IQ to percentile conversion
The calculator subtracts 100 from the score, divides by 15, and applies the standard normal cumulative distribution. Upper-tail rarity uses a numerically stable survival calculation rather than subtracting a rounded percentile from 100. Integer scores 40–160 are published as iq-to-percentile.csv and iq-to-percentile.json with the same limitation attached.
| IQ | Percentile | Directional rarity |
|---|---|---|
| 70 | 2.28th | about 1 in 44 at or below |
| 85 | 15.87th | about 1 in 6.3 at or below |
| 100 | 50.00th | about 1 in 2.0 at or above |
| 110 | 74.75th | about 1 in 4.0 at or above |
| 115 | 84.13th | about 1 in 6.3 at or above |
| 120 | 90.88th | about 1 in 11 at or above |
| 125 | 95.22th | about 1 in 21 at or above |
| 130 | 97.72th | about 1 in 44 at or above |
| 140 | 99.62th | about 1 in 261 at or above |
| 145 | 99.87th | about 1 in 741 at or above |
| 150 | 99.96th | about 1 in 2,331 at or above |
| 160 | 100.00th | about 1 in 31,574 at or above |
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<iframe
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<p>Theoretical mean-100, SD-15 conversion — not a test result. Source: <a href="https://iqcaddy.com/iq-percentile-calculator/">IQ Caddy</a>.</p>Calculator limits
- How do you convert IQ to percentile?
- The calculator uses z = (score − 100) / 15 and the standard normal distribution. That is a theoretical conversion on a Wechsler-style mean-100, SD-15 model, not an official test percentile.
- Is this an IQ test result?
- No. It does not administer a test, authenticate a reported score, or replace the percentile printed on a publisher’s score report.
- Why does the model use a standard deviation of 15?
- Many modern IQ scales, including Wechsler-style scores, are centered on 100 with SD 15. Other instruments use different standard deviations, so the same number is not interchangeable across tests.
See the complete formulas, implementation limits, and fixed verification values in the methodology. Related: IQ scale and chart, average IQ by age, Stanford–Binet scale and SD conversion, IQ bell curve, and Einstein’s IQ evidence.