The RGB-XYZ Matrix Calculator
updated 4/8/2021


The World Wide Web Consortium has published standards for several alternatives to the sRGB color space for use in cascading style sheets.  Two of these spaces (Display P3 and Rec. 2020) are relatively new, and RGB-XYZ conversion matrices are not readily available on the web.  Below is a script that calculates matrices from the primaries and reference white of any RGB color space, based on equations found on brucelindbloom.com.


Enter x, y chromaticity coordinates for the primary colors of a color space (six or nine values in the form 0.6400, with or without Y values), and x, y or X, Y, Z coordinates for the reference white (two or three values).  Separate the values with spaces, line breaks, or any other characters.

The ICC specification for connection space white is 0.9642 1.0 0.8249 (D50), and the recommended chromatic adaptation transform is Bradford.

Then click calculate to generate the RGB-XYZ matrices for the color space.  The chromatic adaptation matrices between the source and destination reference whites, the adapted RGB-XYZ matrices, and the adapted primaries are also displayed.


primaries:  xr yr [Yr] xg yg [Yg] xb yb [Yb]

reference white:  xw yw or Xw Yw Zw

connection space white:  xw yw or Xw Yw Zw

chromatic adaptation transform:




  rx gx bx ry gy by rz gz bz

calculate

RGB–XYZ:

 
 
 

XYZ–RGB:

 
 
 

source–destination whites:

 
 
 

destination–source whites:

 
 
 

adapted RGB–XYZ:

 
 
 

adapted XYZ–RGB:

 
 
 

adapted primaries, xy[Y]

 
 
 

Color space specifications and implementation are somewhat disturbingly inexact.  Published sources differ; and on inspection, .icc profiles have something of a “duct tape and baling wire” quality to them.  A number of different P3 profiles are already available, made to different specifications.  And the ProPhoto transfer function often seems to get lost in the shuffle.  The W3C standards may provide uniformity for html-and-css-based applications and displays; but many other color spaces are widely used, especially for printed media, with a variety of published specifications.  Here is a summary of data from the W3C, ICC, CIE, and brucelindbloom.com.  With the calculator above, you can now use whatever specifications you want!  And if you use Raw Therapee, you can even make your own .icc profiles!


The W3C specifications:

Illuminant x y
D50 0.345704 0.358540
D65 0.3127 0.3290
Color Space Transfer
Function
Reference
White
Red Primary Green Primary Blue Primary
x y x y x y
a98-rgb 563/256 D65 0.6400 0.3300 0.2100 0.7100 0.1500 0.0600
display-p3 (sRGB) D65 0.680 0.320 0.265 0.690 0.150 0.060
prophoto-rgb (ProPhoto RGB) D50 0.734699 0.265301 0.159597 0.840403 0.036598 0.000105
rec2020 2.4 D65 0.708 0.292 0.170 0.797 0.131 0.046
srgb (sRGB) D65 0.640 0.330 0.300 0.600 0.150 0.060

ICC and CIE values:

Illuminant X Y Z
D50 0.9642 1.0000 0.8249
D65 0.9504 1.0000 1.0889

Bruce Lindbloom:

Illuminant X Y Z
A 1.09850 1.00000 0.35585
B 0.99072 1.00000 0.85223
C 0.98074 1.00000 1.18232
D50 0.96422 1.00000 0.82521
D55 0.95682 1.00000 0.92149
D65 0.95047 1.00000 1.08883
D75 0.94972 1.00000 1.22638
E 1.00000 1.00000 1.00000
F2 0.99186 1.00000 0.67393
F7 0.95041 1.00000 1.08747
F11 1.00962 1.00000 0.64350
Color Space Transfer
Function
Reference
White
Red Primary Green Primary Blue Primary
x y Y x y Y x y Y
Adobe RGB (1998) 2.2 D65 0.6400 0.3300 0.297361 0.2100 0.7100 0.627355 0.1500 0.0600 0.075285
Apple RGB 1.8 D65 0.6250 0.3400 0.244634 0.2800 0.5950 0.672034 0.1550 0.0700 0.083332
Best RGB 2.2 D50 0.7347 0.2653 0.228457 0.2150 0.7750 0.737352 0.1300 0.0350 0.034191
Beta RGB 2.2 D50 0.6888 0.3112 0.303273 0.1986 0.7551 0.663786 0.1265 0.0352 0.032941
Bruce RGB 2.2 D65 0.6400 0.3300 0.240995 0.2800 0.6500 0.683554 0.1500 0.0600 0.075452
CIE RGB 2.2 E 0.7350 0.2650 0.176204 0.2740 0.7170 0.812985 0.1670 0.0090 0.010811
ColorMatch RGB 1.8 D50 0.6300 0.3400 0.274884 0.2950 0.6050 0.658132 0.1500 0.0750 0.066985
Don RGB 4 2.2 D50 0.6960 0.3000 0.278350 0.2150 0.7650 0.687970 0.1300 0.0350 0.033680
ECI RGB v2 L* D50 0.6700 0.3300 0.320250 0.2100 0.7100 0.602071 0.1400 0.0800 0.077679
Ekta Space PS5 2.2 D50 0.6950 0.3050 0.260629 0.2600 0.7000 0.734946 0.1100 0.0050 0.004425
NTSC RGB 2.2 C 0.6700 0.3300 0.298839 0.2100 0.7100 0.586811 0.1400 0.0800 0.114350
PAL/SECAM RGB 2.2 D65 0.6400 0.3300 0.222021 0.2900 0.6000 0.706645 0.1500 0.0600 0.071334
ProPhoto RGB 1.8 D50 0.7347 0.2653 0.288040 0.1596 0.8404 0.711874 0.0366 0.0001 0.000086
SMPTE-C RGB 2.2 D65 0.6300 0.3400 0.212395 0.3100 0.5950 0.701049 0.1550 0.0700 0.086556
sRGB ≈2.2 D65 0.6400 0.3300 0.212656 0.3000 0.6000 0.715158 0.1500 0.0600 0.072186
Wide Gamut RGB 2.2 D50 0.7350 0.2650 0.258187 0.1150 0.8260 0.724938 0.1570 0.0180 0.016875

Chromatic Adaptation Transforms:

Method Transform
Bradford 0.8951 0.2664 -0.1614
-0.7502 1.7135 0.0367
0.0389 -0.0685 1.0296
CMCCAT2000 0.7982 0.3389 -0.1371
-0.5918 1.5512 0.0406
0.0008 0.0239 0.9753
CIECAT02 0.7328 0.4296 -0.1624
-0.7036 1.6975 0.0061
0.0030 0.0136 0.9834
Sharp 1.2694 -0.0988 -0.1706
-0.8364 1.8006 0.0357
0.0297 -0.0315 1.0018
Hunt–Pointer–Estevez 0.38971 0.68898 -0.07868
-0.22981 1.18340 0.04641
0.00000 0.00000 1.00000
Von Kries 0.40024 0.70760 -0.08081
-0.22630 1.16532 0.04570
0.00000 0.00000 0.91822
XYZ Scaling 1.0000 0.0000 0.0000
0.0000 1.0000 0.0000
0.0000 0.0000 1.0000

Transfer functions, RGB-XYZ and XYZ-RGB (from the W3C and Bruce Lindbloom):

gamma only

V = Math.pow(V, gamma);

V = Math.pow(V, 1/gamma);

ProPhoto RGB

if (V <= 16*e)
  V = V/16;
else
  V = Math.pow(V, 1.8);

if (V <= e)
  V = 16 * V;
else
  V = Math.pow(V, 1/1.8);

e = 0.001953  // actual Kodak standard
    1/512     // intent of the Kodak standard

sRGB

if (V <= 0.04045)
  V = V/12.92;
else
  V = Math.pow((V + 0.055)/1.055, 2.4);

if (V <= 0.0031308)
  V = 12.92 * V;
else
  V = 1.055 * Math.pow(V, 1/2.4) - 0.055;

L*

if (V <= 0.08)
  V = (100*V)/k;
else
  V = Math.pow((V + 0.16)/1.16, 3);

if (V <= e)
  V = (v*k)/100;
else
  V = 1.16 * Math.pow(V, 1/3) - 0.16;

e = 0.008856  // actual CIE standard
    216/24389 // intent of the CIE standard

k = 903.3     // actual CIE standard
    24389/27  // intent of the CIE standard

The D50-adapted matrices for sRGB and Display P3, based on the W3C specifications for sRGB and Display P3, and the ICC specification for the D50 connection space:

sRGB

adapted RGB–XYZ:

 0.4360413  0.3851129  0.1430458
 0.2224845  0.7169051  0.0606104
 0.0139202  0.0970672  0.7139126

adapted XYZ–RGB:

 3.1341864 -1.6172090 -0.4906941
-0.9787485  1.9161301  0.0334334
 0.0719639 -0.2289939  1.4057537

Display P3

adapted RGB–XYZ:

 0.5151187  0.2919778  0.1571035
 0.2411892  0.6922441  0.0665668
-0.0010505  0.0418791  0.7840713

adapted XYZ–RGB:

 2.4039840 -0.9899069 -0.3976415
-0.8422229  1.7988437  0.0160354
 0.0482059 -0.0974068  1.2740049

References:

https://www.w3.org/TR/css-color-4/#predefined
http://www.color.org/ICC1V42.pdf
http://www.color.org/chadtag.xalter
http://www.brucelindbloom.com/index.html?Eqn_RGB_XYZ_Matrix.html
http://www.brucelindbloom.com/index.html?WorkingSpaceInfo.html
http://www.brucelindbloom.com/index.html?Eqn_ChromAdapt.html
http://www.brucelindbloom.com/index.html?Eqn_RGB_to_XYZ.html
http://www.brucelindbloom.com/index.html?Eqn_XYZ_to_RGB.html
https://developer.apple.com/documentation/coregraphics/cgcolorspace/1408916-displayp3
http://www.color.org/chardata/rgb/DCIP3.xalter
http://www.color.org/chardata/rgb/srgb.pdf
https://www.kodak.com/global/plugins/acrobat/en/professional/products/software/colorFlow/romm_rgb.pdf
https://acescentral.com/aces-documentation/
https://ninedegreesbelow.com/photography/well-behaved-profiles-quest.html


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