Spatial reasoning: turning shapes in your head, and what our test can show

You try to fit a sofa through a doorway and, before lifting it, you picture it tilted, turned on its end and angled through the frame. Or you read a map and work out which way to turn without spinning the map around. In both cases you move objects in your head instead of in the world.

Psychologists call this spatial reasoning: the ability to imagine objects, turn them, fold them and keep track of where things are. Our Spatial Reasoning Test checks three parts of it in 15 questions.

The experiment that measured mental rotation

In 1971 Roger Shepard and Jacqueline Metzler showed people pairs of drawings of three-dimensional block shapes and asked whether the two were the same object turned, or two different objects. The time people needed grew steadily with the angle between the two shapes. A shape turned further took longer, as if people were rotating a mental picture at a fairly constant speed.

That finding made mental rotation one of the most studied tasks in psychology. In 1978 Steven Vandenberg and Allan Kuse turned it into a paper-and-pencil Mental Rotations Test, and in 1993 John Carroll, after reanalysing a large body of ability test data, placed visual and spatial processing among the broad abilities that make up human intelligence.

What our test asks

The test has three parts with five questions each, and every question has four answers with one correct.

Mental Rotation asks what a shape, letter or digit looks like after it is turned. For example: "A square is rotated 90° clockwise. Which description matches the result?"

Spatial Visualization asks you to transform shapes in your mind: count the squares left after one is cut out, fold a triangle along its axis, or work out how many colours a cube needs.

Spatial Memory asks you to hold a layout in mind and use it. One question reads: "On a map: the school is north of the park, the store is east of the school. In which direction from the park is the store?"

All questions are text. The shapes are described in words and symbols, not drawn, so reading carefully is part of the task. In the memory questions the information stays on the screen, so they test whether you can build and use a mental layout more than whether you can recall it later.

We wrote the 15 questions ourselves, inspired by the work of Shepard and Metzler, Vandenberg and Kuse, and Carroll. The test has not been validated or normed. Your result shows how many questions you answered correctly in each part. It is not an IQ score, and it cannot compare you with the population.

Can spatial skills be trained?

Spatial skills respond well to practice. In 2013 David Uttal and colleagues reviewed over two hundred training studies and found that practice improved spatial performance, that the gains lasted, and that they carried over to some tasks that were not trained directly. The skill also matters outside tests. In 2009 Jonathan Wai, David Lubinski and Camilla Benbow followed large groups of American students and found that spatial ability in adolescence predicted later achievement in science, technology, engineering and mathematics, beyond what verbal and maths scores already predicted.

How to read your score

With five questions per part, one mistake changes a part score noticeably. Before drawing conclusions, look at which questions you got wrong. A rotation error is often a matter of direction (clockwise or anticlockwise), and a visualization error often comes from a detail in the question that was read too quickly.

Spatial ability is one part of general reasoning. For a wider picture, try the IQ test, which also includes spatial tasks, or read what an online IQ test measures and how it works.