How to convert a percentile to a z-score
Enter a percentile between 0 and 100 above. The converter inverts the standard normal distribution to find the z-score that has exactly that percentage of the distribution below it.
Why you would work backwards
Percentiles are how results are reported; z-scores are how they are used. A paediatric chart says a child is at the 90th percentile for height; a researcher who wants to model that measurement needs z ≈ 1.28. Exam boards set grade boundaries at percentiles and statisticians then convert them for analysis. Cut-offs work the same way: "the top 5% qualify" is the 95th percentile, z ≈ 1.645.
The 90th percentile converts to z ≈ 1.28. The 75th percentile (the third quartile of a normal distribution) converts to z ≈ 0.67, and the 25th percentile to z ≈ −0.67, mirror images, because the normal curve is symmetric.
Landmarks worth memorising
| Percentile | Z-score |
|---|---|
| 50th | 0 |
| 75th | 0.674 |
| 90th | 1.282 |
| 95th | 1.645 |
| 97.5th | 1.960 |
| 99th | 2.326 |
Below the median the signs flip: the 10th percentile is z ≈ −1.28, the 5th is ≈ −1.645. Symmetry does all the work.
Frequently asked questions
What z-score is the 95th percentile?
Approximately 1.645. This is the famous one-tailed 5% cut-off used throughout hypothesis testing.
What z-score is the 50th percentile?
Zero. The 50th percentile is the median of the standard normal distribution, which is its mean, z = 0.
Can I convert the 100th percentile?
No finite z-score reaches the 100th percentile. The normal curve approaches 100% but never arrives. In practice the 99.9th percentile (z ≈ 3.09) is about as far as anyone needs.