Spatial Reasoning Test: What It Measures and 12 Practice Items

What a spatial reasoning test measures

Spatial reasoning is the ability to hold a shape in mind and act on it: turn it, flip it, fold it, view it from another side. Test items come in a few standard families. Mental rotation asks whether two figures are the same object turned or mirror images. Paper folding asks where punched holes land after a sheet is unfolded. Cube nets ask which flat pattern folds into which box. Orientation items ask where a person faces after a series of turns.

The skill sits inside mainstream IQ testing. Pearson's WAIS-5, the adult Wechsler scale for ages 16 to 90, reports five primary indexes, one of them Visual Spatial, built from the Block Design and Visual Puzzles subtests. Our WAIS-IV guide covers the previous edition's structure, and how IQ tests work explains how index scores combine.

The experiment that defined the field

In 1971 Roger Shepard and Jacqueline Metzler published a short paper in Science that turned mental imagery into something measurable. Participants saw pairs of three-dimensional block figures and judged whether each pair showed the same object or two different ones. The time they needed rose in a straight line with the angle between the two figures.

The finding implied that people rotate mental images much as they would turn a physical object, one degree after another. It made rotation speed and accuracy a standard laboratory measure, and rotation items remain the backbone of most spatial tests today.

Why spatial ability matters for science and engineering

The strongest evidence comes from Project Talent, a stratified random sample of about 400,000 American high school students in grades 9 to 12. Jonathan Wai, David Lubinski and Camilla Benbow reanalyzed it in the Journal of Educational Psychology in 2009, following participants for 11 years. Spatial ability measured in adolescence stood out among those who later earned advanced degrees and jobs in science, technology, engineering and mathematics.

The authors concluded that spatial ability plays a critical role in developing STEM expertise and that talent searches built on verbal and math scores alone miss many capable students. A strong spatial score is no guarantee of anything, but it carries information that a verbal or math score does not.

12 original spatial practice items

Every item is written for this page and described in words. None is taken or adapted from a commercial test. Try each before reading the answer.

1. Rotation. Picture a capital N. Rotate it 90 degrees clockwise. What letter does it resemble?
   Answer: Z. The two upright strokes become horizontal bars at top and bottom, and the diagonal now runs from upper right to lower left.
2. Rotation versus mirror. Rotate a lowercase b by 180 degrees on the page. Which letter appears? Which letter appears if you mirror b left to right instead?
   Answer: q after the rotation; d after the mirror. A rotation in the plane can never produce a mirror image.
3. Mirror clock. An analog clock reads 2:20. What time does it appear to show in a mirror?
   Answer: 9:40. For an analog face, subtract the real time from 12:00.
4. Paper folding. Fold a square sheet in half left to right, then in half bottom to top. Punch one hole through the center of the small folded square. How many holes appear when you open the sheet, and where?
   Answer: four, one in the center of each quarter of the sheet. The punch passes through four layers.
5. Cube net. Six squares form a cross: a vertical column of four squares labeled A (top), B, C and D (bottom), plus E attached to the left of B and F attached to the right of B. Fold it into a cube. Which face is opposite A?
   Answer: C. In a straight run of squares, faces one square apart end up opposite. B is opposite D, and E is opposite F.
6. Valid nets. Start with a row of four squares. Which arrangement cannot fold into a cube? (a) one extra square above the second and one below the third; (b) one extra square above the first and one above the fourth; (c) one extra square above the first and one below the fourth.
   Answer: (b). Both extra squares fold onto the same side, overlapping, and one face of the cube is left open.
7. Painted cube. A 3 by 3 by 3 cube is painted on the outside, then cut into 27 small cubes. How many small cubes have paint on exactly two faces?
   Answer: 12, one in the middle of each edge. Eight corner cubes have three painted faces, six face centers have one, and the single core cube has none.
8. Grid rotation. A 3 by 3 grid has a black cell in the top-left corner and a gray cell in the top-middle position. Rotate the whole grid 90 degrees clockwise. Where do the two cells land?
   Answer: black at top right; gray at middle right.
9. Orientation. You face north. You turn right, right again, then left. Which way do you face?
   Answer: east. North to east, east to south, then south back to east.
10. Gears. Three gears mesh in a row. The first turns clockwise. Which way does the third turn? If the first has 20 teeth and the second has 10, how many turns does the second make for one turn of the first?
    Answer: clockwise, since each meshing reverses direction; and two turns, because 20 teeth pass a 10-tooth gear twice.
11. Mirror word. Which word reads exactly the same in a mirror held beside it: TOOT, BOOT or NOON?
    Answer: TOOT. A mirror reverses the letter order and flips each letter. TOOT is a palindrome built from symmetrical letters; N is not symmetrical, and BOOT is not a palindrome.
12. Stacked cubes. Eight cubes form a 2 by 2 by 2 block. Remove the top cube from the front-left corner. How many cubes remain, and how many squares do you see looking straight down from above?
    Answer: seven cubes, and four squares. The gap exposes the cube beneath it, so the top view is unchanged.

How to solve spatial items faster

• Anchor one feature. Track a single corner or marked face through every move instead of the whole figure.
• Test for mirroring first. If two shapes differ by a flip, no amount of rotation will match them. That check eliminates options in seconds.
• Unfold in reverse. On folding items, undo the last fold first, doubling the holes across each fold line.
• Use the opposite-face rule. On cube nets, squares one apart in a straight line become opposite faces.
• Count by category. On painted-cube items, sort cubes into corners, edges, faces and core rather than counting one by one.

Pattern grids that mix shape and position are covered in our Raven's Progressive Matrices guide and our abstract reasoning test guide.

Can you improve spatial reasoning?

Yes, more clearly than for most abilities. David Uttal, Nora Newcombe and colleagues meta-analyzed 217 training studies in Psychological Bulletin. The average effect of training against control groups was a Hedges' g of 0.47, close to half a standard deviation. The effects were stable across delays between training and testing, and they transferred to spatial tasks that had not been trained.

That is a real gain in skill. Drilling one test's item types is a narrower thing: it mostly builds familiarity with the format. Our free IQ test is a practice screener, not a diagnosis; for a sense of where a score of 125 falls, see the IQ rarity chart. More guides sit in the IQ guides hub.

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.