Formulas converting SAT to IQ scores



Caution: The formulas below do NOT work with "extreme scores" (perhaps over 1250 SAT) as explained by formula originator Frey in the email below. For other SAT scores, one can compare the IQ generated by the formula to an SAT - IQ conversion chart .

1. For SAT scores before 1996, Professors Detterman and Frey of Case Western Reserve University provide this formula:: IQ = (0.126 x SAT combined) + (-.4.71E - 5 x SAT combined x SAT combined) + 40.063 . (Data in chart "a" below. Chart "b" uses a formula with a cube of SAT)

Using this formula with President George W. Bush's 1206 combined SAT scores: (0.126 X 1206) + (-0.0000471 x 1206 x1206) + 40.063 = 124 IQ for Bush. The same 124 number is obtained from an SAT - IQ conversion chart and is close to the 125 estimated by The Bell Curve author Murray for a similar 1206 combined SAT score.

2. For SAT scores from 1996 -2004 to an IQ score, Detterman and Frey provide this formula: IQ =(0.095 X SAT Math) + (0.003 X SAT Verbal) + 50.241 (Small data sample in chart "c" below) Scores for SAT were "re-centered" in 1996, raising the average SAT back to 500.

After 2004 with the new SAT, Detterman thinks that IQ will still be predictable from SAT scores, but a study of the data may lead to a revised formula.


"M. C. Frey" <>



RE: 2nd request to clarify your SAT-IQ formulas


Thu, 20 Jan 2005 11:37:27 -0500

Dear Mr. Sloan:

We would like to thank you for your interest in our article and your thought provoking questions. First, let me clarify the equations by stating that the E is in fact being used as a shorthand for scientific notation as you suspected (this abbreviation is most common in SPSS, the statistical package favored by many of us in the social sciences). Secondly, we have published an erratum for Equation 2 stating that all coefficients should be positive (Frey & Detterman, Psychological Science 15(9), 641). Equation 1 was correct as originally published. Finally, the problems that you and your colleagues are experiencing in applying the regression equation are captured in one of the fundamental characteristics of multiple regression. Whenever a relationship is less than perfect, the dependent variable will display regression to the mean. Those individuals with extreme scores on the predictor variable will necessarily have less extreme scores on the dependent variable. That is to say, the higher SAT scores will tend to predict lower IQ and the lower SAT scores will tend to predict higher IQ. A thorough discussion of regression to the mean can be found in Cohen, Cohen, West, & Aiken, 2003, pg.36-37. Again, thank you for your interest, and please feel free to contact us with any further questions.


Murphy Frey

Department of Psychology
Case Western Reserve University
10900 Euclid Ave.
Cleveland, OH 44106
phone: 216-368-6670

More on these findings from, as reported in the Boston Globe:

Scholastic Assessment or g? The Relationship Between the Scholastic Assessment Test and General Cognitive Ability by Frey and Detterman (abstract)

This research established the relationship between SAT and g, as well as the appropriateness of the SAT as a measure of g, and examined the SAT as a premorbid measure of intelligence. In Study 1, we used the National Longitudinal Survey of Youth 1979. Measures of g were extracted from the Armed Services Vocational Aptitude Battery and correlated with SAT scores of 917 participants. The resulting correlation was .82 (.86 corrected for nonlinearity). Study 2 investigated the correlation between revised and recentered SAT scores and scores on the Raven's Advanced Progressive Matrices among 104 undergraduates. The resulting correlation was .483 (.72 corrected for restricted range). These studies indicate that the SAT is mainly a test of g (general intelligence - or IQ).

Go to: Experts speak on how SAT measures IQ

Go to: SAT scores by Income and Ethnic Groups

Go to: Research findings on how IQ relates to success

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