What the test asks
Each trial shows two figures built from cubes, side by side, or one above the other on a narrow screen. The second one is either the first figure turned, or its mirror image turned. Press F when they are the same and J when they are mirror images. Most people need longer the bigger the turn between the two, as if they turned one figure in their mind until it lines up with the other. The page measures how much longer: your slope in milliseconds per degree, and from it your rotation speed in degrees per second.
A full run has 96 trials in 2 blocks of 48. The second figure is turned by 0, 50, 100 or 150 degrees about the vertical axis of the screen, 12 times at each angle in a block: 6 times the same figure and 6 times its mirror image, with as many turns to the left as to the right. No more than 3 same or 3 mirror pairs follow each other. Each trial starts with a blank stage for 250 ms, and the figures then stay until you answer, at most 7.5 seconds. The first run in each rotation mode starts with 12 practice trials with feedback, which are not counted. A full run takes about 6 minutes, a short run (one block of 48) about 3.
The page builds its own figures: 9 to 11 cubes in 4 straight arms of 2 to 4 cubes, with 3 bends that use all three directions of space. There are 120 figures that differ from each other even after turning and mirroring; the test trials of a run never show the same figure twice, and the practice uses other figures. Before a pair is shown, the page checks both views: no arm points almost straight at you, every arm shows at least half of its outline, both free ends stay visible, and no view looks along an edge of the cubes, which would make the figure look flat.
Things to try
- Watch the point at 150 degrees. In Ganis and Kievit's data the line flattened there; does your point lie below your line?
- Compare your slope with the slope of the same pairs only, shown under the main result. In the published study mirror pairs were answered more slowly than same pairs.
- Switch Rotation to the picture plane: the second figure then turns on the screen like a clock hand. Compare that slope with your slope in depth. No published values are shown for this mode.
- Do one run by keyboard and one by touch, then compare the slopes rather than the times. Moving a finger to a button takes about as long at every angle, so it should raise the whole line more than it tilts it.
- Repeat the test on several days and see in History whether your slope changes by more than the width of its interval.
How the result is calculated
Only correct answers count, and answers under 200 ms are left out. Then, as Ganis and Kievit did, the page leaves out the answers more than 2 standard deviations from the mean of their own angle and pair type (same or mirror), and fits a straight line through all the remaining times:
Here θ is the angle between the figures in degrees, RT(θ) the response time in ms, b the slope in ms per degree and a the time the line gives for no turn at all: seeing both figures, comparing them and pressing a key. Same and mirror pairs go into one line together, as in Ganis and Kievit's table.
The 95% interval is a percentile bootstrap: the page draws 2000 new sets of times from yours, with replacement, inside each angle and pair type, applies the 2 standard deviation rule to each set, fits the line and keeps the middle 95% of the slopes. The speed interval is 1000 divided by the two ends of the slope interval. When the slope is at most 1 ms per degree, or its interval reaches 0, the page gives no speed: your times barely changed with the angle, and a speed computed from such a slope could be any number. For a simulated participant with a true slope of 9.5 ms per degree, a spread of about 850 ms from trial to trial and the error rates of the published table, the interval of a full run was typically 6.7 ms per degree wide and held the true slope in 95% of runs; in a short run it was 8 ms per degree wide and missed the true slope in about 1 run in 10 (simulation of 1 November 2026). A difference of a few ms per degree between two runs may be chance.
Errors are wrong answers and answers after 7.5 seconds, counted at each angle, with a 95% Wilson interval in the table under Show the numbers.
Compared with published values
Giorgio Ganis and Rogier Kievit tested 54 right-handed students (31 women, mean age 22.3) about 60 cm from the screen, with rendered pictures that have shading and foreshortening as depth cues, 96 trials in 2 blocks and the B and N keys. In their pictures the right object was always turned clockwise as seen from above; on this page the second figure turns left and right equally often. Their means, with same and mirror pairs together:
| Angle | Response time, ms (SE) | Errors, % (SE) |
|---|---|---|
| 0° | 1,801 (77) | 5.3 (0.7) |
| 50° | 2,415 (106) | 7.3 (1.0) |
| 100° | 3,026 (120) | 13.4 (1.8) |
| 150° | 3,191 (117) | 18.8 (2.6) |
Their best-fitting line is 9.56 × θ + 1,891.3 ms: about 10 ms per degree, or a speed of about 100 degrees per second. Errors rose by about 0.1 percentage points per degree. They report that this speed is higher than the 60 degrees per second found with the original figures of Shepard and Metzler in a comparable condition. The chart in This run shows their four means with ±1 SE and their line next to yours.
Their mirror pairs were pseudo-mirror images, often made by flipping one end arm, so that no turn about the vertical axis could match them; two of their pairs could be matched by a turn about another axis. The mirror pairs on this page are true mirror images, which no turn about any axis can match. Read their values as landmarks for your line, not as norms.
Why there is no percentile
Gerrit Hirschfeld, Meinald Thielsch and Boris Zernikow (2013) measured how well mental rotation slopes repeat in 99 students, 63 of whom came back after about six weeks, with pictures of hands, feet, faces and cars at 0, 90 and 180 degrees. With all four kinds of picture together, the split-half reliability of the slope was 0.79 when each kind came in its own block and 0.2 when they were mixed, and the slopes of the two sessions correlated at 0.69 and 0.55. For one kind of picture alone, no slope reached a split-half reliability above 0.38. A rank among other people would claim more than one run can show, so History compares you with your own runs on the same input and a similar refresh rate.
Where the task comes from
Shepard and Metzler (1971) showed pairs of drawings of objects made of 10 cubes in 4 arms and asked whether the two were the same object. Response times and errors grew in a straight line with the angle between the objects, which suggested that people turn an inner picture step by step, much as an object turns in space. Ganis and Kievit (2015) built 48 new objects of 7 to 11 cubes with shading, 384 pictures in all, so that studies of training can use figures that a participant has not seen before, and checked them on the 54 students described above.
Limits
- Drawn figures. The page draws the figures itself, in parallel projection without foreshortening, so they look flatter than Ganis and Kievit's rendered pictures, and on most screens they are smaller than in the laboratory.
- True mirrors. The published values come from pseudo-mirror images, so a mirror pair here can be a little harder or easier than there.
- Your device. The screen, the keyboard and the browser add a delay to every answer. Added equally at all angles, it raises the line without changing its slope, so compare times only on the same input. Below 50 Hz or with uneven frames, which remote desktop and power-saving modes often cause, the page warns you first and offers Run anyway: the run is marked less precise and kept apart in History.
- Strategy. Some people compare the arms one by one instead of turning a figure in their mind. The line can then be flatter or bent, and the slope measures something else.
- Practice. Answers get faster with practice: Hirschfeld and colleagues found slower answers on the first trials of each block. Compare runs made after a similar amount of practice.
- A hidden tab. The trial in progress is discarded and repeated later with another figure, and the run waits for Resume.
- Not a medical test. This is not a measure of intelligence or spatial ability for any assessment.
Controls
- Keyboard: F = the same figure, J = mirror images. Enter or Space on the focused button goes on; Esc stops a run.
- Touch and mouse: the Same and Mirror buttons under the figures.
- Pauses: for 0.7 s after a result, the end of a block or Stop the buttons are dimmed and ignore keys still pressed from the task. A second click within 0.7 s of a start does not stop the run, so a double click is safe.
- Language: the link at the end of History switches the app to Slovak.
Sources
- Ganis, G., & Kievit, R. (2015). A new set of three-dimensional shapes for investigating mental rotation processes: validation data and stimulus set. Journal of Open Psychology Data, 3(1), e3. doi:10.5334/jopd.ai
- Hirschfeld, G., Thielsch, M. T., & Zernikow, B. (2013). Reliabilities of mental rotation tasks: limits to the assessment of individual differences. BioMed Research International, 2013, 340568. Full text (PMC3806254)