HueSense

What Is Delta E (ΔE)? — CIE76 vs CIE94 vs CIEDE2000

ΔE expresses the difference between two colors as a single number. We compare the formulas and examples to show where the 1976 straight-line formula fell short and what CIE94 and CIEDE2000 fixed.

ΔE (Delta E) is a single number that describes how different two colors look. Print shops use it to check proofs, paint stores use it when matching colors, and display makers use it to rate panel quality. 0 means the colors are identical, and the higher the number, the more different they look.

But there are several ΔE formulas, and the same two colors can score quite differently depending on which one you use. If you do not know which formula produced a value, you cannot compare it with anything.

The starting point: CIELAB color space

All ΔE formulas are calculated in the CIELAB (L*a*b*) color space defined by the CIE in 1976. L* is lightness (0 black to 100 white), a* runs from green (−) to red (+), and b* runs from blue (−) to yellow (+). A screen's RGB values are linearized by removing the gamma, converted to XYZ tristimulus values and then to Lab.

Lab was designed to be perceptually uniform, meaning distance should be proportional to perceived difference, but in practice it is not fully uniform. The history of ΔE formulas is essentially the story of correcting that non-uniformity.

CIE76 — straight-line distance

ΔE*ab = √(ΔL*² + Δa*² + Δb*²)

This is simply the straight-line distance between two points in Lab space. It is easy to compute and still widely used. A study by Mahy et al. (1994) reported that a ΔE*ab of about 2.3 corresponds to a just noticeable difference (JND), a figure that is often quoted.

The problem is that the same distance feels different in different parts of the color space. With highly saturated colors the number can be large while people barely notice a difference, whereas near low-chroma grays even a small number stands out. In the blue region, the direction in which hue rotates can also disagree with human perception.

CIE94 — weighting by chroma

ΔE94 = √((ΔL/kL·SL)² + (ΔC/kC·SC)² + (ΔH/kH·SH)²), SL = 1, SC = 1 + K1·C, SH = 1 + K2·C

The difference is split into three components, lightness (ΔL), chroma (ΔC) and hue (ΔH), and the higher the chroma (C), the less the chroma and hue differences count. Graphic arts use K1 = 0.045 and K2 = 0.015; textiles use kL = 2, K1 = 0.048 and K2 = 0.014.

One notable trait is that it is asymmetric. Because the weights use the chroma of the reference color, A→B and B→A can give slightly different values. You therefore need to decide which color is the reference (the standard sample) before using it.

CIEDE2000 — today's standard

Developed by Luo, Cui and Rigg (2001) by combining data from multiple visual experiments, this formula was published as CIE 142-2001 and later standardized as ISO/CIE 11664-6. It adds the following on top of CIE94.

The formula is long, but the result is symmetric and tuned so that the same number means a similar perceived difference across hue families. It is tricky to implement, though, and mistakes are common in the step that averages hue angles. Sharma, Wu and Dalal (2005) published implementation notes along with 34 test pairs, and this site's calculation engine has been verified against that data to four decimal places.

Same two colors, three different numbers

Color pair (Lab)ΔE76ΔE94ΔE00
Gray L50 ↔ L50, a −1, b 22.242.242.37
High chroma L50, a 2.68, b −79.78 ↔ L50, a 0, b −82.754.001.402.04

The second row is a highly saturated blue. CIE76 rates it at a large 4.00, but CIEDE2000 gives 2.04, treating it as a perceived difference similar to the gray pair. Because of gaps like this, CIEDE2000 is the fair choice when comparing discrimination across hue families.

Which formula should you use?

References

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