📊Z-score Calculator
A z-score (standard score) expresses a value's distance from the population mean in standard deviation units. z = (x − μ) / σ. Positive z = above average; negative z = below average.
- 1z = (x − μ) / σ
- 2Percentile from z-score: use standard normal CDF
- 3z=1.96 → 97.5th percentile
- 4Enables comparison across different measurement scales
Score 85 · Mean 70 · SD 15=z = 1.0 → 84th percentile(85-70)/15=1.0; P(Z<1)=84.1%
| z-score | Percentile |
|---|---|
| -2.0 | 2.3% |
| -1.0 | 15.9% |
| 0 | 50% |
| 1.0 | 84.1% |
| 1.96 | 97.5% |
| 2.58 | 99.5% |
| 3.0 | 99.9% |
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