CMYK color model

CMYK (sometimes pronounced C-Mike, Smick, Cymkey (Simky) or spelled YMCK or CYM) is a subtractive color model used in color printing.

This color model is based on mixing pigments of the following colors in order to make other colors:

C=cyan
M=magenta
Y=yellow
K=key (black).

The mixture of ideal CMY colors is subtractive (cyan, magenta, and yellow printed together on white result in black). CMYK works through light absorption. The colors that are seen are from the part of light that is not absorbed. In CMYK, magenta plus yellow produces red, magenta plus cyan makes blue and cyan plus yellow generates green.

Why black ink is used

For several reasons, the 'black' generated by mixing the subtractive primaries is not ideal and so four-color printing uses black ink in addition to the subtractive primaries yellow, magenta, and cyan. The reasons for using black ink include:

A mixture of practical cyan, magenta, and yellow pigments is not pure black, but a dark murky color. This is because theoretically cyan, magenta and yellow mixed should create black, but do not because it is near impossible to create pure pigments to make it occur.
Mixing all three process color inks together merely to make black can make the paper rather wet, which is an issue in high speed printing where the paper must dry extremely rapidly to avoid marking the next sheet, and poor quality paper such as newsprint may break if it becomes too wet
Text is typically printed in black and includes fine detail (such as serifs); so to reproduce text using three inks without slight blurring would require impractically accurate registration (i.e. all three images would need to be positioned extremely precisely)
Using a unit amount of black ink rather than three unit amounts of the process color inks can lead to significant cost savings, especially because black ink can be less expensive than any of the color inks.

The black is referred to as K for key – a shorthand for the printing term key plate. This plate impressed the artistic detail of an image, usually in black ink.

The amount of black to use to replace amounts of the other ink is variable, and the choice depends on the technology, paper and ink in use. Processes called under color removal, under color addition, and gray component replacement are used to decide on the final mix, so that different CMYK recipes will be used depending on the printing task. Where black is mixed with the other colors, this is "blacker than black" and is referred to as rich black or registration black.

Comparison with RGB

Use of four-color printing generates a good final printed result with greater contrast. However, the color seen on a computer screen is often different from the color of the same object on a printout since CMYK and RGB have different gamuts. For example, pure blue (rgb 0, 0, 100%) is impossible to produce in CMYK. The nearest equivalent in CMYK is a dissimilar shade of purple.

Computer (and other) screens use an RGB color space, representing colors as additive mixtures of red, green and blue light (whose sum is white light). In printed materials, this light combination cannot be directly reproduced, so computer-generated images must be converted to the CMYK equivalent in ink colors.

Conversions

Note that the conversions here are best described as "nominal". They will produce an invertible conversion between RGB and a subset of CMYK; that is, one can take an RGB color and convert to certain CMYK colors, and from these CMYK colors obtain the corresponding, original RGB equivalents. However, conversion of CMYK colors in general to RGB colors is not invertible; that is, given a CMYK color which is converted to RGB, performing the former conversion may not give the original CMYK color. In addition, CMYK colors may print wildly differently from how the RGB colors display on a monitor. There is no single "good" conversion rule between RGB and CMYK, because neither RGB nor CMYK is an absolute color space.

These conversions should never be used in commercial printing or any other application where color matching is important.

Converting between RGB and CMYK

To convert between RGB and CMYK, an intermediate CMY value is used. Color values are represented as a vector, with each color component varying from 0.0 (no color) to 1.0 (fully saturated color):

$t_{CMYK}$	$= \{C, M, Y, K\}$ is the CMYK quadruple on $\left 1\right^4$ ,
$t_{CMY}$	$= \{C, M, Y\}$ is the CMY triple on $\left 1\right^3$ ,
$t_{RGB}$	$= \{R, G, B\}$ is the RGB triple on $\left 1\right^3$ .

Converting CMYK to RGB

To convert, we first convert CMYK to CMY, then convert the CMY value to RGB

Converting now

$t_{CMYK}$	$= \{C, M, Y, K \}\,$
$t_{CMY}$	$= \{C', M', Y' \}$
	$= \{C(1-K)+K, M(1-K)+K, Y(1-K)+K \}\,$
$t_{RGB}$	$= \{R, G, B \}$
	$= \{1-C', 1-M', 1-Y'\}\,$
$t_{RGB}$	$= \{1 - (C(1-K)+K), 1 - (M(1-K)+K), 1 - (Y(1-K)+K)\}$
	$= \{1 - C(1-K)-K, 1 - M(1-K)-K, 1 - Y(1-K)-K\}\,$

Mapping RGB to CMYK

This is a formula for mapping a given RGB color to one of many possible "semi-equivalent" CMYK colors. In this case: the CMYK color that uses the most black (K) and the least color (CMY). E.g. #808080 (gray, exactly halfway between black and white) will map to (0,0,0,0.5), and not to (0.5,0.5,0.5,0).

Converting RGB → CMY, with the same color vectors as before:

Converting now

t_{RGB} = \{R, G, B\}\,

converting to CMY

t_{CMY} = \{C', M', Y'\} = \{1-R, 1-G, 1-B\}\,

and then to CMYK:

\min\{C', M', Y'\} = 1\,

then

t_{CMYK} = \{0, 0, 0, 1\}\,

else

K = \min\{C', M', Y'\}\,

t_{CMYK} = \left\{ \frac{C' - K}{1 - K}, \frac{M' - K}{1 - K}, \frac{Y' - K}{1 - K}, K \right\}\,