The Cattell–Horn–Carroll theory, or CHC theory, is a psychological theory of human cognitive abilities that takes its name from Raymond Cattell, John L. Horn and John Bissell Carroll. Recent advances in current theory and research on the structure of human cognitive abilities have resulted in a new empirically derived model commonly referred to as the Cattell–Horn–Carroll theory of cognitive abilities. CHC theory of cognitive abilities is an amalgamation of two similar theories about the content and structure of human cognitive abilities. The first of these two theories is Gf-Gc theory (Raymond Cattell, 1941; Horn 1965), and the second is Carroll's (1993) Three-Stratum theory. Carroll's expansion of Gf-Gc theory to CHC theory was developed in the course of a major survey of research over the past 60 or 70 years on the nature, identification, and structure of human cognitive abilities. That research involved the use of the mathematical technique known as factor analysis. In comparison to other well-known theories of intelligence and cognitive abilities, CHC theory is the most comprehensive and empirically supported psychometric theory of the structure of cognitive and academic abilities.
The CHC model was expanded by McGrew (1997), later revised with the help of Flanagan (1998), and extended again by McGrew (2011). There are a fairly large number of distinct individual differences in cognitive ability, and CHC theory holds that the relationships among them can be derived by classifying them into three different strata: stratum I, "narrow" abilities; stratum II, "broad abilities"; and stratum III, consisting of a single "general ability" (or g).
There are 9 broad stratum abilities and over 70 narrow abilities below these. The broad abilities are 
- Crystallized Intelligence (Gc): includes the breadth and depth of a person's acquired knowledge, the ability to communicate one's knowledge, and the ability to reason using previously learned experiences or procedures.
- Fluid Intelligence (Gf): includes the broad ability to reason, form concepts, and solve problems using unfamiliar information or novel procedures.
- Quantitative Reasoning (Gq): is the ability to comprehend quantitative concepts and relationships and to manipulate numerical symbols.
- Reading & Writing Ability (Grw): includes basic reading and writing skills.
- Short-Term Memory (Gsm): is the ability to apprehend and hold information in immediate awareness and then use it within a few seconds.
- Long-Term Storage and Retrieval (Glr): is the ability to store information and fluently retrieve it later in the process of thinking.
- Visual Processing (Gv): is the ability to perceive, analyze, synthesize, and think with visual patterns, including the ability to store and recall visual representations.
- Auditory Processing (Ga): is the ability to analyze, synthesize, and discriminate auditory stimuli, including the ability to process and discriminate speech sounds that may be presented under distorted conditions.
- Processing Speed (Gs): is the ability to perform automatic cognitive tasks, particularly when measured under pressure to maintain focused attention.
A tenth ability, Decision/Reaction Time/Speed (Gt), is considered part of the theory, but is not currently assessed by any major intellectual ability test. For this reason, it does not appear in cross-battery reference materials.
- Decision/Reaction Time/Speed (Gt): reflects the immediacy with which an individual can react to stimuli or a task (typically measured in seconds or fractions of seconds; not to be confused with Gs, which typically is measured in intervals of 2–3 minutes).
McGrew proposes a number of extensions to CHC theory, including Domain-specific knowledge (Gkn), Psychomotor ability (Gp), and Psychomotor speed (Gps). In addition, additional sensory processing abilities are proposed, including tactile (Gh), kinesthetic (Gk), and olfactory (Go).
Many tests of cognitive ability have been classified using the CHC model and are described in The Intelligence Test Desk Reference (ITDR) (McGrew & Flanagan, 1998). CHC theory is particularly relevant to school psychologists for psychoeducational assessment. 5 of the 7 major tests of intelligence have changed to incorporate CHC theory as their foundation for specifying and operationalizing cognitive abilities/processes. Since even all modern intellectual test instruments fail to effectively measure all 10 broad stratum abilities an alternative method of cognitive assessment and interpretation called Cross Battery Assessment (XBA; Flanagan, Ortiz, Alfonso, & Dynda, 2008) was developed.
- Fluid and crystallized intelligence for Gf-Gc theory
- Flanagan, D. P., & Harrison, P. L. (2005). Contemporary intellectual assessment: Theories, tests, and issues. (2nd Edition). New York, NY: The Guilford Press
- McGrew, K. S. (2005). The Cattell-Horn-Carroll theory of cognitive abilities: Past, present, and future. In D. P. Flanagan, J. L. Genshaft, & P. L. Harrison (Eds.), Contemporary intellectual assessment: Theories, tests, and issues (pp.136–182). New York: Guilford.
- McGrew, K. http://www.iapsych.com/CHCPP/CHCPP.HTML Retrieved 12/6/2011.
- Flanagan, D. P., Ortiz, S. O., & Alfonso, V. C. (2007). Essentials of cross-battery assessment. (2nd Edition). New Jersey: John Wiley & Sons, Inc
- Carroll, J.B. (1993). Human cognitive abilities: A survey of factor-analytic studies. Cambridge, England: Cambridge University Press.
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- Cohen, R. J., & Swerdlik, M. E. (2004). Psychological testing and assessment. Chicago, IL: McGraw-Hill (6th ed.)
- Flanagan, D. P., Ortiz, S. O., & Alfonso, V. C. (2013). Essentials of cross-battery assessment (3rd edition). New York: Wiley.
- Flanagan, D. P., Ortiz, S. O., Alfonso, V. C., & Dynda, A. M. (2008). Best practices in cognitive assessment. Best Practices in School Psychology V, Bethesda: NASP Publications.
- Gustafsson, J. E., & Undheim, J. O. (1996). Individual differences in cognitive functions. In D.C. Berliner & R. C. Calfee (Eds.), Handbook of educational psychology (pp. 186–242). New York: Macmillan Library Reference USA.
- Horn, J. L. (1965). Fluid and crystallized intelligence: A factor analytic and developmental study of the structure among primary mental abilities. Unpublished doctoral dissertation, University of Illinois, Champaign.
- McGrew, K. & Flanagan, D. (1998). The Intelligence Test Desk Reference: Gf-Gc cross-battery assessment. Allyn & Bacon.
- Gregory, Robert J. (2011). Psychological Testing: History, Principles, and Applications (Sixth ed.). Boston: Allyn & Bacon. ISBN 978-0-205-78214-7. Lay summary (7 November 2010).
- Kaufman, Alan S. (2009). IQ Testing 101. New York: Springer Publishing. ISBN 978-0-8261-0629-2. Lay summary (10 August 2010).
- Tucker, William H. (2009). The Cattell Controversy: Race, Science, and Ideology. University of Illinois Press. ISBN 978-0-252-03400-8. Lay summary (30 August 2010).