Delta E (ΔE)

Delta E (written ΔE or DeltaE) is a numeric measure of the perceptual difference between two colours, computed in a perceptually-uniform colour space (CIELAB, CIE94, CIEDE2000, or modern OKLab). It’s the standard tool for quantifying “how close are these two colours?”

Standard thresholds (using CIEDE2000, the modern reference):

• ΔE < 1: Indistinguishable to most observers.
• 1 < ΔE < 2: Visible on close inspection.
• 2 < ΔE < 4: Visible at a glance.
• 4 < ΔE < 10: Clearly different but related colours.
• ΔE > 10: Different colours.

Where ΔE is used:

• Printing. Pantone matching and print proofing aim for ΔE < 2 between the spec and the printed sheet.
• Display calibration. Professional monitors are sold with ΔE specifications. A “ΔE < 2 out of the box” monitor is accurate enough for photo and design work.
• Colour matching across materials. Paint, plastic, textile, and ink reproductions targeting a master colour.
• Compression and quality. Image codecs (JPEG, WebP, AVIF) optimise to minimise ΔE rather than raw pixel difference.

Several formulas exist for computing ΔE — the older CIE76 (Euclidean distance in CIELAB), the improved CIE94, and the modern CIEDE2000 which corrects perceptual non-uniformities CIE76 missed. For new work use CIEDE2000 unless you specifically need backward compatibility.

Worked example

Compare two near-greys: sRGB (128, 128, 128) and sRGB (130, 128, 128). Convert both to CIELAB: the first sits at L*≈53.6, a*=0, b*=0; the second at L*≈54.1, a*≈0.5, b*=0. Euclidean (CIE76) distance: √(0.5² + 0.5² + 0²) ≈ 0.71 — well below 1.0, supposedly invisible. CIEDE2000 reports ΔE ≈ 0.62, similar verdict. Now compare two saturated blues: sRGB (0, 0, 200) vs (0, 0, 220). CIE76 gives ΔE ≈ 4.5, suggesting “visible at a glance.” But CIEDE2000 applies its blue-region correction and reports ΔE ≈ 2.1 — the human eye is less sensitive to chroma differences in deep blues than CIE76’s flat Euclidean treats them as. Side-by-side, viewers actually rate the difference as much smaller than CIE76 implies. That correction is why every modern colour-difference workflow has moved away from CIE76.

Note that ΔE values are not interchangeable across formulas. A ΔE of 3 under CIE76 is not the same perceptual gap as ΔE 3 under CIEDE2000 or ΔE-OK — comparing them directly is a category error. Always state the formula when quoting a ΔE figure, and stick to one formula for any comparative study.

When and why it matters

Delta E matters whenever “close enough” needs a number. Print proofing contracts often specify ΔE < 2 between approved proof and production run; failure to meet the spec triggers reprints at the supplier’s cost. Display manufacturers (EIZO, BenQ SW-series, Apple Pro XDR) advertise factory-calibrated ΔE < 1 or < 2 because that level of accuracy is what professional photo retouchers and colourists require to trust their monitor. Image-codec evaluation (comparing JPEG XL vs WebP vs AVIF) uses ΔE-based metrics (MS-SSIM, Butteraugli, SSIMULACRA2) because raw PSNR doesn’t correlate with what viewers notice. The everyday lesson: if your brand guideline specifies a Pantone, the vendor must hit it within ΔE < 3 across substrates — otherwise the logo on the cardboard packaging visibly drifts from the logo on the glossy brochure. Reference: Delta E 101 — practical guide and formulas.

CIEDE2000 corrections — why the formula got so complicated: CIE76 measured perceptual distance as straight Euclidean distance in CIELAB and worked reasonably well for blues and reds but performed badly for neutrals, dark tones, and very saturated colours. CIEDE2000 added five empirical corrections — for lightness L*, chroma C*, hue h*, a hue-chroma interaction term, and a separate adjustment for blues — fitted to subjective just-noticeable-difference data from real viewers. The resulting formula has ~15 numeric constants and resembles applied empirical engineering more than clean theory. The Ottosson 2020 OKLab paper showed that a carefully-designed perceptual space can match CIEDE2000 accuracy with a straight Euclidean distance, which is why modern colour-difference work increasingly uses ΔE-OK (just Euclidean distance in OKLab) for its simplicity. Reference: CIE 142:2001 — Improvement to Industrial Colour-Difference Evaluation.