CMYK color model

Cyan, magenta, yellow, and key (black).

Cyan, magenta & yellow subtractive model. Notice that a 100% combination of C, M & Y inks does not result in black.

An image along with its cyan, magenta, and yellow components.

The same image, this time represented by the CMYK model. It is evident that significantly less color ink would be necessary to print this image when key is used.

CMYK (short for cyan, magenta, yellow, and key (Black)) is a subtractive color model used in color printing.

A common misconception is that this color model is based on actual mixing of pigments, however when seen under a microscope you will see that the dots are printed next to each other and there is very little mixing. This is how a printer is able to reproduce rich red and blue from cyan, magenta, and yellow. By combining small enough ink dots next to each other an optical illusion is caused, for example, humans perceive tiny magenta and yellow dots placed next to each other as red.

In this way the mixture of ideal CMY colors is subtractive (cyan, magenta, and yellow printed together on white result in black). CMYK works on an optical illusion that is based on 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.

Screen angle

To improve print quality and reduce moiré patterns, the screens for individual colors are set at unique angles. While the specific angles depend on how many colors are used, typical CMYK process printing uses any of the following screen angles:

C	75°	15°	105°
M	15°	45°	75°
Y	0°	0°	90°
K	45°	75°	15°

On the press

Though it varies by print house, press operator, press manufacturer and press run, ink is typically applied in the order of the acronym—cyan, magenta, yellow and then black.

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 rarely produces pure black because it is nearly impossible to create sufficiently pure pigments.
• Mixing all three process color inks together merely to make black can make the paper rather wet when not using dry toner, 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 aligned 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 is often cheaper than any of the color inks.

Black is referred to using the letter K (rather than the expected B) for key – a shorthand for the printing term key plate. This plate impressed the artistic detail of an image, usually in black ink. This use of the letter K also helped avoid confusion with the letter B as used in the acronym RGB.

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

Often people compare CMYK printing to that of RGB of a computer screen and blame the differences in results to conversion of an RGB color space to a CMYK color space. However, there are other differences that make it very hard to compare the two. A printer prints in dots per inch (dpi) which is very different to a computer screen which displays graphics in pixels per inch (ppi). Although the two acronyms have a similarities they are very different in many ways. A computer screen (ppi) is capable of mixing millions of shades of Red, Green and Blue to create rich colorful pictures. A CMYK printer must compete with the many millions of shades of RGB with only one shade of Cyan, Magenta and Yellow, which it will mix using dithering, halftoning or some other optical technique; this produces a lower level of detail than the printer's dpi suggests.

It is the lack of shades of color available in the CMYK print model that causes holes in the color spectrum it can reproduce. Some printers come with a CcMmYK option which uses Light Cyan and Light Magenta to give the printer two shades of Magenta and Yellow and fill in holes in its color spectrum and create a cleaner image.

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.

The specific formulas given below will not yield reasonable results for any printing process, and 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). (To convert color components in the range 0 to 255 – one byte values – divide each component by 255.).

$t_{CMYK}$	$=\{C,M,Y,K\}$ is the CMYK quadruple on $\left[0,1\right]^{4}$,
$t_{CMY}$	$=\{C,M,Y\}$ is the CMY triple on $\left[0,1\right]^{3}$,
$t_{RGB}$	$=\{R,G,B\}$ is the RGB triple on $\left[0,1\right]^{3}$.

Converting CMYK to RGB

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

Converting now

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

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:

Start with the RGB vector:

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

convert to an intermediate color vector C'M'Y':

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

and determine a K value:

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

We find the CMY values:

if

$K=1\,$

then

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

else

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

See also

• Hexachrome
• Process color
• Spot color
• CcMmYK color model