Z-Score Calculator
A Z-score measures how many standard deviations a value is from the mean. Enter a value, mean, and standard deviation, and this calculator displays the Z-score. In reverse mode, enter a Z-score, mean, and standard deviation to find the corresponding value. A reference table shows Z-scores and their corresponding percentiles for common values. Z-scores are used to standardize data, identify outliers, and calculate probabilities in statistics.
Z-score formula
Z = (x - mean) / standard deviation
x = mean + Z * standard deviation
Z-score to percentile reference
| Z-score | Percentile |
|---|---|
| -3.00 | 0.13% |
| -2.00 | 2.28% |
| -1.00 | 15.87% |
| 0.00 | 50.00% |
| 1.00 | 84.13% |
| 2.00 | 97.72% |
| 3.00 | 99.87% |
Z-score calculator: frequently asked questions
What is a Z-score?
A Z-score (or standard score) measures how many standard deviations a value is from the mean. Z = (x - mean) / standard deviation. A Z-score of 0 means the value equals the mean. Positive Z-scores are above the mean; negative are below. Z-scores are used to standardize values and compare data from different scales.
What does a Z-score of 2 mean?
A Z-score of 2 means the value is 2 standard deviations above the mean. For normally distributed data, approximately 97.7% of values have a Z-score below 2 (within 2 standard deviations of the mean). A Z-score of 2 is unusual but not extremely rare.
How are Z-scores used?
Z-scores identify outliers (usually values with Z-score > 3 or < -3), compare values from different datasets, and calculate probabilities using the standard normal distribution. They standardize data to have mean 0 and standard deviation 1.
What is the relationship between Z-score and percentile?
The Z-score determines the percentile: a Z-score of 0 is the 50th percentile, Z=1 is approximately 84th percentile, Z=2 is approximately 98th percentile. Use a standard normal table to convert between Z-scores and percentiles.
Can Z-scores be negative?
Yes. Negative Z-scores indicate values below the mean. For example, Z = -1 means the value is 1 standard deviation below the mean, at approximately the 16th percentile.
Official sources
- Statistical definitions: National Institute of Standards and Technology.
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology.