How rare is my IQ?

IQ scores are built to follow a bell curve. The average is 100 and about two in three people score between 85 and 115.

To get "1 in X", subtract 100 from the score and divide by 15. That is the z-score. Then take the share of the curve above that z-score and turn it around. An IQ of 130 has a z-score of +2.0, and 2.3% of the curve is above it, which is about 1 in 44.

For named cities, the IQ city count applies the same maths to real populations. If you start from a percentile instead, use the percentile to IQ converter. If your score is on a different scale, convert it first with the IQ percentile calculator.

The table is a maths result, not a head count. Past about 145 it stops being something a test can check, for three reasons.

• Test ceilings. The WAIS-IV, a common adult test, reports full-scale scores from 40 to 160. It cannot say anything rarer than the 160 line, whatever the person can do.
• Small norm samples. The WAIS-IV was normed on about 2,200 people. At 1 in 31,600, you would expect only 0.07 of them to score 160 or higher. The top of the scale is extended from the middle, not measured.
• Real scores are not a perfect bell. The tails can be fatter or thinner than the curve, and nobody knows by how much at the extremes.

Add the margin of error on any single score, which is several points, and a claimed 1 in 10,000 is better read as "very high". Rarity up to about 1 in 1,000 (an IQ near 146) is a fair guide. Beyond that, treat it as a rough one.

The same caution applies to the Mensa IQ requirement, where one point either side of the line can decide the outcome.