How we convert test scores to IQ

For a test taken by a selected group, we model the score and IQ as two related bell curves and use regression, the standard tool for predicting one measure from another. For a score s on a test where takers average μ with standard deviation σ:

1. Standardise. Find where the score sits among test-takers, as a z-score. When a published percentile table exists we read the percentile from it and convert to z. Otherwise we use the mean and standard deviation.
2. Predict. Expected IQ = M + r × S × z, where M is the assumed mean IQ of test-takers, S is the assumed IQ spread among them and r is the assumed correlation between the score and IQ.
3. Spread. The remaining uncertainty is S × √(1 − r²). The likely range is the expected IQ plus or minus 1.28 of those units, which covers about 80% of people at that score.
4. Rarity view. If r were 1, expected IQ would be M + S × z. That is the “perfect measure” number many converters publish, and we show it for comparison.

Going from IQ to a score runs the same logic backwards: a person at a given IQ is expected to sit at z = r × (IQ − M) / S among test-takers, with the same residual spread.

Among 2025 SAT test-takers, a 1400 is at about the 93th percentile, which is a z-score of 1.48. We assume SAT test-takers average IQ 102 with a spread of 14, and that the SAT correlates 0.75 with IQ among them.

• Expected IQ = 102 + 0.75 × 14 × 1.48 = 117
• Residual spread = 14 × √(1 − 0.75²) = 9.3
• Likely range = 117 ± 1.28 × 9.3 = 106 to 129
• If the SAT were a perfect measure: 102 + 14 × 1.48 = 123

Regression to the mean is why the expected IQ (117) is below the perfect-measure figure (123). It is the same reason children of very tall parents are, on average, tall but slightly closer to average. The idea goes back to Kelley (1927) and is discussed for test scores by Wainer (2000).

Three numbers per test are assumptions rather than published statistics: the average IQ of the people who take it, how spread out their IQs are, and how strongly the score tracks IQ. Where a study reports a correlation we start from it and lower it a little to allow for selection. Where none exists, we say so and choose a moderate value. The evidence grade shows which case applies.

Many test score distributions are not bell-shaped. GRE Quant has a ceiling that many strong test-takers hit, and the GMAT Focus and UCAT scales are skewed. Where the publisher provides a percentile table (SAT, ACT, GRE Verbal and Quant, LSAT, GMAT Focus, MCAT, UCAT deciles) we read percentiles from the table and interpolate between rows. Where it does not (GRE total, Wonderlic) we use a normal curve from the published mean and standard deviation.

The ASVAB AFQT is different in kind. It is a percentile against a nationally representative sample, so it is used directly and needs no assumption about who takes the test.

IQ scores in the population rose by roughly three points a decade through most of the twentieth century (the Flynn effect), and in some countries that has slowed or reversed. Trahan and colleagues (2014) put the average at 2.3 points per decade in a meta-analysis of studies, and about 2.9 for modern Stanford-Binet and Wechsler tests.

We do not adjust for norm dates automatically, because the trend is not stable. Instead each page names the year of its norms, and we update pages when publishers release new tables. A converter built on 1997 norms, such as the AFQT, is flagged as such.

• Moderate. A published study links the test, or the battery it draws on, to a general-ability measure, and the score is referenced to a large, well-described sample. Even so, the studies usually use an older version of the test or a military battery in place of a Wechsler scale.
• Limited. Some published evidence exists, but it is dated, from mixed samples, or contradicted by later work on individuals.
• Weak. We found no published comparison with an IQ measure. The link is an assumption, and the range is deliberately wide.

Test publishers change scales and publish new norms, and we may have made mistakes. If you see a figure that is out of date or wrong, please tell us through the contact page and we will check it against the source and correct it. Our approach to sourcing is described in the editorial policy.