| XYZ | — |
| xyY | — |
| u′v′ | — |
| CCT | — |
| Duv | — |
| L* | — |
| a* | — |
| b* | — |
| C*ab | — |
| hab | — |
| L* | — |
| u* | — |
| v* | — |
| C*uv | — |
| huv | — |
| J | — |
| C | — |
| h | — |
| M | — |
| s | — |
| Q | — |
| J | — |
| C | — |
| h | — |
| M | — |
| s | — |
| Q | — |
| 8-bit | — |
| Linear | — |
| HSV | — |
| HSL | — |
Compare the current colour under 9 standard illuminants. Shows CIELAB, CIECAM02, and CAM16 correlates side-by-side.
| Illum | L* | a* | b* | C* | h° | J₀₂ | J₁₆ |
|---|---|---|---|---|---|---|---|
| Click "Compare illuminants" to run analysis. | |||||||
CIEDE2000 and CIE76 under current illuminant.
CIE 1931 Standard Observer (2°)
The CIE 1931 2° Standard Observer defines the colour-matching functions x̄(λ), ȳ(λ), z̄(λ) based on experiments by Wright (1928–1929) and Guild (1931). The 2° field subtends the fovea.
Tristimulus values: X = ∫ E(λ) · x̄(λ) dλ, Y = ∫ E(λ) · ȳ(λ) dλ, Z = ∫ E(λ) · z̄(λ) dλ.
Standard: CIE 015:2018, ISO 11664-1.
CIE 1964 Supplementary Observer (10°)
The 10° observer extends the field of view from 2° to 10°, better representing large-area colour matching. Recommended for subtense > 4°.
Standard: CIE 015:2018, ISO 11664-1.
CIE 1976 Uniform Colour Space (UCS)
The CIE 1976 u′v′ diagram provides a more perceptually uniform distribution of colours than the 1931 xy diagram.
u′ = 4X / (X + 15Y + 3Z), v′ = 9Y / (X + 15Y + 3Z).
Standard: CIE 015:2018, ISO 11664-5.
CIELAB (L*a*b*)
CIELAB is the most widely used device-independent colour space. L* = lightness, a* = green–red, b* = blue–yellow.
C*ab = √(a*² + b*²), hab = atan2(b*, a*).
Standard: CIE 015:2018, ISO 11664-4.
CIELUV (L*u*v*)
CIELUV is favoured for self-luminous / emissive colours because it preserves additive colour mixing lines.
u* = 13L*(u′ − u′n), v* = 13L*(v′ − v′n).
Standard: CIE 015:2018, ISO 11664-5.
CIECAM02
CIE 159:2004: CIECAM02 is the CIE-recommended colour appearance model. It predicts J (lightness), C (chroma), h (hue angle), M (colourfulness), s (saturation), Q (brightness) under specified viewing conditions.
Known issue: CAT02 can produce negative cone responses for highly saturated blues. CAM16 was developed as a successor.
CAM16 — Successor Model
CAM16 (Li et al., 2017) succeeds CIECAM02. The CAT16 matrix resolves the negative-response problem and provides physiologically plausible cone responses.
Reference: Li, C. et al. (2017). Color Research & Application, 42(6), 703–718.
Correlated Colour Temperature (CCT) & Duv
CCT is the temperature of the Planckian radiator whose chromaticity is closest to that of a given stimulus. Duv measures the signed distance from the Planckian locus. Positive = above (greenish), negative = below (purplish).
CIEDE2000 — Colour Difference Standard
CIE 142-2001: CIEDE2000 (dE00) is the current recommended colour-difference formula. It includes corrections for lightness, chroma, hue, and an interaction term (rotation term RT) addressing the blue region.
Guideline ranges: dE00 <1 imperceptible, 1-2 perceptible only by trained observers, 2-5 visible, 5-10 large, >10 very large.
CIE Standard Illuminants
- Illuminant A (2856 K): Tungsten/incandescent. Defined by Planckian radiator.
- Illuminant B (4874 K): Direct noon sunlight (deprecated).
- Illuminant C (6774 K): Average daylight (deprecated, superseded by D65).
- D50 (5003 K): ICC PCS standard, printing industry.
- D55 (5503 K): Mid-morning/afternoon daylight.
- D65 (6504 K): Standard daylight, sRGB reference white.
- D75 (7504 K): North sky daylight.
- E (equal-energy): Theoretical, equal power at all wavelengths.
- FL series (F1-F12): Fluorescent lamp spectral types.
CIE XYZ Tristimulus Values:
Y = ∫ E(λ) · ȳ(λ) dλ
Z = ∫ E(λ) · z̄(λ) dλ
Chromaticity coordinates:
x = X / (X + Y + Z) y = Y / (X + Y + Z)
CIE 1976 UCS coordinates:
u' = 4X / (X + 15Y + 3Z)
v' = 9Y / (X + 15Y + 3Z)
XYZ to CIELAB (CIE 015:2018):
f(t) = (29/6)^2*t/3 + 4/29 otherwise
L* = 116 * f(Y/Yn) - 16
a* = 500 * [f(X/Xn) - f(Y/Yn)]
b* = 200 * [f(Y/Yn) - f(Z/Zn)]
where (Xn, Yn, Zn) = white-point reference.
LCH (cylindrical):
C* = sqrt(a*^2 + b*^2)
h = atan2(b*, a*) [0-360 degrees]
CIELUV Forward Transform:
v* = 13 * L* * (v' - v'n)
where (u'n, v'n) = white-point u'v' coordinates.
Chroma and hue angle:
C*uv = sqrt(u*^2 + v*^2)
huv = atan2(v*, u*) [0-360 degrees]
CIECAM02 Forward Model (CIE 159:2004):
[R G B]T = M_CAT02 * [X Y Z]T
M_CAT02 =
| 0.7328 0.4296 -0.1624 |
|-0.7036 1.6975 0.0061 |
| 0.0030 0.0136 0.9834 |
Step 2: Adaptation degree:
D = F * [1 - (1/3.6) * exp(-(LA + 42)/92)]
F = 1.0 (average), 0.9 (dim), 0.8 (dark)
Step 3: Non-linear response compression:
La' = 400*(FL*|L'|/100)^0.42 / [(FL*|L'|/100)^0.42 + 27.13] + 0.1
Outputs: J (lightness), C (chroma), h (hue),
M (colourfulness), s (saturation), Q (brightness)
CAM16 Forward Model (Li et al., 2017):
| 0.401288 0.650173 -0.051461 |
|-0.250268 1.204414 0.045854 |
|-0.002079 0.048952 0.953127 |
Steps follow CIECAM02 structure but use the single
CAT16 cone space (no separate HPE transform).
CAT16 ensures all cone responses remain positive
for all spectral stimuli.
Designed for CAM16-UCS (Jab uniform space).
Correlated Colour Temperature:
n = (x - 0.3320) / (y - 0.1858)
CCT = -449n^3 + 3525n^2 - 6823.3n + 5520.33
Distance from Planckian locus (Duv):
Duv = sign * sqrt[(u - up)^2 + (v - vp)^2]
Positive Duv = above locus (greenish tint)
Negative Duv = below locus (purplish tint)
Colour Difference Metrics:
dE*ab = sqrt[(dL*)^2 + (da*)^2 + (db*)^2]
CIEDE2000 (dE00):
G = 0.5 * [1 - sqrt(C_bar^7 / (C_bar^7 + 25^7))]
a'i = ai * (1 + G)
C'i = sqrt(a'i^2 + bi^2), h'i = atan2(bi, a'i)
dH' = 2*sqrt(C'1*C'2) * sin(dh'/2)
SL = 1 + 0.015*(L_bar'-50)^2 / sqrt(20+(L_bar'-50)^2)
SC = 1 + 0.045 * C_bar'
SH = 1 + 0.015 * C_bar' * T
T = 1 - 0.17cos(h_bar'-30) + 0.24cos(2h_bar')
+ 0.32cos(3h_bar'+6) - 0.20cos(4h_bar'-63)
RT = -sin(2*dTheta) * RC (rotation term)
dE00 = sqrt[(dL'/SL)^2 + (dC'/SC)^2
+ (dH'/SH)^2 + RT*(dC'/SC)*(dH'/SH)]
- dE < 1: Imperceptible to most observers.
- dE 1-2: Perceptible on close inspection by trained observers.
- dE 2-5: Clearly noticeable difference.
- dE > 5: Colors appear distinctly different.
sRGB to/from XYZ (IEC 61966-2-1, D65):
if C_srgb <= 0.04045: C_lin = C_srgb / 12.92
else: C_lin = ((C_srgb + 0.055) / 1.055)^2.4
Linear RGB to XYZ (D65):
|X| |0.4124564 0.3575761 0.1804375| |R_lin|
|Y| = |0.2126729 0.7151522 0.0721750| |G_lin|
|Z| |0.0193339 0.1191920 0.9503041| |B_lin|
XYZ to Linear RGB (D65):
|R_lin| | 3.2404542 -1.5371385 -0.4985314| |X|
|G_lin| = |-0.9692660 1.8760108 0.0415560| |Y|
|B_lin| | 0.0556434 -0.2040259 1.0572252| |Z|
sRGB Gamma (linear to companding):
if C_lin <= 0.0031308: C_srgb = 12.92 * C_lin
else: C_srgb = 1.055 * C_lin^(1/2.4) - 0.055
CIE Standards
[2] CIE (2004). A colour appearance model for colour management systems: CIECAM02. CIE Publication 159:2004.
[3] ISO 11664-1:2007. Colorimetry — Part 1: CIE standard colorimetric observers.
[4] ISO 11664-4:2008. Colorimetry — Part 4: CIE 1976 L*a*b*.
[5] ISO 11664-5:2009. Colorimetry — Part 5: CIE 1976 L*u*v*.
[6] ISO 11664-6:2014. Colorimetry — Part 6: CIEDE2000.
Key Publications
[8] Luo, M.R., Cui, G., & Li, C. (2006). Uniform colour spaces based on CIECAM02. CRA, 31(4), 320-330.
[9] McCamy, C.S. (1992). Correlated color temperature as an explicit function of chromaticity coordinates. CRA, 17(2), 142-144.
[10] Sharma, G., Wu, W., Dalal, E.N. (2005). The CIEDE2000 color-difference formula: Implementation notes. CRA, 30(1), 21-30.
Textbooks
[12] Hunt, R.W.G. & Pointer, M.R. (2011). Measuring Colour, 4th Ed. Wiley.
[13] Wyszecki, G. & Stiles, W.S. (2000). Color Science, 2nd Ed. Wiley.
[14] Schanda, J. (Ed.) (2007). Colorimetry: Understanding the CIE System. Wiley.
Industry Standards
[16] ICC (2022). ICC.1:2022 Image technology colour management.
[17] ISO 3664:2009. Graphic technology and photography — Viewing conditions.
About this tool
This tool implements CIE XYZ, xy/u′v′ chromaticity, CIELAB, CIELUV, CIECAM02, CAM16, CCT/Duv, CIEDE2000/CIE76, CMF visualisation, illuminant SPD, multi-illuminant comparison, and batch analysis — entirely client-side (zero network). Not a substitute for calibrated measurement or official CIE software.
Paste hex codes (one per line or comma-separated) to analyse under current illuminant. Outputs XYZ, CIELAB, CIELUV, CIECAM02, CAM16 for each colour.
The CIE 1931 2° CMFs (x̄, ȳ, z̄) are the foundation of all CIE colorimetry. The CMF plot on the Lab tab shows these over 380–780 nm.
x-bar(lambda) has two peaks — minor near 440 nm (blue)
and major near 600 nm (red).
y-bar(lambda) peaks at 555 nm, matching the photopic
luminous efficiency V(lambda).
z-bar(lambda) peaks at ~445 nm and drops to zero by ~560 nm.
Metameric pairs produce identical XYZ despite different SPDs.
Data: 81 points at 5 nm intervals from CIE 015:2018 Table 1.
Analysis of gamut boundaries for standard colour spaces in the CIE xy chromaticity diagram.
| Gamut | Red | Green | Blue | Coverage |
|---|---|---|---|---|
| sRGB / Rec. 709 | (0.64, 0.33) | (0.30, 0.60) | (0.15, 0.06) | ≈ 35.9% |
| Display P3 | (0.68, 0.32) | (0.265, 0.690) | (0.15, 0.06) | ≈ 45.5% |
| Rec. 2020 | (0.708, 0.292) | (0.170, 0.797) | (0.131, 0.046) | ≈ 75.8% |
Illuminant A is Planckian at 2856 K (incandescent tungsten).
Illuminant E is the equal-energy illuminant (flat SPD).
F-series (F2, F7, F11) represent fluorescent sources with
emission lines.
Two object colours matching under one illuminant may differ
under another — illuminant metamerism.
CCT alone does not specify an illuminant — two sources with
same CCT can have different SPDs.