What Is a Z-Score and How Do You Calculate One?
October 8, 2026
A z-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 values are above average, negative values are below, and the further from zero, the more unusual the value is relative to the rest of the data.
Skip the math and get your answer instantly:
Open the Standard Deviation Calculator →Worked Example
A test has a mean score of 75 and a standard deviation of 8. A student who scored 91 has a z-score of (91 − 75) / 8 = 2.0 — meaning they scored exactly 2 standard deviations above the mean.
Z-Score to Percentile Reference
For roughly normally distributed data, a z-score converts to an approximate percentile — how much of the data falls below that value.
| Z-Score | Approximate Percentile |
|---|---|
| −2.0 | ~2nd percentile |
| −1.0 | ~16th percentile |
| 0 | 50th percentile |
| +1.0 | ~84th percentile |
| +2.0 | ~98th percentile |
Where Z-Scores Are Used
Standardized testing uses z-scores to compare a score against the full distribution of test-takers, independent of the test's own raw scale. Finance uses z-scores to flag unusually large price moves relative to historical volatility. Manufacturing quality control uses z-scores (often via Six Sigma methodology) to flag measurements that fall suspiciously far from a process's expected average, signaling a possible defect or process drift.
Frequently Asked Questions
How do I calculate a z-score?
Subtract the mean from your value, then divide by the standard deviation: z = (x − mean) / standard deviation.
What does a z-score of 0 mean?
A z-score of 0 means the value is exactly equal to the mean of the data set — neither above nor below average.
What's considered a 'high' z-score?
There's no universal cutoff, but values beyond ±2 are often considered notably unusual for roughly normal data (about the top or bottom 2-3%), and values beyond ±3 are quite rare (about 0.1-0.2% of the distribution).
Can z-scores be negative?
Yes — a negative z-score simply means the value is below the mean. The sign indicates direction (above or below average), and the magnitude indicates how far.
Does a z-score work for any data distribution?
You can calculate a z-score for any numeric data, but converting it to a percentile using the standard reference table only applies accurately to data that's roughly normally (bell-curve) distributed — skewed data won't match those percentiles precisely.