📊 Z-Score Calculator
Standard score, percentile & probability
Common Z-Score Thresholds
| Z-Score | Percentile | Meaning |
|---|---|---|
| -3.0 | 0.13% | Extremely below average |
| -2.0 | 2.28% | Well below average |
| -1.0 | 15.87% | Below average |
| 0.0 | 50.00% | Exactly average |
| 1.0 | 84.13% | Above average |
| 1.645 | 95.00% | Top 5% (90% CI boundary) |
| 1.96 | 97.50% | Top 2.5% (95% CI boundary) |
| 2.0 | 97.72% | Well above average |
| 2.576 | 99.50% | Top 0.5% (99% CI boundary) |
| 3.0 | 99.87% | Extremely above average |
Understanding Z-Scores
A z-score tells you how many standard deviations a value is from the mean. Z = (X - μ) / σ. A z-score of 1.0 means the value is one standard deviation above the mean. A z-score of -2.0 means two standard deviations below. In a normal distribution, 68% of values fall within ±1 SD, 95% within ±2 SD, and 99.7% within ±3 SD (the 68-95-99.7 rule).
Z-scores are used everywhere: grading on a curve, quality control in manufacturing, medical test results, standardized testing (SAT, GRE), and scientific research. If a test score has a z-score of 1.5, you scored better than approximately 93.3% of test-takers.