This version was machine-translated from German and has not been medically reviewed. The authoritative version is the German version.
Z-score ↔ percentile
Convert z-score to percentile and back (standard normal distribution)
Conversion table
| Z-score | Percentile (%) | Remark |
|---|---|---|
| −4.000 | 0.003 | |
| −3.000 | 0.13 | WHO: severe malnutrition (< −3 SD) |
| −2.500 | 0.62 | |
| −2.000 | 2.3 | WHO: underweight / stunting (< −2 SD) |
| −1.880 | 3.0 | ≈ P3 (short stature limit) |
| −1.645 | 5.0 | P5 |
| −1.500 | 6.7 | |
| −1.280 | 10.0 | P10 |
| −1.000 | 15.9 | |
| −0.674 | 25.0 | P25 |
| −0.500 | 30.9 | |
| 0.000 | 50.0 | Median |
| +0.500 | 69.1 | |
| +0.674 | 75.0 | P75 |
| +1.000 | 84.1 | |
| +1.280 | 90.0 | P90 |
| +1.500 | 93.3 | |
| +1.645 | 95.0 | P95 |
| +1.880 | 97.0 | ≈ P97 |
| +2.000 | 97.7 | WHO: overweight (> +2 SD) |
| +2.500 | 99.38 | |
| +3.000 | 99.87 | |
| +4.000 | 99.997 |
Percentile = Φ(z) · 100 with the cumulative distribution function Φ of the standard normal distribution; inversion via Φ⁻¹ (Acklam algorithm with Newton refinement).
Frequently asked questions
How are z-score and percentile related?
The percentile is the value of the cumulative distribution function of the standard normal distribution at z, times 100. z = −1.88 corresponds to P3, z = 0 to the median, z = +1.88 to P97.