Raven's Progressive Matrices: The Test, the Rules Behind It and 10 Practice Items

What Raven's measures

Raven's strips language out of intelligence testing. There are no words to define and no sums to calculate: only shapes, arranged by rules the test taker must discover. Psychologists treat it as a nonverbal estimate of fluid intelligence, the capacity Raymond Cattell described in 1943 as solving novel reasoning problems. The test targets the eductive component of Charles Spearman's general factor, g: the ability to think clearly and make sense of complexity.

Pearson, the current publisher, describes the test as a measure of clear-thinking ability and intellectual capacity. Because the items carry no vocabulary, a weak grasp of the test language costs far less than it would on a verbal test. Full clinical batteries, explained in how IQ tests work, sample many abilities. Raven's samples one, deeply.

The classic forms and the current edition

Three versions dominated the 20th century. Each targets a different ability band.

Raven's 2 replaced the old booklets with updated, colorized items and new norms. Pearson lists ages 4 to 90 and both paper and digital delivery. Its digital forms are assembled from an item bank to limit overlap between test takers; the French distributor puts that bank at more than 300 items. Pearson's brochure for the Spanish edition gives the clock: 36 items in 30 minutes for children aged 4 to 8 years 11 months, 48 items in 45 minutes from age 9, and a 24-item digital short form in 20 minutes. Purchase requires Pearson's qualification level B.

How the score is calculated

The raw score is a count of correct answers. The test then converts that count against people of the same age, producing a standard score and a percentile rank. The percentile is the plain-English number: the 90th percentile means a performance above 90 percent of the norm group. Standard scores on modern deviation scales sit at 100 for the average, and the bands are laid out in our IQ classification guide. A standard score of 120, for example, is covered in our page on IQ 120.

Norm age matters more on Raven's than on almost any other test. James Flynn compiled decades of Raven's results and showed that scores rose from one generation to the next, the pattern now called the Flynn effect. An old norm table therefore flatters a modern test taker. Any score worth trusting comes from current norms.

The five rules inside most matrix items

In 1990 Patricia Carpenter, Marcel Just and Peter Shell of Carnegie Mellon University broke the Advanced Progressive Matrices into their working parts. They found that most items combine a handful of rules:

• Constant in a row: one attribute stays the same across a row.
• Quantitative pairwise progression: an attribute grows or shrinks by a fixed step from cell to cell.
• Figure addition or subtraction: the third cell is the first two combined, or one minus the other.
• Distribution of three values: three values each appear once per row.
• Distribution of two values: two values of a feature are spread through a row, and the third value is null: that cell lacks the feature.

Everyone solved the items the same basic way, comparing cells pair by pair and building rules step by step. What set high scorers apart was the ability to induce more abstract relations and to hold more open goals in working memory at once. Hard items are hard because they stack several rules, not because any single rule is obscure.

10 original practice items

These items are written for this page in words and numbers. None comes from Raven's or any other published test. Read each grid left to right, top to bottom; the question mark is the missing ninth cell.

1. Grid: Row 1: one circle, two circles, three circles. Row 2: one square, two squares, three squares. Row 3: one triangle, two triangles, ?
   Answer: three triangles. The shape is constant in each row and the count rises by one.
2. Grid: Row 1: black circle, white square, gray triangle. Row 2: white triangle, gray circle, black square. Row 3: gray square, black triangle, ?
   Answer: white circle. Every row holds each shape once and each shade once. Row 3 lacks a circle and lacks white.
3. Grid: Row 1: a vertical line, a horizontal line, a cross. Row 2: a circle, a center dot, a circle with a center dot. Row 3: a square, a diagonal from top left to bottom right, ?
   Answer: a square crossed by that diagonal. The third cell overlays the first two.
4. Grid of letter sets: Row 1: {A, B, C}, {B, D}, {A, C, D}. Row 2: {E, F}, {F, G, H}, {E, G, H}. Row 3: {J, K, L}, {K, L, M}, ?
   Answer: {J, M}. Elements found in both of the first two cells cancel; elements found in only one survive.
5. Grid: Row 1: one arrow pointing up, one pointing right, one pointing down. Row 2: two arrows pointing right, two pointing down, two pointing left. Row 3: three arrows pointing down, three pointing left, ?
   Answer: three arrows pointing up. The count is constant within a row, and the direction turns 90 degrees clockwise per cell.
6. Grid: Row 1: triangle, square, pentagon. Row 2: square, pentagon, hexagon. Row 3: pentagon, hexagon, ?
   Answer: a heptagon, with seven sides. Sides rise by one moving right and by one moving down.
7. Number grid: Row 1: 3, 5, 7. Row 2: 4, 6, 5. Row 3: 8, 1, ?
   Answer: 6. Every row sums to 15.
8. Number grid: Row 1: 2, 3, 6. Row 2: 4, 5, 20. Row 3: 7, ?, 56
   Answer: 8. The third number is the product of the first two, and 56 divided by 7 is 8.
9. Grid of marks: Row 1: dot and bar, dot, bar. Row 2: dot, bar, dot and bar. Row 3: bar, dot and bar, ?
   Answer: a dot alone. In every row and every column the dot appears exactly twice and the bar exactly twice.
10. Letter grid: Row 1: A, C, E. Row 2: B, D, F. Row 3: C, E, ?
    Answer: G. Each row skips one letter at a time, and each row starts one letter later than the row above.

A method that works on any matrix

Strong solvers name variables before they hunt for answers. Run this sequence on every item:

1. List the attributes that change: shape, number, shade, size, position, orientation.
2. Check each attribute across the rows, then down the columns.
3. Match what you see to one of the five rules above. Expect two or three rules at once on harder items.
4. Describe the missing cell in words before reading the options.
5. Eliminate options that break any rule. If two survive, one rule is still unfound.

Items 2 and 9 above hold their rule down the columns as well as across the rows. Checking both directions confirms an answer and catches rules that a row-only reading misses. For a wider set of pattern formats, read our abstract reasoning test guide; for rotation and folding, see the spatial reasoning test guide.

What practice changes, and what it does not

Familiarity raises scores. A 2018 meta-analysis by Jana Scharfen, Judith Marie Peters and Heinz Holling in the journal Intelligence pooled 174 samples from 122 studies, covering 153,185 people. Scores on cognitive ability tests rose with repeated testing and stopped rising after the third administration. Knowing the five rules does the same work faster. Neither changes the underlying ability.

That is why a practiced score is a less clean measure than a first attempt, and why publishers rotate items from banks. Our free online IQ test is a practice screener, not a clinical instrument; for what a home test can and cannot tell you, read are online IQ tests accurate. More guides sit in our IQ guides hub, including a matrix-based screener in the Mensa Norway test explained.

Editorial standard: IQ figures for historical figures are retrospective estimates and are labeled as such; scores for living people appear only when the person disclosed them or a reputable outlet reported them. Corrections: contact the editors.