Can You Rotate Shapes in Your Head?

weirdly accurate.

Can You Rotate Shapes in Your Head?

Can you rotate shapes in your head?

Yes, and you do it at a fairly steady speed. In Shepard and Metzler’s classic 1971 mental rotation test, the time people needed to tell whether two block shapes were the same grew in a straight line with the angle between them, as if one shape were being turned in the head. In the open data of 54 students tested by Ganis and Kievit in 2015, the middle person turned at about 120 degrees a second.

This mental rotation test uses the same task as a short climb. Each round shows two figures of nine to eleven cubes joined in four arms; the second is the first turned, or its mirror image turned by the same amount, and you tap Same or Mirror. There are four levels, turned 0, 50, 100 and then 150 degrees, the same four angles as the study, with two pairs per level, one turned within the picture and one in depth. The first miss is free; the second ends the climb. Your result is how far you got, plus a turning speed from your right answers: how much longer you take for every extra degree, which a fixed finger or screen delay doesn’t change. To compare fairly, each of the 54 students was run through these same four levels 2,000 times using their own recorded answers and times, and scored exactly like you; 77% of those runs got through all four.

It is not an IQ test. Mental rotation is one spatial skill, and eight pairs can’t estimate intelligence or anything clinical. The students answered on a keyboard in a lab with their pairs in shuffled order, while yours climb from small turns to big ones, and practice makes most people faster as they go, so your rank is a guide, not a calibrated norm, and a second run can land quite differently. If the angle didn’t slow you down, or you got too few right, the test says it can’t read a speed instead of making one up.

What the test measures

One thing: how fast you can turn a shape in your mind and still get it right.

The task

  • Shepard–Metzler figures: nine to eleven cubes joined face to face in four arms, each arm at right angles to the last, with no symmetry, so a figure and its mirror image can never be turned into each other
  • Four levels, each turned further: 0, 50, 100 and 150 degrees, the angles Ganis and Kievit used; each level is announced as it starts
  • Two pairs per level, one turned within the picture and one in depth about the vertical axis; a new figure every round
  • Two misses end the climb, so a run is four to eight pairs
  • After each answer the second shape turns back and tries to fit into the first, so you can see why it was a match or a mirror

Your result

  • How far you climbed, and a headline rank among 54 students from Ganis and Kievit’s 2015 study, each simulated on the same four levels from their own answers
  • Your turning speed in degrees per second, and how many extra seconds each 90 degrees cost you, beside the 54 students’ own speeds
  • A chart of your time against the angle, with the students’ median time at each angle and the middle half of them
  • Breakdowns by level, by same versus mirror, and by turns in the picture versus in depth
  • A shareable card, and a challenge link that carries your result inside the link itself

Before you start

  • About a minute; free, with no sign-up
  • Works on a phone or a computer; it needs a browser with 3D graphics (WebGL) switched on
  • Sound is optional: it only adds small clicks and taps
  • Answer as fast as you can while still getting it right: speed only counts on right answers, and two misses end the run

Mental rotation FAQ

Is this test free? Do I need to sign up to see my result?

Yes, it’s free, and there’s nothing to sign up for: no account, no email, no payment. Your result appears on this page the moment you finish, and you can share it or play again straight away.

What is a mental rotation test?

A mental rotation test shows two objects at different angles and asks whether they are the same object or mirror images. Roger Shepard and Jacqueline Metzler introduced the version with block figures in 1971 and found that answer time rises in a straight line with the angle, which suggests people turn a mental image at a steady rate. That rate is what this test measures.

What is a normal mental rotation speed?

About 120 degrees a second for the middle person in Ganis and Kievit’s 2015 sample of 54 psychology students, computed from their open data; the middle half fell between roughly 90 and 160 degrees a second. In the same study, answers took about 1.8 seconds with no turn and 3.2 seconds at 150 degrees, and errors rose from about 5% to 19%.

How does the mental rotation test calculate turning speed?

Turning speed comes from the slope of your answer time against the angle, using right answers only. If 90 more degrees adds 0.75 seconds, you turn at 120 degrees a second. Any constant delay, from your finger, the screen or deciding to press, adds the same time to every answer and drops out of the slope, which is why the slope and not raw time is the measure.

Does a mental rotation test measure IQ?

No. A mental rotation test measures one spatial skill: how quickly and accurately you can turn a shape in your mind. Eight pairs say nothing reliable about general intelligence, and this test is not a clinical or educational assessment. A rank here compares one short climb with 54 students whose own lab answers were replayed on the same four levels.

Can you get better at mental rotation?

Yes. A 2013 meta-analysis by Uttal and colleagues pooled 217 studies of spatial training and found an average improvement of about half a standard deviation (Hedges’s g = 0.47) over control groups. The gains lasted after delays and carried over to spatial tasks that weren’t trained. Repeating this particular test will also make you faster simply through familiarity.

Is rotating a shape in depth harder than rotating it flat on the page?

Not in the original study. Shepard and Metzler reported in 1971 that turns in depth took no longer than turns of the drawing in its own picture plane. People differ, though, so this test mixes both kinds and shows you which one cost you more mistakes or time.

Why did I get a different result the second time?

Eight pairs is a short run, so one slow answer or one slip moves the slope and the rank noticeably, and a second miss ends the climb early. Practice also makes most people faster: in Ganis and Kievit’s data, students answered about a fifth faster in the second half of their session than in the first. Several runs tell you more than one. Switching devices moves your raw answer time more than your turning speed, because a constant delay drops out of the slope.

Where the numbers come from

Ranks compare your run with the 54 psychology students in Ganis & Kievit (2015), whose raw data is openly published: 96 pairs each (24 at each of 0, 50, 100 and 150 degrees), keyboard answers, turns about the vertical axis, 7.5 seconds per pair, in shuffled order. Each student was run through this test’s four levels 2,000 times by drawing from their own answers and times, and every simulated run was scored with the same code as yours; 77% of those runs cleared all four levels. Their turning speeds shown beside yours come from all 96 of each student’s pairs with the same line fit. Because this test climbs from small to large turns, uses touch and includes turns in the picture plane, the rank is a reference, not a calibrated norm. The site does not publish its own players’ data.

How the score is worked out

Turning speed

A straight line is fitted to the time of your right answers against the angle, allowing a constant extra moment for mirror images. The slope, in milliseconds per degree, becomes degrees per second (1000 ÷ slope). Very slow outliers, such as a glance away, are left out.

When there is no speed

With fewer than five usable right answers, fewer than three different angles, angles spanning less than 100 degrees, or no slowdown as the angle grows, the test gives no turning speed. A run that ends early on two misses often has too few right answers for one.

Rank

Each of the 54 reference students was run through these four levels 2,000 times by drawing from their own answers at each angle, with the same two-miss rule and the same scoring. Your rank is the share of those simulated runs you beat, ties counting half: first by how many levels you cleared, then, among runs that cleared as many, by turning slope (a run with no slowdown ranks first, one with no reading last).