How to Solve Raven's Progressive Matrices: The 5 Rules
To solve Raven's Progressive Matrices, work row by row and test five rule types that researchers found running through the items: a feature stays constant, a feature changes step by step, three values are spread across each row, shapes add or subtract, and two values are shared with one cell left empty. Name which rule each feature follows, predict the missing cell, then match it to an answer. Hard items just stack several rules at once.
If Raven's-style puzzles make you lose the thread halfway through, IQ Tester checks whether that's working memory, pattern spotting or scattered attention, and trains the one that's yours: Find my weak spots.
What Raven's matrices are
Raven's Progressive Matrices is a non-verbal reasoning test first published by the British psychologist John C. Raven in 1938. Each item shows a pattern or grid with a piece missing, and you pick the piece that completes it. There are no words to read and no sums to do.
"Progressive" means the items get harder as you go. The test comes in a few versions:
| Version | Who it's usually for | What it looks like |
|---|---|---|
| Coloured Progressive Matrices | Younger children and some older adults | Shorter, with colored items |
| Standard Progressive Matrices | General use, teens and adults | Black-and-white items, easy to hard |
| Advanced Progressive Matrices | Higher-ability groups | Harder 3×3 items |
What does Raven's matrices measure?
Raven's is widely used as a measure of fluid reasoning: working out rules in new problems without relying on facts you've learned. Because it avoids language, it's often used where reading level or first language might get in the way. Like any test, it measures how you perform on these items right now, not a fixed limit.
The five rules behind Raven's items
In 1990, the psychologists Patricia Carpenter, Marcel Just and Peter Shell published a detailed study of how people solve the Advanced Progressive Matrices. They found the items could be described with a small set of rule types. Here they are in plain English.
Rule 1: constant in a row
A feature is the same in every cell of a row, even if it changes between rows.
Example: Row 1 has three triangles. Row 2 has three squares. Row 3 has two circles and a gap. The missing cell will have a circle.
It sounds too easy to matter. But on hard items, the constant is often one of three rules at once, and people forget to carry it into their answer.
Tip: once you've spotted a constant, write it down as a fact about the answer: "must be a circle." Then find the other rules.
Rule 2: steady change
A feature increases or decreases by the same step across the row. The research calls this a "quantitative pairwise progression," which just means each cell is one step on from the one before.
Examples of what can progress:
- Number of objects (1, 2, 3)
- Size (small, medium, large)
- Position (moving along a line)
- Rotation (turning 45° each time)
- Line thickness or darkness
Example: Row 1 has a line tilted 0°, 45°, 90°. Row 3 starts at 90° then 135°. The missing line is at 180° (flat again, pointing the other way).
Rule 3: three values spread out
The research calls this "distribution of three values." Three different versions of a feature appear once each in every row, just in a different order.
Example:
- Row 1: diamond, circle, square
- Row 2: circle, square, diamond
- Row 3: square, diamond, ?
Each row has one diamond, one circle and one square. Row 3 is missing the circle.
This rule is the one people most often miss, because nothing seems to change within a row. The trick is to look across the whole grid and ask: "Which things appear exactly three times?"
For a general walk-through of grid puzzles using the same approach, see how to solve matrix reasoning.
Rule 4-5: add, subtract and hidden attributes
Rule 4: figure addition or subtraction
The third cell is made by combining the first two, either adding their parts together or taking one away from the other.
Example:
- Row 1: a circle; a square; a circle and a square together
- Row 2: a horizontal line; a vertical line; a plus sign
- Row 3: a triangle; a dot; ?
Answer: a triangle with a dot.
Subtraction works the other way: cell 1 minus what's in cell 2 gives cell 3.
Rule 5: distribution of two values
This is the sneakiest rule. Some feature appears in two of the three cells in a row, and the third cell has nothing where you'd expect it. It often looks like lines are appearing and disappearing at random, until you check each line on its own.
How to spot it: pick one line or part and track it across the row. Is it in cell 1? Cell 2? Cell 3? If it shows up exactly twice in every row, you've found a two-value rule. Do the same for the next part. The answer contains only the parts that should be "on" in the missing cell.
Hidden attributes like these are what make the last items in a Raven's test so hard. The shapes are simple. It's the number of rules running at once.
This is where solving Raven's matrices alone gets hard. The same research linked harder items to having more rules to keep track of at once, and it's tough to know whether you're missing a rule or dropping one you already found. IQ Tester's 16-question check sorts working memory from pattern spotting, then gives you a daily drill with tips like "Chunk it" aimed at the one you need. Find my weak spots
How to work a Raven's item, step by step
Here's a method you can use on any Raven's-style problem.
- Cover the answers. Work out what the gap should be first.
- List the features. Shape, number, size, shading, position, orientation, individual lines.
- Take one feature at a time. For each, test the five rules in order: constant, steady change, three values, add/subtract, two values.
- Write each finding as a fact about the answer. "Black. Two dots. Pointing left."
- Build the missing cell in your head from those facts.
- Uncover the answers and pick the match. If two options fit, you've missed a feature. Go back to step 2.
- Move on if you're stuck. The items get harder, so time spent on one hard item costs you easier ones later.
Raven's test tips for when you're stuck
- Rows, then columns. Most items work left to right. If not, try top to bottom.
- Break shapes into parts. A complex figure is often three simple parts, each with its own rule.
- Say each rule out loud. Naming the rule makes it easier to hold in your head.
- Eliminate. Each wrong answer usually breaks one rule. Cross them out one feature at a time.
The same "find the rule, then test it" habit shows up in abstract reasoning tests, which use similar shapes but more varied formats.
Find out which rule you drop
Now you know how to solve Raven's Progressive Matrices with five rules and a fixed order. What's harder to see alone is whether you miss rules because you can't spot them or because you can't hold several at once. IQ Tester finds that in about two minutes, gives you a reasoning tier, and then sets one tip and one 10-minute drill a day, weighted toward your weak spots.
FAQ
What is Raven's Progressive Matrices?
It's a non-verbal reasoning test, first published by John C. Raven in 1938, where you complete visual patterns by choosing the missing piece. The items get harder as the test goes on. It comes in Colored, Standard and Advanced versions.
What are the rules in Raven's progressive matrices?
A well-known 1990 study by Carpenter, Just and Shell described five rule types: constant in a row, steady progression, distribution of three values, figure addition or subtraction, and distribution of two values. Most items use one or more of these at the same time.
Can you practice for Raven's matrices?
You can get more familiar with the format and the rule types, and familiarity helps you work more calmly and systematically. Practicing a few items daily, naming each rule and tracking which rules you miss is a sensible way to do it. Be aware that an official test result may be affected if you've seen the exact items before, so practice on similar puzzles rather than the real ones.
What does Raven's matrices measure?
It's mainly used as a measure of fluid reasoning, the ability to solve new problems by finding rules and patterns. Because it has no words, it's often used when language could affect results. It's one measure among many and doesn't capture everything about how someone thinks.
Is the Raven's matrices test an IQ test?
Raven's is widely used as an intelligence or reasoning test, and scores can be converted to IQ-style scores against norms. It focuses on non-verbal reasoning only, so it doesn't cover areas like vocabulary or mental arithmetic that full IQ batteries include.