Delta E turns measured color differences into a usable number. This guide explains how to calculate Delta E with CIE76, CMC l:c, and CIEDE2000 using the same L*a*b* color pair.
Before Calculating Delta E
Before calculating Delta E, you need two sets of color measurements: one for the standard color and one for the sample color. Most industrial color difference calculations use L*, a*, and b* values from the CIELAB color space.
CIELAB is specified in ISO/CIE 11664-4:2019, which defines the CIE 1976 L*a*b* color space and the basic Euclidean color difference calculation.

Measuring L*a*b* Values
A spectrophotometer or colorimeter measures color and reports three values:
| Value | Meaning | Direction |
| L* | Lightness | Higher = lighter, lower = darker |
| a* | Red-green axis | Positive = redder, negative = greener |
| b* | Yellow-blue axis | Positive = yellower, negative = bluer |
For reliable results, measure the standard and sample under the same conditions. Keep the illuminant, observer angle, measurement geometry, sample backing, surface condition, and instrument settings consistent.
Standard Color vs. Sample Color
Delta E compares a standard color with a sample color.
The standard is the approved reference, such as a master sample, target shade, lab dip, or customer-approved color. The sample is the production batch, dyed fabric, printed piece, coating, or test material being evaluated.
In this article, we will use the following color pair:
| Color | L* | a* | b* |
| Standard | 50.00 | 2.50 | -10.00 |
| Sample | 52.00 | 3.10 | -8.80 |

Using One Color Pair for All Examples
The same color pair is used for all three formulas. This makes the comparison easier because any difference in the final result comes from the formula itself, not from different input data.
First, calculate the basic differences:
- ΔL* = 52.00 – 50.00 = 2.00
- Δa* = 3.10 – 2.50 = 0.60
- Δb* = -8.80 – (-10.00) = 1.20
These values are enough for CIE76. CMC l:c and CIEDE2000 also use chroma, hue, and weighting adjustments, which are explained in their sections below.
CIE76 Delta E Calculation
CIE76 is the simplest Delta E formula. It calculates the straight-line distance between two colors in L*a*b* space.
The Formula Explained
The CIE76 formula is: ΔE*ab = √[(ΔL*)² + (Δa*)² + (Δb*)²]
This formula treats lightness, red-green difference, and yellow-blue difference equally. It is easy to calculate, but it does not always match how people visually judge color differences.
Worked Example
Using the example values:
- ΔE*ab = √[(2.00)² + (0.60)² + (1.20)²]
- ΔE*ab = √[4.00 + 0.36 + 1.44]
- ΔE*ab = √5.80
- ΔE*ab = 2.41
The CIE76 Delta E result is 2.41.
When CIE76 Is Enough
CIE76 is useful for quick calculations, simple spreadsheet checks, basic lab comparisons, and older specifications that still use ΔE*ab.
For textile shade approval or more demanding industrial color control, CMC l:c or CIEDE2000 is often more practical because these formulas account for visual sensitivity more carefully.
CMC l:c Delta E Calculation
CMC l:c is widely used for practical color tolerance assessment, especially in textiles. It adjusts the importance of lightness, chroma, and hue differences instead of treating all L*a*b* directions equally.
How the Weighting Functions Work
CMC separates the color difference into three parts:
- Lightness difference
- Chroma difference
- Hue difference
Its general structure is: ΔEcmc = √[(ΔL / lSL)² + (ΔC / cSC)² + (ΔH / SH)²]
Where:
- ΔL is the lightness difference
- ΔC is the chroma difference
- ΔH is the hue difference
- SL, SC, and SH are weighting functions
- l and c are user-selected lightness and chroma factors
These weighting functions help the formula better reflect practical visual judgment.
Choosing the l:c Ratio
The l:c ratio controls the relative importance of lightness and chroma.
Common choices include:
- CMC 2:1, often used for acceptability decisions in textiles
- CMC 1:1, often used when perceptibility is the main concern
For fabric shade approval, CMC 2:1 is common because lightness variation is often judged differently from hue or chroma variation.
Worked Example
Using the same color pair:
- Standard: L* = 50.00, a* = 2.50, b* = -10.00
- Sample: L* = 52.00, a* = 3.10, b* = -8.80
Using the standard as the reference, the main component differences are approximately:
- ΔL = -2.00
- ΔC = 0.98
- ΔH = 0.92
After applying the CMC 2:1 weighting functions, the result is: ΔEcmc(2:1) = 1.75
This result is lower than the CIE76 result because CMC weights the difference according to lightness, chroma, hue, and the selected l:c ratio.
Why CMC Works Better for Fabric
Fabric color differences are not judged only by mathematical distance. A small hue shift may be more noticeable than a lightness shift, depending on fiber type, dye class, shade depth, texture, and final use.
That is why CMC is widely used in textile color control. It helps connect instrument readings with practical fabric approval decisions.
Skychem Group has worked in the chemical and textile dye industry for nearly 30 years, supporting manufacturers with colorants, specialty chemicals, and application-focused technical service. Skychem Group’s textile color solutions help with dyeing, shade matching, and color development across different fiber and fabric requirements.
CIEDE2000 Delta E Calculation
CIEDE2000 is a more advanced color difference formula. It improves on CIE76 by correcting known visual non-uniformities in the CIELAB color space.
The official CIE publication ISO/CIE 11664-6:2022 defines the CIEDE2000 color difference formula, including corrections for lightness, chroma, hue, and chroma-hue interaction.
What Makes CIEDE2000 Different
CIEDE2000 is designed to better match human color perception. Compared with CIE76, it adds corrections for:
- Lightness weighting
- Chroma weighting
- Hue weighting
- Neutral color behavior
- Blue-region behavior
- Chroma-hue interaction
Because of these corrections, CIEDE2000 is more complex but often more visually meaningful.
Key Formula Components
The simplified structure of the CIEDE2000 formula is:
ΔE00 = √[(ΔL′ / kLSL)² + (ΔC′ / kCSC)² + (ΔH′ / kHSH)² + RT(ΔC′ / kCSC)(ΔH′ / kHSH)]
The main components are:
- ΔL′: adjusted lightness difference
- ΔC′: adjusted chroma difference
- ΔH′: adjusted hue difference
- SL, SC, SH: weighting functions
- RT: rotation term for chroma-hue interaction
- kL, kC, kH: parametric factors, often set to 1 under reference conditions
Because the formula includes several intermediate adjustments, CIEDE2000 is usually calculated with a verified calculator, spreadsheet, color software, or instrument system rather than by hand.
Worked Example
Using the same standard and sample values, the CIEDE2000 calculation is run with the standard reference settings:
- kL = 1
- kC = 1
- kH = 1
Result: **ΔE00 = 2.40**
This means the sample has a CIEDE2000 color difference of 2.40 from the standard. If the agreed tolerance is ΔE00 ≤ 2.00, the sample fails. If the tolerance is ΔE00 ≤ 3.00, it passes.
Reading the Result
A Delta E number is not automatically pass or fail. It must be compared with the agreed tolerance for the material, formula, customer, and application.
For example:
- If the agreed limit is ΔE00 ≤ 2.00, this sample fails because ΔE00 = 2.40.
- If the agreed limit is ΔE00 ≤ 3.00, the same sample passes.
The formula and tolerance must always be specified together. A requirement such as “Delta E ≤ 2” is incomplete unless it also states whether the calculation uses CIE76, CMC l:c, CIEDE2000, or another formula.
CIE76 vs CMC vs CIEDE2000 Results
The same L*a*b* color pair can produce different Delta E values depending on the formula. This is expected because each formula models color differences differently.
Same Color Pair, Three Different Answers
| Formula | Result | What It Represents |
| CIE76 | 2.41 | Simple geometric distance in L*a*b* space |
| CMC l:c 2:1 | 1.75 | Textile-oriented tolerance result |
| CIEDE2000 | 2.40 | More perceptual color difference result |
The CIE76 and CIEDE2000 values are close in this example. The CMC result is lower because the formula weights lightness, chroma, and hue differently.

Why Formula Choice Changes Pass or Fail
Assume the tolerance limit is 2.00. With the same color pair:
- CIE76 result = 2.41, fail
- CMC 2:1 result = 1.75, pass
- CIEDE2000 result = 2.40, fail
The measured colors did not change. Only the calculation method changed. This is why color specifications should always name the formula:
- ΔE*ab ≤ 2.00 by CIE76
- ΔEcmc(2:1) ≤ 2.00
- ΔE00 ≤ 2.00 by CIEDE2000
Without the formula, the tolerance can be misunderstood.
Applying Delta E Tolerances
After calculating Delta E, the next step is deciding whether the result is acceptable. This depends on the product, customer requirement, viewing conditions, and production process.
Setting an Acceptable Delta E Limit
There is no single Delta E limit that fits every industry or material. A tolerance that works for one fabric, coating, plastic part, or printed product may be too loose or too strict for another.
When setting a tolerance, consider material type, end-use application, customer approval standard, measurement settings, surface texture, gloss, production variation, and visual inspection conditions.
A high-visibility fashion fabric may need tighter control than a utility textile. A brand color or safety color may also require a narrower tolerance than a background or internal component.
In textile production, Delta E tolerance is often connected with broader quality, safety, and sustainability requirements. Skychem Group supports these requirements through certified textile chemical systems and quality control practices, helping manufacturers align color performance with customer, brand, and production expectations.
Elliptical vs. Spherical Tolerancing
CIE76 uses spherical tolerancing. It measures equal distance in every direction of L*a*b* space.
CMC and CIEDE2000 use more advanced weighting. Their tolerance behavior is closer to elliptical tolerancing, where some directions of color difference are treated more strictly than others.
This matters because visual color judgment is not uniform. A formula that better reflects perception can reduce disagreements between instrument readings and visual approval.

Matching the Formula to the Application
The best Delta E formula depends on the material, tolerance method, and purpose of the comparison.
- CIE76 is suitable for simple comparisons, quick internal checks, and older specifications that still use ΔE*ab.
- CMC l:c is often preferred for textile shade approval because it gives more practical weight to lightness, chroma, and hue differences on fabric.
- CIEDE2000 is useful when a more perceptual color difference model is needed for demanding color quality control.
Skychem Group develops textile application solutions for dyeing, finishing, and performance-focused fabric production. Its application support covers areas such as fashion textiles, outdoor sportswear, workwear, home textiles, denim, wool, and garment washing, helping manufacturers choose suitable colorants and chemical systems for specific fabric requirements.
Conclusion
Delta E is most useful when the input data, formula, and tolerance are clearly defined. CIE76 offers a simple baseline, CMC l:c supports practical textile tolerance control, and CIEDE2000 provides a more perceptual color difference result. For technical support or product selection, contact Skychem Group for a quote.
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