IQ comparison: the gap between two IQ scores

Compare scores in standard deviations, not raw points. On the Wechsler scale one standard deviation is 15 points, so IQ 130 and IQ 100 are two standard deviations apart. Both scores must be on the same scale and ideally the same test. A Stanford-Binet 132 and a Wechsler 130 are the same place on the curve, as the IQ percentile calculator shows.

The same gap in points means different things at different heights. 100 to 110 moves a person 24.8 percentile points, from the 50th to the 74.8th. 130 to 140 moves them only 1.9, from the 97.7th to the 99.62th. Near the middle the curve is dense with people, so a few points pass many of them. In the tail it is thin.

The gap is 15 points, which is 1.0 standard deviation. IQ 115 is the 84.1th percentile and IQ 130 the 97.7th, so the gap in rank is 13.6 percentile points. In rarity terms it is 1 in 6.3 against 1 in 44.

Before reading much into a gap, remember that each score carries error. If two scores differ by less than the error of one of them, they may not differ at all. Use the IQ confidence interval calculator to see the range around each. Scores from an online estimate are less precise than a clinical test, and a gap between a clinical score and an online one mixes two different kinds of measurement.

For the rarity of each score by itself, see how rare is my IQ. Two people with different scores can also have very different profiles across verbal reasoning, spatial ability, processing speed and working memory, which a single number hides.