Mental Rotation Test

Roger Shepard and Jacqueline Metzler put pairs of block figures in front of people in 1971 and timed the answers. What they found is one of the tidiest results in the whole of psychology.

The time to answer rose in a straight line with the angle between the two figures. A pair turned by 40 degrees took a fixed amount longer than an upright pair. A pair turned by 80 degrees took twice that much longer.

A line like that is hard to explain by looking. If people compared features one at a time, the angle would not matter in such an even way. It looks instead as though something is being turned, at a steady rate, until the two line up.

That is why the task is called mental rotation rather than mental comparison. The name is a claim about the method, and the straight line is the evidence for it.

This page reproduces the measurement rather than the story. It sets the angle itself. It times each answer from the frame the pair reached the screen, then fits a line through your times at each angle.

The headline here is the slope of that line, converted into something you can picture: the extra seconds a quarter turn costs you.

It is deliberately not a mark out of twenty. Almost everybody gets these pairs right, because there is no clock on the canvas and people slow down rather than guess. A score that everybody nearly maxes out tells you very little.

A gradient does not have that problem. It ignores how quick you are in general and asks only what the turning adds. Two people with the same total time can have very different lines through it.

The card carries the two ends of the line as well, so you can see where the number came from. One is your time on the upright pairs, which involves no turning at all. The other is your time on the half turns.

Only pairs you called correctly are timed. A wrong call is not a turn you finished. Including it would flatten the line with the trials where you gave up and guessed.

The published times at each angle are set out in mental rotation accuracy by angle. That page also explains why a share correct compares so badly from one version of this task to another.

Every figure here is a chain of cubes in three straight runs. Each run sits at right angles to the one before it.

That construction makes the shape handed, the way a left glove is handed. Hold a left glove up to a mirror and you see a right one. Turn the left glove any way you like and it stays a left glove.

So a mirror pair can never be settled by turning the figure far enough. Half the pairs here are the same shape and half are the opposite one, and no angle makes an opposite pair match.

The three faces of each cube are the same colour at three strengths. Nothing on the canvas is signalled by colour, so a visitor who cannot separate two hues loses nothing.

Both figures are drawn at the same size inside the same square box. A box that hugged the shape would shrink a diagonal figure, and its size would then answer the question before you had turned anything.

The right figure is turned within the flat of the screen, like a photograph rotated on a table. It is not tipped away from you into depth.

Shepard and Metzler ran both kinds and got the same straight line from each. A turn into depth is a harder drawing problem, and the flat turn measures the same rate. So the flat turn is what this page uses.

That has an honest consequence worth stating. Because both figures are the same drawing, a determined visitor can sometimes match one arm rather than turn the whole shape.

People do that in a laboratory too, and it shows up as a flatter line rather than as a broken measurement. If your gradient is very shallow and your accuracy is high, that is probably what you were doing.

The block count is a setting for the same reason. Longer arms give a shape with more to hold at once, which makes matching a single arm less useful.

The bar under your score is a reference distribution rather than our own data, and the page says so wherever it appears.

Its middle is the one number the original paper hands over. Shepard and Metzler put the average rate near sixty degrees a second, and ninety degrees at that rate is a second and a half.

The spread either side of that middle is a modelled shape. Marcel Just and Patricia Carpenter took the task apart in 1985 and found the gradient is where people differ. The quick end sits near a second a quarter turn and the slow end near three.

Nobody has published percentiles for a browser version of this task. The group test that does carry norm tables is scored as marks on paper. A mark on paper is not a gradient in milliseconds, so its figures do not transfer.

Our own norm replaces the model when a thousand runs have been recorded here, and not one run before that. The same rule governs every figure on the site, including how processing speed changes with age.

A shallow line means you turned these particular block figures quickly today. It does not mean you have a good sense of direction or would be better at packing a car.

Spatial tasks look alike from outside and behave differently from each other. Folding paper, reading a map and turning a solid all draw on different things. That is why this hub will hold several tests rather than one.

Practice moves this number, and moves it fast. Most people take a chunk off their gradient over the first few runs simply by learning what the figures look like.

Whether that carries anywhere else is a separate question with a disappointing answer. There is more on it in whether brain training games are worth it.

Compare your recent runs with each other rather than your first run with somebody else's tenth. One run is a snapshot and a gradient from twenty pairs is a rough one.