IQ Percentile Calculator: IQ Score to Percentile, Rarity and Classification
Convert an IQ score to a percentile and rarity (1 in N) on SD 15, 16 or 24 scales, or a percentile back to IQ, with Wechsler classification, z-score and the share of people in any IQ range.
How it works
z = (IQ − 100) ÷ SD · Percentile = Φ(z) × 100, where Φ is the standard normal cumulative distribution · Rarity = 1 ÷ (1 − Φ(z)) above the mean · IQ from percentile = 100 + SD × Φ⁻¹(percentile) · Equivalent SD-15 score = 100 + 15z
Modern IQ tests are “deviation IQs”: they are normed so that the average adult or child of the same age scores 100 and scores spread out in a bell curve with a fixed standard deviation, 15 points on the Wechsler scales (WAIS, WISC) and the Stanford-Binet 5. Your percentile is the share of that norm group scoring at or below you, found from the normal distribution: IQ 115 is 1 SD above the mean (84th percentile) and IQ 130 is 2 SD above (97.7th percentile, about 1 in 44). Some tests use other spreads, such as 16 for older Stanford-Binet forms and 24 for the Cattell Culture Fair, so the same rank gives a different number; pick the scale on your report. This calculator converts a score to a percentile, rarity and z-score, gives the Wechsler descriptive label (current WISC-V wording and the older WAIS-IV wording), shows the same rank on the other common scales and the 98th-percentile score that Mensa uses, and can work backwards from a percentile or give the share of people in any range. A generic percentile-rank or z-score tool can do the arithmetic, but it does not know IQ scales, labels or rarity. Results describe a test score only: scores carry measurement error, and an online quiz is not a valid IQ test.
Worked example
An IQ of 130 on an SD-15 test is z = (130 − 100) ÷ 15 = 2.0000 standard deviations above the mean. Φ(2) = 0.97725, so the percentile is 97.72%: 2.28% of people score higher, about 1 in 44. On the WISC-V the label is “Extremely high” (WAIS-IV: “Very superior”). The same rank is 132 on an SD-16 scale and 148 on an SD-24 scale, and the 98th percentile (Mensa’s qualifying level) is 130.8 on this scale.
Sources: Wikipedia: IQ classification (WISC-V, WAIS-IV and Stanford-Binet tables; SD 15 and 16 scales) · Omni Calculator: IQ percentile (SD 15/16, 70 → 2nd, 125 → 95th, 150 → 99.96th percentile) · American Mensa: Testing (98th percentile qualifying score)
Frequently asked questions
What percentile is an IQ of 130?
On the usual SD-15 scale, 130 is 2 standard deviations above the mean, the 97.72nd percentile. About 2.28% of people, roughly 1 in 44, score 130 or higher.
What IQ is the 98th percentile?
About 130.8 on an SD-15 test, 132.9 on an SD-16 test and 149.3 on an SD-24 test. Mensa admits people who score at or above the 98th percentile on an approved test, which is why 130, 132 and 148 are often quoted as qualifying scores.
What is the percentile of an IQ of 115 or 100?
115 is the 84.13th percentile (1 SD above the mean) and 100 is exactly the 50th percentile. About 68% of people score between 85 and 115.
How rare is an IQ of 145 or 160?
On an SD-15 scale, 145 is 3 SD above the mean: 99.865th percentile, about 1 in 741. 160 is 4 SD: about 1 in 31,574. Tests are rarely normed that far out, so such scores are imprecise.
What is an average IQ?
By definition the average is 100, and the “Average” classification covers 90 to 109, which includes about half of all people. Scores from 110 to 119 are “High average” and 80 to 89 “Low average”.
Why does my score differ between tests?
Tests use different standard deviations (15, 16 or 24), different norm groups and different content, and every score has a margin of error of several points. Compare percentiles, not raw IQ numbers, across tests.
Related calculators
This calculator converts scores using the normal distribution. It is not an IQ test or a diagnosis; only a qualified psychologist can give and interpret a standardized intelligence test.