How Raven's Progressive Matrices work

Last reviewed 9 September 2026

What the test is

John C. Raven published the Progressive Matrices in 1938. Each item shows a matrix of figures with one cell left blank, and asks you to choose the piece that completes it. The items are "progressive" in that they get harder as you go, and each one is meant to teach you a little of the logic needed for the next.

There are no words, no arithmetic and no facts to recall. Everything needed to answer is present in the figure. That property is why the test spread so widely: it can be administered across languages with only the instructions translated, and it has been used in more cross-cultural research than any other cognitive measure.¹

Why a grid of shapes

The design descends directly from Charles Spearman, who in 1904 observed that performance on wildly different mental tasks was positively correlated - people good at one tended to be good at the others - and proposed a general factor, g, underlying them all.³

Raven wanted a task that loaded on that general factor as purely as possible, stripped of the vocabulary and schooling that contaminate verbal tests. He described the ability being tapped as eductive - the capacity to make sense of confusion, to generate high-level rules from apparently disorganised material.

That maps closely onto what Raymond Cattell would later call fluid intelligence: reasoning applied to novel problems, as distinct from crystallised knowledge you have accumulated.⁴ Matrices remain the canonical measure of fluid reasoning, and when researchers need a single short index of general ability, matrices are usually what they reach for.

What makes an item hard

The most influential answer came from a 1990 analysis that built computer models capable of solving matrix items, then compared their behaviour with that of human test-takers.²

Two things predicted difficulty:

• The number of rules operating at once. An item governed by one rule is easy. An item where three or four independent rules run simultaneously is hard, because you must hold each partial conclusion in mind while working out the next.
• The type of rule. Some relations are much harder to spot than others, with rules requiring you to combine or cancel elements across cells being among the most difficult.

The analysis identified a small taxonomy of rules that accounts for most items - constancy along a row, quantitative progression, distribution of three values across rows and columns, and figure addition or subtraction. Later work confirmed that difficulty is largely a function of how many of these must be induced and combined.⁸

The practical upshot for anyone taking such a test: when an item defeats you, the problem is usually not that you cannot see a rule. It is that you have found one rule and stopped, while a second rule is also running.

The three versions

The existence of three versions makes a general point about measurement: a test only discriminates well over the range it was built for. Give the Standard version to a group of doctoral students and most will approach the ceiling, and the scores will say more about who made a careless slip than about who reasons best. This is the same reason a 30-item test cannot resolve scores at the extremes - a point we make on score ranges and enforce by refusing to report beyond 65 to 135.

What matrices miss

Matrices are excellent at one thing, which is also their limitation.

• They measure fluid reasoning, not general intelligence in full. A matrices score tells you little about verbal comprehension, acquired knowledge, or processing speed. A full clinical battery samples several domains for exactly this reason.
• They are culture-reduced, not culture-free. No vocabulary is required, but familiarity with grids, abstract puzzles and formal testing is - and that is a product of schooling. See are IQ tests biased.
• They show the largest Flynn effect. Raw scores on fluid measures rose faster across the twentieth century than crystallised ones - roughly 0.41 points a year against 0.21.⁵ A matrices score is therefore especially dependent on when the norms were collected.
• The published versions are copyrighted and widely leaked. Item security is a real problem for any fixed, famous item set.

How this site uses the format

This test uses matrix items, but not Raven’s - those are copyrighted, and the widely circulated copies would compromise any test that used them.

Instead the items here are generated from explicit rule specifications. Each matrix declares which attributes vary and under which rule, and the completing cell is then derived by applying those rules rather than drawn by hand. This is the automatic item generation approach recommended for public-domain ability measures,⁷⁶ and it buys two things:

• the keyed answer is correct by construction, and every distractor violates at least one stated rule - both machine-checked on every build;
• difficulty is set by structure - how many rules run at once - which is the property the research says drives it.

The methodology page lists the rule taxonomy used, and there are worked examples with the reasoning spelled out in the practice questions.

Common questions

References

1. Raven, J. (2000). The Raven Progressive Matrices: Change and stability over culture and time. Cognitive Psychology, 41(1), 1-48. doi:10.1006/cogp.1999.0735
2. Carpenter, P. A., Just, M. A., & Shell, P. (1990). What one intelligence test measures: A theoretical account of the processing in the Raven Progressive Matrices Test. Psychological Review, 97(3), 404-431.
3. Spearman, C. (1904). General intelligence, objectively determined and measured. American Journal of Psychology, 15(2), 201-292.
4. Cattell, R. B. (1963). Theory of fluid and crystallized intelligence: A critical experiment. Journal of Educational Psychology, 54(1), 1-22.
5. Pietschnig, J., & Voracek, M. (2015). One century of global IQ gains: A formal meta-analysis of the Flynn effect (1909-2013). Perspectives on Psychological Science, 10(3), 282-306. doi:10.1177/1745691615577701
6. Condon, D. M., & Revelle, W. (2014). The International Cognitive Ability Resource: Development and initial validation of a public-domain measure. Intelligence, 43, 52-64. doi:10.1016/j.intell.2014.01.004
7. Arendasy, M., Sommer, M., Gittler, G., & Hergovich, A. (2006). Automatic generation of quantitative reasoning items. Journal of Individual Differences, 27(1), 2-14.
8. Verguts, T., & De Boeck, P. (2002). The induction of solution rules in Raven Progressive Matrices Test. European Journal of Cognitive Psychology, 14(4), 521-547.

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