Tool
IQ percentile calculator
Enter an IQ score to see its percentile, how rare it is, and what it equals on the other common scales.
- Percentile
- 90.9
- Rarity
- 1 in 11.0
- Range
- High
An IQ of 120 on the SD 15 scale is higher than 90.9% of people. About 1 person in 11.0 scores this high or higher. The same result is 120 on SD 15, 121 on SD 16 and 132 on SD 24.
The formula
- z = (IQ − 100) ÷ SD. This is how many standard deviations the score sits above or below average.
- Percentile = Φ(z) × 100, where Φ is the cumulative normal distribution: the share of people below that z.
- Rarity = 1 ÷ (1 − Φ(z)) for scores above 100, or 1 ÷ Φ(z) for scores below.
Worked example for 125 on SD 15: z = 25 ÷ 15 = 1.67. Φ(1.67) = 0.952, so the percentile is 95.2 and the rarity is 1 ÷ 0.048, about 1 in 21.
Limits
The normal curve is a model. It fits well in the middle and less well at the extremes, where few people have ever been tested. Percentiles above about 145 are extrapolations. And a percentile is only as good as the score that went in: a result from a short online test carries a margin of error of around ten points, which at 130 is the difference between the 91st and 99th percentile.
The full table of ranges is on the IQ scale page.
Questions people ask
How do you calculate an IQ percentile?
Subtract 100 from the score, divide by the standard deviation of the scale (usually 15) to get a z-score, then look up the share of a normal distribution that falls below that z-score. For 115: (115 − 100) ÷ 15 = 1.0, and 84.1% of a normal distribution lies below 1.0.
What percentile is an IQ of 130?
About the 97.7th percentile on the SD 15 scale: higher than roughly 98 in 100 people, or about 1 person in 44.
What IQ is the 99th percentile?
About 135 on the SD 15 scale. The 98th percentile, the usual threshold for high-IQ societies, is about 131.
What does “1 in N” rarity mean?
How many people you would need, on average, to find one with a score at least that extreme. An IQ of 145 is about 1 in 741, meaning roughly one person in 741 scores 145 or higher.
Why are there different scales?
Different test publishers chose different standard deviations. Wechsler tests and most modern ones use 15, older Stanford-Binet editions used 16, and Cattell tests use 24. A score only means something once you know its scale.