AbilityBenchFree random-dot stereogram, 3 routes
Stereopsis test with the arcseconds worked out in front of you
A square hidden in a field of random dots sits at a different depth from its surround, and you say whether it is at the top, right, bottom or left. Neither half of the pair contains it on its own, so only two cooperating eyes can find it. The page is free and holds nothing back, but it will not start until you have matched a bank card against the screen and typed how far away you are sitting — without those two numbers a shift in pixels cannot become an angle, and every site that prints arcseconds without asking for them is guessing.
- 100% free
- No signup
- Free fusion or red-cyan
- Arcseconds from your own screen
- Refuses to score a failed fusion
A field of random dots hides a square that sits at a different depth from the rest — top, right, bottom or left. It is invisible to one eye, and invisible to two eyes that are not cooperating: each half of the pair is a plain random field with nothing in it. Before any of that can be turned into an angle, this page needs two measurements it cannot take itself.
The floor, before you start
At 60 cm from a screen with 3.79 device pixels per millimeter, the smallest shift that can be drawn is one pixel, and one pixel subtends 91 arcseconds. That is the finest disparity this page can present to you — coarser than the 20 to 40 arcseconds a polarized plate test resolves in a consulting room. Sitting further back makes the angle smaller and the dots harder to see; both effects are real and neither is under this page’s control.
Those 4 run at 5 pixels of shift — 454 arcseconds here, which is coarse enough that anybody who has fused the pair will see the square immediately. They decide whether there is a measurement to make, and they are not part of it.
How to run the stereogram ladder
Calibrate, pick how the two images reach your eyes, pass four easy ones, then let the shift shrink.
Give the page a millimeter and a distance
Hold a bank card, driving license or travel pass flat against the glass and drag the outline until the edges coincide; every one of them is 85.6 mm wide by ISO/IEC 7810, which is what makes a wallet a ruler. Then measure — do not estimate — how far your eyes are from the panel, in centimeters, because that figure divides straight into every angle the page reports. A fifth off the distance is a fifth off the answer, in the flattering direction if you guessed short.
Choose how each eye gets its own picture
Crossing your eyes on a fingertip held in front of the screen is the route that always works, since converging is something everyone can do; looking through the screen at an imaginary distant point is easier on the eyes once learned but only possible while the two panels sit closer together than your own pupils, which is why the page derives the panel width from the pupil distance you entered. Red-cyan glasses need no technique at all, red lens on the left, at the cost of filter leakage that raises the smallest shift you can resolve.
Pass four coarse ones, then follow the ladder down
Four stereograms at five pixels of shift decide whether there is anything to measure: that square is unmissable to fused eyes and invisible without fusion, so three of four gets you into the measurement and fewer stops the page rather than producing a number from guesses. After that the shift drops by a pixel each time you are right twice running and climbs a pixel the moment you are wrong, and the threshold is the average of the turnarounds once the first two have been discarded.
Technical specifications
| Stimulus | A random-dot stereogram in Julesz's construction: two dot fields identical except inside one square, whose content is copied from the shift distance along and whose vacated band is refilled with fresh noise. Dot cells are 2 device pixels at 50% density, and the hidden square is 34% of the field's width |
|---|---|
| The conversion, in full | 206265 x pixel width in mm / viewing distance in mm = arcseconds. At 96 CSS pixels per inch, a pixel ratio of 1 and 60 cm, that is about 91 arcseconds for a one-pixel shift; at a pixel ratio of 2 it halves to about 46 |
| Resolution floor | One device pixel. Nothing finer can be drawn, so a visitor who resolves the smallest available shift is reported as having reached the screen's limit rather than given a threshold — clinical plates resolve 20 to 40 arcseconds, which a 96 px/inch panel at arm's length cannot present at all |
| Response and chance | Four positions — top, right, bottom, left — on the arrow keys or four on-screen buttons, so guessing scores 25%. The page prints the exact one-sided binomial probability of the run against that floor and withholds the threshold when it is above 0.05 |
| The ladder | Two correct answers step the shift down by one pixel, one wrong answer steps it up by one, starting at 5 and capped at 14. It converges where 70.7% of answers are right, and the threshold is the mean of the last 4 or 6 turnarounds with the first 2 discarded, printed with their standard deviation |
| Panel separation | Derived, not chosen: the two half-images are sized so their centers sit no further apart than the interpupillary distance you entered, defaulting to Dodgson (2004), Variation and extrema of human interpupillary distance, SPIE Stereoscopic Displays and Virtual Reality Systems XI. Parallel fusion of panels wider apart than your own eyes would require divergence, which is why so many stereogram pages cannot be fused on a large monitor |
| Depth equivalent | Viewing distance x pixel width / interpupillary distance. At 60 cm with a 63 mm pupil separation, one pixel of shift stands for roughly 2.5 mm of depth in front of the glass — the figure that makes an arcsecond mean something physical |
| What is never claimed | No stereoacuity grade, no percentile and no prevalence figure. Screen luminance, ambient light, filter crosstalk on the glasses route and your actual head position are all uncontrolled, and the page names them instead of averaging over them |
Frequently asked questions
Is this the same as the test at an optometrist?
No, and the difference is mostly in what is held still. A clinical stereoacuity test fixes the viewing distance with a rod or a chinrest, fixes the illumination, uses plates whose disparities were manufactured to a tolerance, and separates the two eyes with polarizing filters that leak far less than colored ones. The Titmus fly and the Randot use polarization; the TNO uses red-green anaglyph over random dots, which is the closest published relative of what runs here; the Lang plates use lenticular strips and need no glasses at all. This page reproduces the principle and none of the control, and reports a raw angle rather than a grade.
Why does the page refuse to give me a number sometimes?
Because a ladder fed guesses still converges, and the number it converges on is meaningless. The four-position judgment has a 25% floor, so a visitor who never fuses the pair will still be right about a quarter of the time, the shift will oscillate around some middling value, and the arithmetic will happily turn it into arcseconds. The page runs an exact binomial test on the whole run instead: if the accuracy is not separable from chance, or if the ladder spent its time pinned against the one-pixel floor, it says which of those happened and prints no threshold. That is the whole reason the four coarse stereograms come first.
Cross-eyed and parallel gave me opposite depth. Which is right?
Both, and the reversal is why this page asks where the square is rather than whether it sticks out. Under parallel fusion each eye receives the panel on its own side; crossing swaps them, so a shift that reads as nearer one way reads as further the other. Pages that ask you to say which shape is in front therefore have an answer key that depends on a technique they cannot observe. Asking for a position sidesteps it completely: the square is at a different depth from its surround either way, and where it sits does not move. The renderer also swaps the two fields for the crossed route so the geometry it reports is the geometry you saw.
Do I need the red-cyan glasses, and does it matter which eye the red goes over?
You do not need them — both free-fusion routes are complete tests — and yes, the red lens belongs over the left eye here. A red filter passes the red channel and blocks cyan, so the eye behind it sees the dots drawn in red and nothing else; putting the glasses on backwards inverts which eye gets which field and flips the depth, the same way crossing does. The glasses route is also the one to skip if separating red from green is hard for you, since the filters work by removing exactly those wavelengths, and the anaglyph field has to be drawn as bright dots on black rather than dark dots on light, which changes the mean luminance and with it the threshold.
Why does sitting further away make the test finer but not better?
Because distance divides into the angle, so doubling it halves the arcseconds a single pixel is worth — and it also halves the angular size of every dot in the field. The disparity floor improves and the stimulus gets harder to see at the same time, and past a certain point the dots stop being resolvable and you are measuring acuity instead of stereopsis. The useful move is the opposite one: a display with more pixels per millimeter lowers the floor without shrinking anything, which is why a phone at 30 cm can present a finer shift than a desktop monitor at 60 cm despite the shorter distance.
I could not fuse it at all. Does that mean I have no stereopsis?
It means the pair was not fused, and free fusion is a skill that most people fail at before they learn it. Try the other direction, try the glasses, and try again on another day — a few minutes with a fingertip is the usual difference between a failure and a success. What a repeated failure across all three routes is worth is an appointment rather than another run: reduced or absent stereopsis is common, it often traces to a squint or an amblyopia from childhood that nobody mentioned, and it is diagnosed with plates and a cover test rather than with dots on a web page. No percentage of the population appears anywhere on this page, and the reason is given in the results panel.
Can I compare my number with somebody else's?
Only if you also compare the calibrations, which is why the copy button includes them. An arcsecond figure here is a pixel count multiplied by a conversion built from three quantities you typed — card width, distance and pupil separation — and two of those are estimates. Somebody who set the distance twenty centimeters short reports a coarser threshold than they achieved; somebody who left the card slider at its default on a high-density laptop reports a finer one. The comparison the page is designed for is against your own run on the same screen at the same distance, and the standard deviation printed beside the threshold is there so you can see whether the two differ by more than the run's own precision.
How a shifted pixel becomes an angle, and where the honesty runs out
Stereopsis is the depth sense built from the small mismatch between the two retinal images, and it is unusually good: the smallest disparity a healthy visual system can use is finer than the spacing of the photoreceptors that detect it, which is the property Westheimer named a hyperacuity — Westheimer (1979), Cooperative neural processes involved in stereoscopic acuity, Experimental Brain Research. Clinically the figure is quoted in arcseconds, and a normal result sits somewhere in the twenties to forties. The stimulus that isolates the sense cleanly is the random-dot stereogram, which Julesz introduced precisely because it contains no other cue at all — Julesz (1971), Foundations of Cyclopean Perception, University of Chicago Press. Each half is a field of noise; the shape exists only in the comparison between them, so there is nothing for one eye, a camera or a pattern-matching visitor to find. That property is what makes it worth building here, and it is also what lets this page tell a failed fusion apart from a poor threshold instead of blurring the two together.
The arithmetic is the short part. A horizontal shift of d millimeters at a viewing distance of D millimeters subtends d divided by D radians, and multiplying by 206265 turns radians into arcseconds. Everything difficult is upstream of it, in getting d and D at all. A browser knows its own dimensions in CSS pixels, a unit defined so that 96 of them make an inch on a nominal display and calibrated to nothing on a real one, and it knows a device pixel ratio that also moves when you zoom. It has no idea how far away your face is. So this page asks: a card of a standardized width is matched on screen for the millimeter, and the distance is typed. Run the numbers and the awkward result falls out immediately — at 96 CSS pixels per inch, a pixel ratio of 1 and a 60 cm viewing distance, the finest shift the display can draw is one pixel and one pixel is worth about 91 arcseconds. Against the 20 to 40 arcseconds a consulting-room plate resolves that is coarser by a factor between two and five, so the floor of this measurement is the panel and not the person, and a visitor who reaches it has been told about a screen rather than about their eyes. A denser display lowers the floor in proportion, which is the one lever that helps; nothing on the software side does. The reference module this site draws its figures from declines to supply norms here at all, and its reasoning is worth reading in its own words: “Clinical stereoacuity is measured in arcseconds with polarized or vectographic plates at a fixed distance. A browser cannot control viewing distance, screen size or pixel pitch, and a red-cyan anaglyph adds crosstalk and color loss that shift the threshold on its own. Prevalence figures for reduced stereopsis also vary widely with the criterion used and this file has no citation it would stake the page on.”
Two smaller decisions carry more weight than they look. The panels are sized from the pupil separation rather than chosen for the layout, defaulting to Dodgson (2004), Variation and extrema of human interpupillary distance, SPIE Stereoscopic Displays and Virtual Reality Systems XI: parallel fusion asks each eye to look straight ahead at its own half-image, so once the centers are further apart than the eyes themselves the technique needs divergence, which is not a thing people can do — the commonest reason a stereogram page works on a phone and not on a monitor. And the question is deliberately “where is the square” rather than “is it in front or behind”, because crossed and parallel fusion invert the sign of the depth and the page cannot see which one you used. That is the same class of problem as the one the dominant eye test runs into when two accepted methods disagree on the same person, and it is why both pages report what was actually observable rather than the tidier claim. If the fusion never comes, the measurements on this site that need only one eye are the depth perception test, which works entirely in ratios and needs no calibration, the blind spot test, the peripheral vision test and the color perception test, which is also the page to visit before trusting the red-cyan route. For an unlit-panel problem of a different kind there is the contrast sensitivity test, and for a judgment that is bent rather than measured, the optical illusion test. Anyone here because a job application mentioned a vision screen should know that the reasoning parts of those packs are practiced on the Wonderlic-format practice test and the Mensa-style practice test, and that the depth part is done with plates on a bench.
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.
No trial here has a deadline and none is scored on speed: a fusion takes seconds to settle and the stereogram stays on screen until you answer, so the times printed with the result are in seconds and describe how long the fusing took rather than how quickly you saw. The floor is stated because the same clock produces both figures, and because a trial the tab lost focus during is thrown out — losing focus is losing the fusion, and a re-fused pair is a new trial rather than a slow one.
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 stereoblindness, amblyopia, a squint or any other reason two eyes might not cooperate. Only a qualified professional, working with more than a browser, can make that judgment.
Where the card width and the distance go
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 three numbers you type — card width, viewing distance, pupil separation — stay in this tab's memory for the length of the run and are not written to storage, so a reload asks for them again. That is deliberate rather than lazy: a remembered calibration is a wrong calibration the moment you move to another screen or another chair, and a stale one would silently rescale every arcsecond on the page.