MacAdam Ellipses: Why the Color Diagram Lies About Distance
The horseshoe-shaped chromaticity diagram looks like a map of color - so surely two colors twice as far apart look twice as different? They don't. In the 1940s David MacAdam measured how far you can move before a color looks different, and found the answer changes wildly across the diagram: a huge leap in the greens, a tiny nudge in the blues. Those ellipses revealed that the diagram is a beautiful liar about distance - and launched the search for a fair one. This is the interactive guide.
A map that lies about distance
The CIE 1931 chromaticity diagram - the famous horseshoe - places every hue at an
(x, y) coordinate. It's a triumph, and it's genuinely a map of color. But it was built
from color-matching math, not from how different colors look, and those turn out
to be very different questions. On this map, geometric distance and perceived difference simply
don't agree.
David MacAdam proved it experimentally. He asked observers to find the smallest color change they could detect at points all over the diagram, and drew a little region around each - the set of colors indistinguishable from the center, one just-noticeable difference across. If the diagram were perceptually fair, these would be identical tiny circles. Instead they came out as ellipses: stretched, tilted, and up to ten times larger in the greens than in the blues. The same step on the map means a barely-there change in one place and a glaring one in another.
The ellipses of indistinction
Here they are, scattered across the diagram. Each ellipse marks how far you can wander from its center before the color visibly changes - so a big ellipse means the eye is insensitive there, a small one means it's picky. Watch how they swell toward the green and shrink to dots in the blue-violet. (They're drawn several times life-size so you can see them.)
Where the eye is picky, and where it isn't
The chromaticity diagram with just-noticeable-difference ellipses at a grid of colors. Each is the region indistinguishable from its center. Adjust the exaggeration to see them clearly; note how green ellipses dwarf blue ones - the eye tolerates far larger changes in green than in blue.
Equal step, unequal difference
Make the point concrete. Take a fixed step - the same distance on the xy diagram - once in the green region and once in the blue. The green pair looks nearly identical; the blue pair looks obviously different. Same distance on the map, wildly different to the eye. The demo measures the perceived difference of each in a uniform space so you can see the gap.
One ruler, two verdicts
A fixed xy step you set, applied at a green anchor and a blue anchor. The swatch pairs show how different each looks, and the readout gives the perceived difference (a u'v' distance, in just-noticeable units). Equal geometric steps, unequal perceived differences - often by many times.
Straightening the space
The fix is to reshape the diagram so equal distances mean equal differences. The CIE 1976 u'v' diagram is a simple projective stretch of xy that pulls the crowded blue corner open and squeezes the sprawling green - and the wild ellipses become far more even and circular. Toggle between the two and watch them regularize.
Reshape the map, even the ellipses
The same JND ellipses, plotted in the CIE 1931 xy diagram and in the 1976
u'v' diagram. In xy they vary wildly; in u'v' they become much more uniform circles,
because u'v' opens the blues and compresses the greens. It isn't perfect - CIELAB and OKLab go
further - but it's the first big correction.
Counting just-noticeable differences
Perceived distance is best counted in JNDs - how many just-noticeable steps
separate two colors - not in millimeters on a diagram. Slide a pair of points across the xy diagram and the
demo counts both: the raw geometric distance, and the perceptual one in JND units. They rarely
agree, which is exactly why color tolerances are set as a ΔE in a uniform space, never
as a distance in xy.
How far, really?
Move two colors around the diagram. The demo reports the straight-line xy distance and the perceptual distance in just-noticeable differences. Slide the pair from the blue corner to the green and watch the two numbers diverge - equal on the map, unequal to the eye.
The vocabulary
The terms of perceptual uniformity.
Best practices and pitfalls
Test your understanding
Six questions on MacAdam ellipses, perceptual uniformity, u'v', and ΔE. Instant feedback, no scores recorded - a wrong answer comes with a short explanation.
Quick check
Continue your journey
The ellipses are the bridge from the chromaticity diagram to uniform spaces and ΔE - here's where to go next.
Chromaticity Diagrams Without the Intimidation
The diagram whose distances the ellipses correct.
Colorimetry · 9CIELAB and LCH Explained
The uniform space built to fix the non-uniformity.
Colorimetry · 22Oklab and Oklch: Modern Perceptual Color Spaces
The current best answer to MacAdam's problem.
Colorimetry · 72Color Difference in Practice: Tolerances and Pass/Fail QC
Where ΔE tolerances come from - and why not xy.
Colorimetry · 92Dominant Wavelength and Purity
What the xy diagram is good for.
Foundations · 56The Color Solid: Visualizing All Colors in Three Dimensions
Uniformity extended into the full 3D color solid.