Useful Color Equations

The following table contains links to mathematical equations for converting among various CIE color representations. An implementation of these may be found in my CIE Color Calculator. You can see from this table that some color conversions may be accomplished by single steps, while others may require several intermediate steps to reach the final goal.

From	To
From	XYZ	xyY	Lab	LCH_ab	Luv	LCH_uv	RGB
Spectrum	Spectrum to XYZ	Spectrum to XYZ XYZ to xyY	Spectrum to XYZ XYZ to Lab	Spectrum to XYZ XYZ to Lab Lab to LCH(ab)	Spectrum to XYZ XYZ to Luv	Spectrum to XYZ XYZ to Luv Luv to LCH(uv)	Spectrum to XYZ XYZ to RGB
XYZ	-	XYZ to xyY	XYZ to Lab	XYZ to Lab Lab to LCH(ab)	XYZ to Luv	XYZ to Luv Luv to LCH(uv)	XYZ to RGB
xyY	xyY to XYZ	-	xyY to XYZ XYZ to Lab	xyY to XYZ XYZ to Lab Lab to LCH(ab)	xyY to XYZ XYZ to Luv	xyY to XYZ XYZ to Luv Luv to LCH(uv)	xyY to XYZ XYZ to RGB
Lab	Lab to XYZ	Lab to XYZ XYZ to xyY	-	Lab to LCH(ab)	Lab to XYZ XYZ to Luv	Lab to XYZ XYZ to Luv Luv to LCH(uv)	Lab to XYZ XYZ to RGB
LCH_ab	LCH(ab) to Lab Lab to XYZ	LCH(ab) to Lab Lab to XYZ XYZ to xyY	LCH(ab) to Lab	-	LCH(ab) to Lab Lab to XYZ XYZ to Luv	LCH(ab) to Lab Lab to XYZ XYZ to Luv Luv to LCH(uv)	LCH(ab) to Lab Lab to XYZ XYZ to RGB
Luv	Luv to XYZ	Luv to XYZ XYZ to xyY	Luv to XYZ XYZ to Lab	Luv to XYZ XYZ to Lab Lab to LCH(ab)	-	Luv to LCH(uv)	Luv to XYZ XYZ to RGB
LCH_uv	LCH(uv) to Luv Luv to XYZ	LCH(uv) to Luv Luv to XYZ XYZ to xyY	LCH(uv) to Luv Luv to XYZ XYZ to Lab	LCH(uv) to Luv Luv to XYZ XYZ to Lab Lab to LCH(ab)	LCH(uv) to Luv	-	LCH(uv) to Luv Luv to XYZ XYZ to RGB
RGB	RGB to XYZ	RGB to XYZ XYZ to xyY	RGB to XYZ XYZ to Lab	RGB to XYZ XYZ to Lab Lab to LCH(ab)	RGB to XYZ XYZ to Luv	RGB to XYZ XYZ to Luv Luv to LCH(ab)	-

Other Assorted Equations

• Color differences

• Convert from the correlated color temperature of a CIE D-illuminant to the chromaticity of that D-illuminant.

• Chromatic adaptation.

• Computing RGB-to-XYZ and XYZ-to-RGB matrices.

• Murray-Davies dot gain equation.

• Finding the best gamma from a data set.

• Spectral power distribution of a blackbody radiator.