MacAdam Ellipses: How Far Can Color Move Before You See It?

The CIE 1931 diagram is a faithful map of color matching, but a terrible ruler for color difference: equal distances on it are nowhere near equally visible. A chromaticity error you could never spot in green is glaring in blue; the discrimination threshold varies by roughly 20:1 across the diagram. Before 1942 that was a qualitative complaint. MacAdam made it quantitative, and the ellipses above are the measurement.

David MacAdam, at Kodak Research Laboratories, built a split-field instrument where an observer adjusted one half of a 2° field to match a fixed test color, at constant luminance (~48 cd/m²). His observer, "PGN" (Perley G. Nutting Jr.), repeated such matches tens of thousands of times around 25 chromaticity centers. The matches never landed exactly; they scattered. The scatter formed ellipses, not circles, and their standard deviation became the unit: each ellipse is the 1σ contour of color-matching error at that point. A just-noticeable difference is commonly taken as about 3σ. One observer, one field size, one luminance: the caveats are real (later Brown–MacAdam and Wyszecki studies added observers and ellipsoids in 3D), but the shape of the result has held for eighty years.

Inside the ellipse, color is, to the observer, the same. The boundary is where difference begins. The long axis points in the direction vision is most forgiving; the short axis, where it is most acute. Notice the pattern as you click around: enormous, elongated ellipses in green (the eye tolerates large xy shifts there), tiny ones in blue and violet (minute shifts are visible). That anisotropy is why "±0.005 in x,y" is a meaningless tolerance without saying where; the same box that is invisible in green is several JND wide in blue.

If the ruler is broken, redraw the map. The CIE 1960 uv diagram (built directly on MacAdam's data) and its 1976 successor u′v′ (u′ = 4x/(−2x+12y+3), v′ = 9y/(−2x+12y+3)) stretch and squeeze the 1931 diagram so the ellipses come out as close to equal circles as a projective transform allows. Flip the DIAGRAM SPACE toggle and watch it happen. It isn't perfect (nothing 2D is), but it's why CCT/Duv, LED specs, and most chromaticity tolerances are stated in u′v′, and why 0.001 in u′v′ is a usable, roughly uniform unit of "how far."

Every modern color-difference metric is an heir to these ellipses. CIELAB's ΔE*ab (1976) aimed for "1.0 = one JND" in three dimensions, and inherited the same non-uniformity problem in miniature. ΔE94 and then ΔE2000 added elliptical corrections (the SL, SC, SH terms and the rotation term in blue) that are, in effect, MacAdam's anisotropy written into a formula. For HDR and wide gamut, ΔE-ITP (BT.2124, built on ICtCp) plays the same role. When a calibration report says ΔE2000 < 1.5, it is speaking the language this page teaches: distances scaled by what the eye can actually see.

The ellipses survive verbatim in one modern spec: SDCM, "standard deviations of colour matching", literally MacAdam steps. LED manufacturers bin white emitters by how many ellipses their chromaticity can wander from the target: ≤3 SDCM reads as one color to almost everyone; 5 SDCM is visibly mixed on a white wall; 7 is bargain-bin. It's why two "3000 K" fixtures can disagree, why LED video walls are binned tightly and recalibrated per panel as they age, and why a fixture spec sheet that quotes only CCT, with no SDCM or Duv, is telling you half the story.

A white-point tolerance is an ellipse, not a box: the question is never "how far in x,y" but "how many JND." That is how we judge a wall of LED panels (do adjacent panels sit within ~1 SDCM of each other?), how grade-suite monitors are matched (ΔE2000 across the gray ramp), and why a probe-verified report quotes u′v′ or ΔE rather than raw xy deltas. The eye is the final instrument; MacAdam just measured its error bars. Book a calibration →