Percentile calculator
Enter a score with the mean and standard deviation of the test to see where it sits on a normal curve, in several standard scales. Or enter a percentile to find the score it matches.
Runs in your browser: nothing you enter is sent anywhere.
How to use it
- Choose Percentile from a score, or Score from a percentile.
- Enter the mean and standard deviation of the test.
- Enter the score (or the percentile) and read the results.
How it works
The z-score is z = (score − mean) / SD. The percentile is the standard normal cumulative probability Φ(z) times 100. The other scales are linear in z: T = 50 + 10z, IQ-scale = 100 + 15z, NCE = 50 + 21.06z, and stanine = round(2z + 5) limited to 1 to 9. To go from a percentile to a score the calculator inverts Φ numerically, then uses score = mean + z × SD.
Worked example
A test has mean 100 and SD 15, and you score 115:
- z = (115 − 100) / 15 = 1, which is the 84.13th percentile;
- T score = 50 + 10 = 60, stanine = round(2 + 5) = 7, NCE = 50 + 21.06 = 71.06.
For the 90th percentile on the same test, z = 1.2816, so the score is 100 + 1.2816 × 15 = 119.2.
Tips
- Percentiles bunch up near the middle: moving from the 50th to the 60th takes about 4 points here, from the 90th to the 99th about 16.
- Report the scale with the number, for example “IQ-scale 115”, because the same z gives different numbers on different scales.
Frequently asked questions
What does the percentile mean?
It is the share of the group that scores at or below your score. A percentile of 84 means you scored as well as or better than about 84 percent of the group. It is not the same as a percentage of questions answered correctly.
Does this assume a normal distribution?
Yes. The percentile is read from the normal curve using the mean and standard deviation you give. Standardised tests are usually scaled to be close to normal, but for skewed data the percentile can be off, and published norm tables are better.
What are T scores, stanines and NCE?
They are standard scales built from the z-score. A T score is 50 plus 10 times z. A stanine is the whole number nearest 2z plus 5, kept between 1 and 9. A normal curve equivalent is 50 plus 21.06 times z, which makes NCE 1, 50 and 99 match the percentiles 1, 50 and 99.
Why is an IQ-scale score shown?
Many ability tests report scores with a mean of 100 and a standard deviation of 15, so 100 plus 15 times z shows what the score would be on that scale. Some tests use a different SD, such as 16, so check your test manual.