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T9 · Testing / StandardsColor Science & Masterbatch TechnologyGATE 2027 Syllabus (XE5)Shop-Floor Standard

CIE L*a*b* Delta-E 1976 Color Difference Formula

Calculates the total color difference (DeltaE*) between a production molded part and a target color master standard in 3D CIE L*a*b* color space.

Mathematical Canonical Relation
ΔEab∗=(ΔL∗)2+(Δa∗)2+(Δb∗)2\Delta E^*_{ab} = \sqrt{ (\Delta L^*)^2 + (\Delta a^*)^2 + (\Delta b^*)^2 }
Plain Formula: DeltaE = sqrt((L1 - L2)^2 + (a1 - a2)^2 + (b1 - b2)^2)

Live Engineering Parameter Solver

Input your production or test values below for instant, verified output.

Verified Engine
dL
Range: -5 – 5 units
da
Range: -5 – 5 units
db
Range: -5 – 5 units
Calculated Engineering Result:
0.54 units
Engineering Verification:Acceptable industrial match.

When & Where to Apply

Use in quality control lab spectrophotometry to determine if a masterbatch color match passes customer specification.

Common Engineering Pitfalls

  • Confusing DeltaE 1976 with DeltaE 2000 (dE2000 includes perceptual weighting for chroma and hue)

Physical Assumptions & Validity Limits

  • Standard D65 illuminant, 10° observer angle
  • Euclidean distance model in L*a*b* color space

Variable Symbols, SI Units & Dimensional Specifications

SymbolVariable MeaningSI UnitTypical Industrial Range
\Delta E^*Total color difference distanceunits—
\Delta L^*Lightness difference (L_sample - L_target)units0.3
\Delta a^*Red/Green difference (a_sample - a_target)units-0.4
\Delta b^*Yellow/Blue difference (b_sample - b_target)units0.2

Worked Industrial Numerical Example: Automotive Yellow Door Handle Color Pass/Fail QC

Problem Statement:

A target color standard has L*=72.4, a*=14.2, b*=48.5. Molded production part reads L*=72.7, a*=13.8, b*=48.7. Calculate DeltaE* and check against DeltaE <= 0.80 automotive tolerance.

Step-by-Step Numerical Solution:
  1. Calculate squared differences: (0.3)^2 = 0.09, (-0.4)^2 = 0.16, (0.2)^2 = 0.04
  2. Sum squares: 0.09 + 0.16 + 0.04 = 0.29
  3. Take square root: sqrt(0.29) = 0.5385
Final Answer: DeltaE* = 0.54 units (PASS)
💡 Engineering Interpretation: DeltaE = 0.54 is below the 0.80 automotive pass threshold, indicating a commercially acceptable visual match.

Authoritative Technical Reference & Source Provenance

Colorimetry: Understanding the CIE System by Janos Schanda (Wiley-Interscience, 2007), 1st Edition, Page 65-72.
Connected Curriculum Lesson

CIE L*a*b* Color Space & Spectrophotometric Color Matching

Study Full Lesson