How to convert a z-score to a percentile
Enter your z-score above. The converter uses the standard normal distribution to find what percentage of values fall below it (that percentage is its percentile) and also shows the area above, which is what most significance tables call the upper tail.
Why this conversion works
Once a value is expressed as a z-score, its distribution is the standard normal: mean 0, standard deviation 1, total area 1. Every z-score therefore corresponds to exactly one "area to the left", and that area is the percentile. Z = 0 splits the curve in half, the 50th percentile. Each step outward claims more (or less) of the curve in a way the normal table tabulates.
A z-score of 1.25 converts to the 89.4th percentile: about 89.4% of a normal distribution falls below it, and 10.6% above. Test-setters use this constantly in reverse: "top 10% passes" quietly means "z above about 1.28".
Handy landmarks
| Z-score | Percentile | Reading |
|---|---|---|
| −2 | 2.3 | Unusually low |
| −1 | 15.9 | Below average |
| 0 | 50 | Exactly average |
| +1 | 84.1 | Above average |
| +1.96 | 97.5 | Edge of the middle 95% |
| +2 | 97.7 | Unusually high |
Notice the squeeze near the edges: from z = 0 to 1 you gain 34 percentile points; from 2 to 3 you gain barely 2. Percentiles compress at the extremes. One more reason statisticians prefer working in z.
Frequently asked questions
What percentile is a z-score of 1?
About the 84th percentile: 84.1% of a normal distribution lies below z = 1.
What percentile is a z-score of 0?
The 50th percentile. Z = 0 is the mean of the standard normal distribution, so exactly half the area lies below it.
Is the percentile the same as the area under the curve?
Yes, for the area to the left of the z-score. Percentile = 100 × Φ(z), where Φ is the standard normal cumulative distribution.