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 | 0,00 | |
| −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 | 100,00 |
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.