Calculate Delta E

Calculate the color difference (Delta E CIE76) between two colors specified in L*a*b* values.

Color 1 (Reference)

Color 2 (Sample)

L*a*b* Input Values

Component	Color 1	Color 2
L*	50	52
a*	0	1
b*	0	1

What is Delta E (ΔE)?

Delta E (ΔE, dE, or “dE*”) is a metric used to quantify the difference between two colors as perceived by the human eye. It’s a standard measurement in color science, particularly important in industries where color accuracy is critical, such as printing, paint manufacturing, textiles, and digital imaging. To calculate delta e is to find a single number that represents the “distance” between two colors in a perceptually uniform color space, most commonly the CIE L*a*b* (CIELAB) color space.

A Delta E value of 1.0 is generally considered the smallest color difference the human eye can perceive, although this can vary depending on the color and viewing conditions. The lower the Delta E value, the closer the two colors are, and the harder it is to distinguish between them. Higher values indicate a more noticeable difference. When you calculate delta e, you are essentially measuring this perceptual difference.

Who Should Use It?

• Graphic Designers & Printers: To ensure color consistency between digital designs and printed output.
• Paint & Coating Manufacturers: For quality control and matching paint colors.
• Textile Industry: To match fabric colors and ensure consistency across batches.
• Photographers & Videographers: For color correction and grading.
• Plastics Industry: To control the color of manufactured plastic parts.

Common Misconceptions

• A single Delta E formula is always best: Different formulas (CIE76, CIE94, CIEDE2000) have been developed over time to better model human perception, especially for certain color ranges or industries. CIEDE2000 is often considered more accurate but is more complex to calculate delta e with.
• A Delta E of 1.0 is always the limit of perception: The just noticeable difference (JND) can vary. For some colors, a ΔE below 1.0 might be visible, while for others, a ΔE above 1.0 might not be easily noticeable.
• Delta E is the only factor in color matching: Other factors like gloss, texture, and viewing conditions (lighting, observer) also play a significant role.

Delta E Formula and Mathematical Explanation

The simplest and most common formula used to calculate delta e is the CIE76 (or ΔE*_ab) formula, derived from the Euclidean distance in the L*a*b* color space:

ΔE*_ab = √((L*₂ – L*₁)² + (a*₂ – a*₁)² + (b*₂ – b*₁)²)

Where:

• L*₁, a*₁, b*₁ are the coordinates of the first color (reference).
• L*₂, a*₂, b*₂ are the coordinates of the second color (sample).
• ΔL* = L*₂ – L*₁ (difference in lightness)
• Δa* = a*₂ – a*₁ (difference in green-red)
• Δb* = b*₂ – b*₁ (difference in blue-yellow)

Later formulas like CIE94 and CIEDE2000 introduce weighting factors to account for the non-uniformity of human color perception across different parts of the color space, making the calculation more complex but often more accurate to how we see color differences.

Variables Table (CIE76)

Variable	Meaning	Unit	Typical Range
L*	Lightness	None	0 to 100
a*	Green-Red axis	None	-128 to +127 (approx)
b*	Blue-Yellow axis	None	-128 to +127 (approx)
ΔE*ab	Color Difference	None	0 upwards

You can use a color difference calculator like the one on this page to easily find ΔE*_ab.

Practical Examples (Real-World Use Cases)

Example 1: Paint Matching

A customer wants to match a paint color on their wall. The original paint (Color 1) has L*a*b* values of (L*=85, a*=2, b*=10). The paint store mixes a batch (Color 2) with L*a*b* values of (L*=84, a*=2.5, b*=11).

Inputs:

• L1=85, a1=2, b1=10
• L2=84, a2=2.5, b2=11

To calculate delta e:
ΔL* = 84 – 85 = -1
Δa* = 2.5 – 2 = 0.5
Δb* = 11 – 10 = 1
ΔE*_ab = √((-1)² + (0.5)² + (1)²) = √(1 + 0.25 + 1) = √2.25 = 1.5

A Delta E of 1.5 is noticeable but might be acceptable for a small touch-up, though a closer match (ΔE < 1) would be preferable for larger areas.

Example 2: Printing Quality Control

A brand’s logo color (Color 1) is defined as L*=50, a*=45, b*=40. A print run (Color 2) produces the logo with L*=51, a*=44, b*=39.

Inputs:

• L1=50, a1=45, b1=40
• L2=51, a2=44, b2=39

To calculate delta e:
ΔL* = 51 – 50 = 1
Δa* = 44 – 45 = -1
Δb* = 39 – 40 = -1
ΔE*_ab = √((1)² + (-1)² + (-1)²) = √(1 + 1 + 1) = √3 ≈ 1.73

A Delta E of 1.73 indicates a noticeable difference, and the printer might need to adjust the process to get closer to the target color, especially if the brand guidelines are strict. Using a color converter can help verify L*a*b* values from other color spaces.

How to Use This Delta E Calculator

1. Enter L*a*b* values for Color 1: Input the L*, a*, and b* values for your reference color into the “Color 1 (Reference)” section. L* ranges from 0-100, while a* and b* typically range from -128 to +127.
2. Enter L*a*b* values for Color 2: Input the L*, a*, and b* values for the color you are comparing (sample color) into the “Color 2 (Sample)” section.
3. View the Results: The calculator will automatically calculate delta e (ΔE*ab using the CIE76 formula) and display it, along with the intermediate differences (ΔL*, Δa*, Δb*).
4. Interpret the Delta E:
   • ΔE < 1: Not perceptible by human eyes (very close match).
   • 1 < ΔE < 2: Perceptible through close observation.
   • 2 < ΔE < 10: Perceptible at a glance.
   • 10 < ΔE < 50: Colors are more similar than opposite.
   • ΔE > 50: Colors are considered opposite.
5. Use the Chart: The bar chart visually compares the L*, a*, and b* values of the two colors.
6. Reset or Copy: Use the “Reset” button to clear inputs to defaults or “Copy Results” to copy the values and formula.

Key Factors That Affect Delta E Results

• Delta E Formula Used: CIE76 is simple but less accurate than CIE94 or CIEDE2000, especially for saturated colors or near neutrals. The choice of formula significantly impacts the calculated value.
• Lighting Conditions: The perceived color of an object changes under different light sources (e.g., daylight, fluorescent, incandescent). Delta E should ideally be calculated based on L*a*b* values measured under standard illuminants.
• Observer Metamerism: Two colors might look the same to one person under specific lighting but different to another person or under different lighting. This is due to differences in how individuals perceive color.
• Sample Texture and Gloss: The surface texture and gloss level of the samples can affect how light reflects and thus how color is perceived and measured, influencing the L*a*b* values.
• Measurement Instrument Geometry: The geometry of the spectrophotometer or colorimeter used to measure the L*a*b* values (e.g., d/8°, 45°/0°) can influence the readings and thus the Delta E.
• Color Space Uniformity: The L*a*b* color space is designed to be perceptually uniform, but it’s not perfectly so. This is why more complex formulas like CIEDE2000 were developed to improve the correlation between calculated Delta E and perceived difference across the entire color space. To properly calculate delta e, understanding the color space is crucial.

For more about color perception, see our guide on color theory.

Frequently Asked Questions (FAQ)

What is a “good” Delta E value?

It depends on the application. For critical color matching, a Delta E (CIE76) below 1 is often desired. For less critical applications, values up to 2 or even 5 might be acceptable. Many industries now prefer using CIEDE2000, where a ΔE₀₀ of 1 is a more reliable indicator of a just noticeable difference.

Why are there different Delta E formulas?

The original CIE76 formula is a simple Euclidean distance but doesn’t perfectly match human perception across all colors. CIE94 and CIEDE2000 were developed to introduce corrections based on lightness, chroma, and hue differences, providing a better correlation with how we see color differences, especially the CIEDE2000 CIEDE2000 calculator.

How do I get the L*a*b* values of my colors?

You typically need a color measurement device like a spectrophotometer or colorimeter to measure the L*a*b* values of a physical sample. For digital colors, software like Adobe Photoshop can provide L*a*b* values, or you can convert from RGB or Hex using RGB to Lab converters.

Can I use this calculator for CIEDE2000?

No, this calculator specifically uses the CIE76 formula to calculate delta e. CIEDE2000 is much more complex and requires a different calculation.

What does it mean if ΔL* is positive or negative?

A positive ΔL* means Color 2 is lighter than Color 1. A negative ΔL* means Color 2 is darker than Color 1.

What do Δa* and Δb* represent?

Δa* represents the difference along the red-green axis. A positive Δa* means Color 2 is redder or less green than Color 1. Δb* represents the difference along the yellow-blue axis. A positive Δb* means Color 2 is more yellow or less blue than Color 1.

Is a Delta E of 0 possible?

Yes, a Delta E of 0 means the L*a*b* values of the two colors are identical, and they are a perfect match under the conditions they were measured.

Does the order of Color 1 and Color 2 matter?

No, for the Delta E (CIE76) calculation, the order doesn’t matter because the differences are squared, so (L2-L1)² is the same as (L1-L2)². However, the signs of ΔL*, Δa*, and Δb* will be reversed, indicating the direction of the difference.

Related Tools and Internal Resources

• CIEDE2000 Delta E Calculator: For a more perceptually accurate color difference calculation.
• RGB to L*a*b* Color Converter: Convert sRGB, Adobe RGB, etc., to L*a*b* values for use in this calculator.
• HEX to L*a*b* Color Converter: Convert web HEX codes to L*a*b*.
• Understanding Color Theory: Learn more about color models and perception.
• Color Management Basics: Introduction to maintaining color consistency.
• Color Difference Calculator Hub: Explore various color difference metrics.