84% of scores in a normal distribution.
Who should use it
- Comparing a test score, measurement, or data point to a known mean and standard deviation.
- Checking whether a value is a statistical outlier.
Industry applications
- Statistics and data analysis education
- Quality control and process monitoring
Advantages
- Reports both the z-score and its corresponding normal-distribution percentile.
- Includes a plain-language interpretation of how unusual the value is.
Limitations
- Percentile conversion assumes an approximately normal distribution.
Common mistakes to avoid
- Applying the normal-distribution percentile to data that isn't actually normally distributed, which can give a misleading percentile.
- Mixing up the value and the mean when substituting into the formula, which flips the sign of the result.
Best practices
- Check whether your data is reasonably close to a normal (bell-curve) distribution before relying heavily on the percentile interpretation.
Tips
- A z-score of 0 always means the value equals the mean exactly — use that as a quick sanity check on your inputs.