An IQ of 100 sits at the 50th percentile, 115 at roughly the 84th, 120 at the 91st, 130 at the 97.7th, and 145 at about the 99.9th. Those numbers come from the shape of the distribution rather than from counting test takers: IQ scores are defined to follow a normal curve with a mean of 100 and a standard deviation of 15, so every score converts to a percentile by measuring how far it sits from the middle.
The full percentile table
Percentile means the share of the population scoring at or below a given point. Someone at the 84th percentile scored higher than 84 of every 100 people.
| Score | Percentile | People who score lower | Rarity |
|---|---|---|---|
| 145 | 99.9th | 999 in 1,000 | About 1 in 1,000 |
| 140 | 99.6th | 996 in 1,000 | About 1 in 250 |
| 135 | 99th | 99 in 100 | About 1 in 100 |
| 130 | 97.7th | About 98 in 100 | About 1 in 44 |
| 125 | 95th | 95 in 100 | About 1 in 20 |
| 120 | 91st | 91 in 100 | About 1 in 11 |
| 115 | 84th | 84 in 100 | About 1 in 6 |
| 110 | 75th | 3 in 4 | About 1 in 4 |
| 105 | 63rd | Almost 2 in 3 | Common |
| 100 | 50th | Half | The midpoint |
| 95 | 37th | More than 1 in 3 | Common |
| 90 | 25th | 1 in 4 | About 1 in 4 |
| 85 | 16th | 16 in 100 | About 1 in 6 |
| 80 | 9th | 9 in 100 | About 1 in 11 |
| 70 | 2nd | 2 in 100 | About 1 in 44 |
Notice how the percentiles compress at the top. Moving from 100 to 115 takes you past 34% of the population. Moving from 130 to 145, the same 15-point step, takes you past barely 2%. That compression is why small differences between high scores mean much less than they look like they do.
Where the numbers come from
IQ is a normalised score, not a count of correct answers. Raw performance is converted so that the population average lands on 100 and one standard deviation equals 15 points. Everything else follows from the properties of the normal distribution.
That gives the familiar bands: about 68% of people fall within one standard deviation of the mean, so between 85 and 115. Roughly 95% fall within two, so between 70 and 130. About 99.7% fall within three, so between 55 and 145.
One consequence catches people out. Because the scale is defined relative to a reference population, a score is only meaningful against the group the test was normed on. A test normed on university students will place the same person lower than one normed on the general adult population, and neither result is wrong.
Why some tests use a standard deviation of 16 or 24
Not every test uses 15. The Stanford-Binet historically used 16, and the Cattell III B uses 24. Those choices change what a given number means quite dramatically.
An IQ of 132 on the Stanford-Binet is the 98th percentile. To reach the 98th percentile on the Cattell scale you need 148. Both describe the same person. This is why high-IQ societies publish separate cutoffs per test rather than a single number, and why comparing scores from different tests without knowing the scale is meaningless.
Any score you see quoted without its scale should be assumed to use SD 15, which is the modern convention and what the Wechsler tests use.
What a percentile does not tell you
The rank is precise; the underlying measurement is not. A professionally administered test reports a confidence interval, typically around five points either side, so a reported 118 is really a statement that the true score probably lies between 113 and 123. That range spans the 81st to the 94th percentile.
Percentiles also flatten the profile. Two people at the 91st percentile can have completely different cognitive shapes, one carried by verbal ability and the other by spatial reasoning. For anything practical, the subtest pattern is more useful than the rank.
And the rank says nothing about outcomes. Cognitive ability predicts job performance and academic results moderately well, more strongly as tasks get more complex, but it competes with conscientiousness, opportunity, and health in explaining where people end up.
Questions people also ask
What percentile is an IQ of 130?
The 97.7th, on the standard scale where one standard deviation is 15 points. That means roughly 2.3% of people score at or above 130, or about one person in 44. It is the conventional threshold for the gifted band.
Is the 50th percentile a bad score?
It is the exact middle, which by definition describes more people than any other region of the scale. Half the population scores below it. Treating average as a deficiency is a misreading of what the scale is for, since it was constructed so that most people land near the middle.