Free tool · Scores
How rare is my IQ?
Updated
The short answer
On the standard scale (mean 100, SD 15), about 1 in 44 people score 130 or higher, 1 in 740 score 145 or higher and 1 in 32,000 score 160 or higher. In a random group of 30, you would expect 0.7 people at 130 or above, and the chance of at least one is about 50%.
About 1 in 44
people score 130 or higher. That is 2.3% of people, and the score sits at percentile 97.7.
| Group | Expected | At least one |
|---|---|---|
| A class of 30 | 0.68 | 50% |
| A school of 1,000 | 23 | over 99.9% |
| A town of 50,000 | 1,138 | over 99.9% |
| A city of 1,000,000 | 22,750 | over 99.9% |
Expected = group size × 2.3%. At least one = 1 − (1 − p)^n. Both assume the group is a random draw from the general population, which a real class or school is not.
Curious where you would land? The IQ Octopus test gives your estimated IQ with its percentile and range.
Rarity by score
Read across: the share of people at or above each score on an SD 15 scale, the same thing as 1 in N, and what that means for a room of 1,000. The 68-95-99.7 pattern of the normal curve is where these come from (NIST/SEMATECH e-Handbook, normal data).
The method
IQ scores are standardized so that, within each age group, the mean is 100 and the standard deviation is 15 (Wechsler, 2008). The share of people at or above a score is the area of the normal curve beyond its z score, z = (IQ − 100) ÷ 15. Rarity is one over that share. For scores below 100 the calculator flips to the lower tail: how many people score this low or lower.
The group view adds two numbers. Expected is the group size times the share, an average over many groups. At least one is 1 − (1 − share)n: the chance a random group of n people holds one or more. For a 130 and a group of 30 those are 0.68 and 50%, which is why a 130 can feel common in one setting and rare in another.
What this cannot tell you
- Real groups are not random. A university class, a profession or a neighborhood can differ a lot from the population average.
- The tails are modeled. The Stanford-Binet 5 norms come from 4,800 people (PRO-ED: SB5), so anything rarer than about 1 in a few thousand is the curve's prediction, not a count.
- A single score has measurement error. A 130 from one sitting is a range, as the confidence interval calculator shows.
For the percentile view of the same math, use the IQ percentile calculator. The rarity calculator is free to embed on your own page.
Sources
- NIST/SEMATECH e-Handbook of Statistical Methods, section 6.5.1, "What do we mean by Normal data?" National Institute of Standards and Technology. www.itl.nist.gov/div898/handbook/pmc/section5/pmc51.htm
- Wechsler, D. (2008). WAIS-IV Technical and Interpretive Manual. Pearson.
- Roid, G. H. Stanford-Binet Intelligence Scales, Fifth Edition (SB5), PRO-ED product page. 2003. proedinc.com/products-13290.html