How do you use the calculator?
Enter an IQ score or a percentile, then pick the scale your test used. The calculator converts between them using the selected scale’s normal curve.
If you are unsure of the scale, check your score report or the test publisher’s materials. Wechsler scores use a mean of 100 and SD 15. Older Stanford-Binet editions report SD 16. Mensa’s own page says SDs of 16 or 24 points are used and gives 148 as its Cattell-scale qualifying score. Read more about IQ standard deviation.
What do percentile and 1 in N mean?
A percentile tells you the share of scores at or below a point on the selected scale. At the 97.7th percentile, about 97.7 percent of scores fall at or below that point under the model.
The “1 in N” figure describes how rare a score at or above that point is under the same model. For IQ 130 on SD 15, the estimate is 1 in 44. It describes a proportion, not a count of people, and depends on the scale and curve used.
Why does the same IQ have different percentiles?
The same IQ score sits farther from the mean on a narrower scale, so it maps to a higher percentile. IQ 130 is at the 97.7th percentile on SD 15, the 97.0th percentile on SD 16, and the 89.4th percentile on SD 24.
The top 2 percent begins at 130.8 on SD 15, 132.9 on SD 16, and 149.3 on SD 24. These are calculations from the normal curve and show why a score needs its scale for context. See the IQ scale for more information.
Why are far-tail rarity figures model estimates?
Far-tail figures come from extending the curve into ranges where observed test scores may not provide a direct count. They describe what the model predicts, not how many people have those scores.
Treat far-tail percentiles and 1-in-N figures as model estimates, not exact population totals. Results also depend on the test’s norms and scale. The free timed reasoning test does not print an IQ score.