AbilityBenchFree Shepard-Metzler run with an angle-by-time plot
Mental rotation test that plots your response time against angle
Two block figures appear side by side and you say whether they are the same object seen from a different angle or a mirror image that no rotation can bring together. Because the angular separation is set to 0, 40, 80, 120 or 160 degrees ten times each, the run can do what a single average cannot: draw your response time against angle, fit a straight line to it, and report the slope in milliseconds per degree. That chart is the page. The average time under it is mostly encoding and finger movement, and the slope is the part that is actually rotation.
- 100% free
- No signup
- 50 scored trials
- 5 angular separations
- Slope in ms per degree
- Chart of your own trials
Two cube figures, side by side. The one on the right has been turned about its vertical axis by 0, 40, 80, 120 or 160 degrees — and on half the trials it was reflected first, so no amount of turning will ever bring it into line. Decide which, 50 times, and the run fits a straight line through your times.
The run, in full
- Figures
- arms of 11 or 12 cubes, three straight runs meeting at right angles
- Turn
- 0, 40, 80, 120, 160 degrees about the figure's own vertical axis, in depth
- Half the trials
- the comparison is reflected first, and no turn will ever match it
- Keys
- S = same object, L = mirror image
- Trials
- 50 scored — 5 at each turn in each answer, one break after 25
- Window
- 15 seconds per pair, which is long because rotating 160 degrees is not fast
- Fitted on
- correct same-pair trials only, after a 3-MAD outlier rule
Practice pairs have no clock on them at all and name the right answer afterwards. They are excluded from the fit, from the accuracy figure and from the chart.
How to take the mental rotation test
Two keys, fifty pairs, and one line fitted through the result.
Learn the two keys on six practice pairs
S says the two figures are the same object turned; L says the right-hand figure is the mirror image. Six practice pairs tell you after each one whether the key was right, and none of them enters the chart. Get the mapping into your fingers here — a run where you are still thinking about which key is which produces a slope contaminated by key hunting, and key hunting does not scale with angle in any interesting way.
Answer fifty pairs, resting once at trial 25
Each pair starts with a fixation cross, then a short unpredictable gap, then the two figures until you answer or fifteen seconds pass. Take the time you need to be right: this measurement is built on correct answers, and a fast wrong answer contributes nothing to the line. The break at the halfway point is yours to end when you want, and nothing is timed while it is on screen.
Read the slope, then look at the scatter it came from
The result gives milliseconds per degree, the degrees per second that works out to, and how much of the variation the straight line accounts for. Underneath it, every correct same-pair trial is drawn as a dot against its angle, with the median at each angle marked and the fitted line through them. A high figure with dots that follow the line is a measurement; the same figure with dots scattered everywhere is not, and the chart is the only way to tell those apart.
Technical specifications
| Trials | 50 scored — five angular separations by two pair types, five repetitions each — plus six practice pairs with feedback that reach no figure |
|---|---|
| Angular separations | 0, 40, 80, 120 and 160 degrees, about the figure's own vertical axis. Depth rotation rather than picture-plane rotation, because a shape turned in the plane of the screen can be matched by tilting your head |
| Figures | Ten-cube arms in the Shepard-Metzler form: three straight segments meeting at right angles, drawn with hidden faces removed and depth ordering computed per frame rather than baked into an image |
| Mirror pairs | Half the trials show a reflected figure, which no rotation can bring into correspondence. They are answered, counted for accuracy, and excluded from the line — a mirror trial ends when you give up searching, and the moment somebody gives up is not a rotation time |
| Trial structure | 400 ms fixation cross, a gap drawn uniformly between 250 and 650 ms, then the pair until an answer or 15,000 ms, then 450 ms blank. The gap is jittered so the onset cannot be anticipated |
| The fit | Least squares through the correct same-pair trials, after a median-based outlier rule removes the trials where attention left the screen. The slope, its intercept and the proportion of variance explained are all printed, and the trials the rule dropped are counted in the open |
| Reference figure | ≈ 17 ms per degree — Shepard & Metzler (1971), Mental rotation of three-dimensional objects, Science. It is a rate from one landmark study on this stimulus, so the page prints it next to yours as an order of magnitude and never converts either into a rank |
| Timing floor | The display refresh rate is measured on the start screen and the frame time printed with the result. A slope is a ratio of a time to an angle, so a constant frame delay shifts the intercept and leaves the slope alone — which is the second reason the slope is the number reported |
Frequently asked questions
What does a slope of 17 milliseconds per degree actually mean?
It means that for every extra degree between the two figures you needed about another 17 thousandths of a second, which is a rotation rate of roughly 60 degrees a second. Read it as the speed of an imagined turn: 180 degrees of separation costs about three seconds of turning on top of whatever the trial costs anyway. The reason this is the interesting number, rather than your average response time, is that the average is dominated by seeing the figures, deciding and pressing a key — all constants that add to every trial equally and tell you nothing about rotation.
Why does the chart use only the trials where the figures matched?
Because a mirror trial has no rotation that ends it. On a same pair you turn one figure until it lines up and answer the moment it does, so the time is the turn. On a mirror pair the alignment never comes, and what ends the trial is a decision that you have searched enough — a threshold that varies with mood and confidence and does not rise with angle in the same lawful way. Shepard and Metzler reported the linear relation on same pairs for exactly this reason. The mirror trials are still shown, still counted for accuracy, and still listed in the result table.
My line is nearly flat. Did I do something wrong?
Probably not, but look at the scatter before concluding anything. A flat line with tight dots means the angle genuinely cost you little, which is what practiced participants and some very fast rotators produce. A flat line with dots sprayed everywhere means the fit had nothing to hold on to, and the proportion of variance explained printed beside the slope will be small — that is the run to repeat rather than to interpret. A third possibility is a strategy that is not rotation at all: some people match a distinctive feature such as the end cube and answer without turning anything, which produces a flat line by construction.
Are the figures turned in the plane of the screen or in depth?
In depth, about the figure's own vertical axis, and that choice is load-bearing. A figure rotated in the plane of the screen can be brought into correspondence by tilting your head or by moving your eyes along its outline, so a page that rotates a flat drawing is measuring something considerably easier and reports a much shallower slope for it. Turning a three-dimensional arm in depth changes which faces you can see and which cubes occlude which, and there is no head position that undoes it.
Is it true that men score higher on this test?
A group mean difference of this size is reported in the literature — 0.5-0.9 Cohen's d, per Voyer, Voyer & Bryden (1995), Magnitude of sex differences in spatial abilities: a meta-analysis and consideration of critical variables, Psychological Bulletin — and it is the largest of the spatial differences, which is why this test in particular attracts the claim. What that figure cannot do is say anything about you. At this effect size the two distributions overlap across most of their range, so knowing somebody's group leaves their score almost as uncertain as before, and the difference itself moves with the test used, with whether guessing is penalized and with how much practice the participants had. This page reports your slope and your accuracy and places you in no group at all.
Why is there a fifteen-second limit if I am meant to take my time?
Because a trial with no limit at all eventually stops being a trial. Fifteen seconds is far longer than a 160-degree pair needs even when it is hard, so the limit almost never fires during normal work; what it catches is the pair you walked away from, or the one where you decided to count cubes instead of turning anything. Those produce times that would drag the fitted line badly, and the honest way to handle them is a window that ends the trial rather than an outlier rule quietly removing them afterwards.
Can I compare my slope with a published one?
As an order of magnitude, yes; as a score, no. The published rate comes from a small number of practiced participants working with a specific set of ten-cube figures, answering by lever, in a laboratory. Yours comes from a browser, with a keyboard whose latency nobody has measured, on figures drawn to the same recipe but not the same figures. What genuinely compares is you against you: run this twice a week apart on the same machine and the change in slope is interpretable in a way that the gap between your number and a 1971 number is not.
What Shepard and Metzler found, and why the slope is the whole result
The 1971 experiment is famous for a chart rather than for a score. Participants judged pairs of block figures, and their response times rose almost perfectly linearly with the angular difference between the two — a straight line, at a roughly constant rate, right up to 180 degrees. That linearity is the argument. If people were matching features or checking a stored description, there is no reason the time should track the angle at all, let alone track it in a straight line; a continuous, analog transformation is the simplest thing that produces that shape. The rate that line implies, ≈ 17 ms per degree, appears in every textbook account since, and it is the number this page reproduces from your own fifty trials rather than quoting at you.
Three details separate a version that measures this from one that only looks like it. The first is the axis: turning in depth, not in the plane of the screen. The second is using several separations rather than one hard angle, because a slope needs at least three points before the word means anything and this run uses five. The third is which trials the line is fitted through — same pairs only, correct answers only. A slope computed over everything would mix a rotation that succeeded with a search that was abandoned, and the two are not the same event. The result panel says how many trials the outlier rule removed and why, because a fit is only as honest as its exclusions.
Rotation is also narrower than it looks from inside. Being fast here predicts less than people expect about the rest of spatial ability: imagining a sheet folding is a different operation, measured on the paper folding test, and imagining yourself somewhere else entirely is a further one again, measured in degrees of error on the spatial orientation test. If you want all three sampled at once before choosing where to dig, the spatial reasoning test runs eight items of each. Two neighbors outside this cluster are worth a run for a different reason: the same slope-from-many-trials method is what the lexical decision task applies to word recognition, and if the cube figures look flat or effortful to you, the stereopsis test checks whether depth is reaching you from both eyes before you read anything into a spatial score.
A reaction time here is the interval between the frame that painted the stimulus and the timestamp the browser attached to your key, both read from the same monotonic clock. What neither can see is the display pipeline behind it, so on a 60 Hz screen roughly 16 ms of every figure below is the machine rather than you. That is the timing floor: two numbers closer together than that are the same number, and this page reports no precision it cannot support.
For a slope this floor is unusually benign. A constant delay between the frame and your finger is added to every trial regardless of angle, so it lifts the whole line and leaves its steepness untouched — the intercept absorbs it. That is why the intercept is printed but not interpreted, and why the slope survives being measured on hardware nobody calibrated.
This is a measurement exercise, not a clinical assessment. It reports what you did on this page against a stated reference and nothing more — it cannot establish a spatial deficit, dyspraxia or anything neurological. Only a qualified professional, working with more than a browser, can make that judgment.
A rotation slope is a description of how one afternoon went on one machine. It is not stable enough across sessions to support a claim about a person, and no clinician would accept it as evidence of anything.
Where your fifty response times are fitted
Every number on this page is worked out by JavaScript running in the tab you are reading it in. Your answers, your reaction times and your score are never uploaded, logged or kept — which is also why the test carries on working after you disconnect from the network, and why nothing here can be held back behind an email address.
The fit happens in this tab, on an array of timestamps that never leaves it. Nothing is uploaded when the chart is drawn, the chart is vector markup built from your own dots rather than a picture fetched from anywhere, and the copy button is the only route by which any of it reaches somewhere else — into your own clipboard, as plain text.