Spatial Reasoning and Spatial Intelligence

What is spatial reasoning?

The American Psychological Association defines spatial ability as "the skill required to orient or perceive one's body in space or to detect or reason about relationships within or between objects in space", adding that "spatial ability is required in map reading and assembling jigsaw puzzles" (APA Dictionary). A tighter research definition, from the psychologist David Lohman, is "the ability to generate, retain, retrieve, and transform well-structured visual images" (quoted in Wai, Lubinski and Benbow, 2009).

In everyday terms, spatial reasoning is what you use to:

• Turn a map round in your head to match the street you are standing in.
• Picture how flat-pack furniture goes together from the diagrams.
• Pack a suitcase or car boot so that everything fits.
• Judge whether a sofa will go through a doorway if you tip it on its end.
• Rotate a block in a game such as Tetris so it slots into a gap.

People often call the first part of this, knowing where your own body is among the things around you, spatial awareness: it matches the APA's opening words, to "orient or perceive one's body in space". Spatial reasoning goes further, to working things out about shapes and spaces in your head. You will sometimes see it spelled "spacial reasoning". The standard spelling is spatial, but both refer to the same thing.

What is spatial intelligence?

Spatial intelligence is the name the ability gets when it is treated as one of the main kinds of intelligence. The APA defines it as "the ability to mentally manipulate objects in space and to imagine them in different locations and positions", and notes that it is "one of the distinct intelligences in Gardner's multiple-intelligences theory and also a primary mental ability (S) in Thurstone's theory of primary abilities" (APA Dictionary).

Howard Gardner included spatial intelligence among his original intelligences in Frames of Mind (1983). In a later summary he described its core as the "capacities to perceive the visual-spatial world accurately and to perform transformations on one's initial perceptions", gave the navigator and the sculptor as its typical end-states, and noted that "surgeons require both the acuity of spatial intelligence to guide the scalpel and the dexterity of the bodily-kinesthetic intelligence to handle it" (Gardner and Hatch, 1989).

In the Cattell-Horn-Carroll (CHC) model, the framework behind most modern IQ tests, the same ground is covered by the broad ability called visual processing, "the ability to perceive, analyze, synthesize, and think with visual patterns" (Riverside Insights, WJ V). Spatial skill is closely tied to fluid intelligence, since both involve working with unfamiliar material in your head.

The main spatial reasoning skills

A classic 1985 review by Marcia Linn and Anne Petersen sorted spatial tests into three families, and researchers still use the grouping (as described by Uttal and others, 2013).

A newer scheme, used in the same 2013 review, crosses two questions: are you thinking about one object (intrinsic) or the relations between several (extrinsic), and is it still (static) or changing (dynamic)? The review's own example is a garden rake:

Spatial skill also includes some quicker perceptual abilities, such as recognising an object from a partial or blurred picture, finding a figure hidden in a busy pattern and tracing a path out of a maze.

Free spatial reasoning test: mental rotation

In 1971 Roger Shepard and Jacqueline Metzler showed people pairs of drawings of 3-D block shapes and asked whether they were the same shape or mirror images. The time people needed was "a linearly increasing function of the angular difference" between the two (Shepard and Metzler, 1971): the further one shape was turned, the longer the answer took, as if people were turning a mental picture at a steady speed. For their highly practised participants, that speed was roughly 60 degrees per second (Emory University course notes).

You can repeat the experiment here as a short spatial reasoning test, using a flat shape. Each trial shows two shapes: decide whether the right one is the same shape turned, or a mirror image. There are 20 trials, and at the end your average time at each angle is plotted.

Two things usually show up. First, the time rises with the angle, because the larger turns take longer to imagine. Second, mirror trials feel harder: there is no angle that lines a mirror image up, so you keep turning until you are sure. A paper version, the Mental Rotations Test, was built from Shepard and Metzler's own figures.

How spatial ability is tested

In IQ tests: the Visual Spatial Index

There is no official "spatial IQ", but both main Wechsler tests report a Visual Spatial Index (VSI), on the same scale as IQ: an average of 100 and a standard deviation of 15. On the adult WAIS-5 and the children's WISC-V it combines two subtests (Pearson WAIS-5 overview):

• Block Design: arrange coloured blocks to copy a pattern, against the clock.
• Visual Puzzles: choose the pieces that would combine to make a given shape, which Pearson describes as measuring "the ability to analyze and synthesize information" (Pearson WISC-V scales).

The WAIS-5 reports visual spatial and fluid reasoning as separate index scores, where its predecessor merged them. Our guide to the Wechsler IQ test explains all five indexes, and any index score can be read like an IQ score: a VSI of 115, for example, is about the same percentile as an IQ of 115.

Spatial reasoning tests in research and selection

• Mental Rotations Test (Vandenberg and Kuse, 1978): a paper version of the rotation task, with high reliability and "virtually no association with tests of verbal ability" (Vandenberg and Kuse, 1978).
• The ETS factor-referenced kit (1976): a research set of 72 tests that includes card rotations and cube comparisons for spatial orientation, and paper folding, form board and surface development tests for visualisation (ETS kit manual).
• Purdue Spatial Visualization Test: Rotations (PSVT:R): a 30-item rotation test used to screen engineering students.
• ASVAB Assembling Objects: the US military entrance test's spatial section, the "ability to determine how an object will look when its parts are put together", with 25 questions in 15 minutes on paper (official ASVAB site).
• AFOQT: the US Air Force officer test includes tasks such as working out "the position of an airplane in flight from reading instruments" and Block Counting, which tests "your ability to 'see into' a 3-dimensional pile of blocks" (AFOQT practice pamphlet).

The meaning of spatial orientation in an IQ test is usually these quick same-or-mirror and "how would it look from here" judgements. The APA defines spatial orientation as "the ability to perceive and adjust one's location in space in relation to objects in the external environment" (APA Dictionary). In the same way, the usual meaning of advanced spatial reasoning is visualisation tasks, which Linn and Petersen described as "complicated, multistep manipulations of spatially presented information". Our sample IQ test questions include three spatial items, from a mirror image to a painted-cube puzzle, and the free IQ test has a full spatial reasoning section.

Why spatial reasoning matters: STEM, surgery and more

The most striking evidence comes from Project TALENT, a survey of about 400,000 US high school students tested shortly after the launch of Sputnik and followed for more than 11 years. Of those who went on to STEM doctorates, "45% ... were in Stanine 9 (or within the top 4%) on spatial ability 11+ years earlier", and fewer than 10% had been below the top quarter. The authors argued that leaving spatial tests out of talent searches means missing "many adolescents with potential for STEM" (Wai, Lubinski and Benbow, 2009).

The link with maths is moderate and holds for boys and girls and across school grades: a 2022 meta-analysis put it at r = .36, and found it was only partly explained by fluid reasoning and verbal skill (Atit and others, 2022).

In medicine, a 2020 review found that 59 of 117 studies reported significant correlations between spatial tests and surgical performance, mostly in simulators and especially for beginners, though it remains "unclear whether VSA should be incorporated into trainee selection" (Canadian Medical Education Journal, 2020). In point-of-care ultrasound, spatial ability correlated about 0.39 with competence (Ultrasound Journal, 2023).

Spatial reasoning in engineering means reading 2-D drawings as 3-D parts and turning them in your head. At Michigan Tech, first-year engineering students who score 60% or lower on the PSVT:R rotation test have, since 2009, been required to take a spatial skills course; in the first randomly assigned group, average scores rose from 51.7% to 82.0% (Sorby and Veurink, 2010).

Spatial reasoning in the brain: London's taxi drivers

To earn a licence, a London black-cab driver must pass "the Knowledge": the layout of about 25,000 streets within six miles of Charing Cross, plus thousands of landmarks, which typically takes three to four years to learn. When Katherine Woollett and Eleanor Maguire scanned 79 trainees before and after, only 39 qualified, and only those who qualified showed "a selective increase in gray matter (GM) volume in their posterior hippocampi", a brain region central to navigation (Woollett and Maguire, 2011). An earlier study had found the posterior hippocampi of experienced drivers were larger than those of non-drivers (Maguire and others, 2000).

The expertise came with a cost. Compared with London bus drivers, who drive just as much but on fixed routes, taxi drivers were worse at learning new visual-spatial information (Maguire, Woollett and Spiers, 2006). Spatial skill, in other words, is not one fixed quantity: it is shaped by what you spend years doing.

Spatial reasoning, age and sex

Age. A review of 137 results from studies published between 1958 and 2011 found a large average gap (d = 1.01) between younger adults and adults in their 60s and 70s on spatial tests, larger on timed measures than on accuracy (Techentin, Voyer and Voyer, 2014). Index scores compare people with their own age group, so this doesn't push an older person's VSI down.

Sex. Mental rotation shows one of the larger average sex differences in cognitive tests, with men scoring higher; the gap is smaller for spatial perception and small for visualisation (d of about 0.56 to 0.73, 0.44 and 0.19, from Voyer and colleagues' 1995 meta-analysis, as summarised by Arrighi and Hausmann, 2022). Three points keep this in proportion: the size depends heavily on the test (Voyer, Voyer and Bryden, 1995); men and women overlap a great deal; and in training studies both improve by about the same amount (Uttal and others, 2013). Across 106 meta-analyses of all kinds of psychological sex differences, the average gap was small, d = 0.21 (Zell, Krizan and Teeter, 2015).

How to improve spatial reasoning

Spatial skill responds to practice better than most abilities. The largest review, of 217 training studies, found an average gain of 0.47 standard deviations compared with control groups. "Training effects were stable and were not affected by delays between training and posttesting", and "training also transferred to other spatial tasks that were not directly trained" (Uttal and others, 2013). The authors worked out that raising everyone's spatial skill by 0.40 standard deviations, the effect in the most rigorous studies, would roughly double the number of people with the spatial ability of today's engineering graduates.

Ways to practise that research supports:

• Mental rotation and visualisation practice: rotation tasks like the one above, paper folding puzzles, nets of cubes and 3-D drawing. These are what most training studies used.
• A spatial skills course: Sorby's sketching-based course for engineers produced large gains in rotation scores and better results in first-year engineering and maths courses.
• Action video games: after just 10 hours of an action game, the gap between women and men in mental rotation narrowed, while a non-action game produced no improvement (Feng, Spence and Pratt, 2007).
• Everyday navigation: finding your own way, reading maps and building things with your hands all give spatial practice, as the taxi-driver studies suggest.

For a broader look at what can and can't be trained, see our guide to improving fluid and crystallized intelligence, and for other kinds of reasoning, the guides to abstract reasoning and pattern recognition.

Frequently asked questions

Sources

• American Psychological Association, APA Dictionary of Psychology: spatial ability, spatial intelligence, spatial orientation.
• Wai, J., Lubinski, D. and Benbow, C. P. (2009). Spatial ability for STEM domains: aligning over 50 years of cumulative psychological knowledge solidifies its importance. Journal of Educational Psychology, 101(4), 817–835.
• Gardner, H. and Hatch, T. (1989). Educational implications of the theory of multiple intelligences. Educational Researcher, 18(8), 4–10.
• Riverside Insights. WJ V Tests of Cognitive Abilities: CHC definitions.
• Uttal, D. H. and others (2013). The malleability of spatial skills: a meta-analysis of training studies. Psychological Bulletin, 139(2), 352–402.
• Shepard, R. N. and Metzler, J. (1971). Mental rotation of three-dimensional objects. Science, 171, 701–703.
• Vandenberg, S. G. and Kuse, A. R. (1978). Mental rotations, a group test of three-dimensional spatial visualization. Perceptual and Motor Skills, 47, 599–604.
• Ekstrom, R. B., French, J. W., Harman, H. H. and Dermen, D. (1976). Manual for Kit of Factor-Referenced Cognitive Tests. Educational Testing Service.
• Pearson. WAIS-5 overview; WISC-V test content and scales; WISC-V interpretive report (sample), for the index score scale.
• Official ASVAB: what to expect; US Air Force, AFOQT practice pamphlet.
• Atit, K. and others (2022). Examining the relations between spatial skills and mathematical performance: a meta-analysis. Psychonomic Bulletin & Review, 29, 699–720.
• Recent evidence on visual-spatial ability in surgical education: a scoping review (2020). Canadian Medical Education Journal.
• Unravelling the skillset of point-of-care ultrasound: a systematic review (2023). The Ultrasound Journal.
• Sorby, S. A. and Veurink, N. (2010). Long-term results from spatial skills intervention among first-year engineering students. ASEE Engineering Design Graphics Division.
• Woollett, K. and Maguire, E. A. (2011). Acquiring "the Knowledge" of London's layout drives structural brain changes. Current Biology, 21(24), 2109–2114.
• Maguire, E. A. and others (2000). Navigation-related structural change in the hippocampi of taxi drivers. PNAS, 97(8), 4398–4403.
• Maguire, E. A., Woollett, K. and Spiers, H. J. (2006). London taxi drivers and bus drivers: a structural MRI and neuropsychological analysis. Hippocampus, 16, 1091–1101.
• Techentin, C., Voyer, D. and Voyer, S. D. (2014). Spatial abilities and aging: a meta-analysis. Experimental Aging Research, 40, 395–425.
• Voyer, D., Voyer, S. and Bryden, M. P. (1995). Magnitude of sex differences in spatial abilities: a meta-analysis and consideration of critical variables. Psychological Bulletin, 117(2), 250–270.
• Arrighi, L. and Hausmann, M. (2022). Spatial anxiety and self-confidence mediate sex/gender differences in mental rotation. Learning & Memory, 29, 312–320.
• Zell, E., Krizan, Z. and Teeter, S. R. (2015). Evaluating gender similarities and differences using metasynthesis. American Psychologist, 70(1), 10–20.
• Feng, J., Spence, I. and Pratt, J. (2007). Playing an action video game reduces gender differences in spatial cognition. Psychological Science, 18(10), 850–855.
• Mental rotation, Emory University cognitive psychology course notes.