# CMYK color model

**CMYK** (or sometimes **YMCK**) 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:

The mixture of ideal CMY colors is subtractive (Cyan, Magenta and Yellow printed together on white result to 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, cyan plus yellow generates green and the combination of cyan, magenta and yellow form black.

Because the 'black' generated by mixing the subtractive primaries is not as dense as that of a genuine black ink (one that absorbs throughout the visible spectrum), four-color printing uses black ink in addition to the subtractive primaries yellow, magenta and cyan. (The black is referred to as **key** as a shorthand for the printing term **key plate**. This plate impressed the artistic detail of an image, usually in black ink.)

Use of four-color printing generates a superior final printed result with greater contrast. However the color a person sees on a computer screen is often slightly different from the color of the same object on a printout since CMYK and the RGB color model used in computer monitors have different gamuts. RGB color is made by the emission of light (additive color) whereas CMYK works by the absorption of it (subtractive color).

## Table of contents |

## Conversions

Note that the conversions here are best described as "nominal". They will produce a reversible conversion from RGB to CMYK and back again (though not vice versa). However, the 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.

### 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):

<math>t_{CMYK}<math> | <math>= \{C, M, Y, K\}<math> is the CMYK quadruple on <math>\left[0, 1\right]^4<math>, |

<math>t_{CMY}<math> | <math>= \{C, M, Y\}<math> is the CMY triple on <math>\left[0, 1\right]^3<math>, |

<math>t_{RGB}<math> | <math>= \{R, G, B\}<math> is the RGB triple on <math>\left[0, 1\right]^3<math>. |

### Converting CMYK to RGB

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

Converting now

- <math>t_{CMYK} = \{C, M, Y, K \}<math>

then

- <math>t_{CMY} = \{C', M', Y' \} = \{C(1-K)+K, M(1-K)+K, Y(1-K)+K \}<math>

and

- <math>t_{RGB} = \{R, G, B \} = \{1-C', 1-M', 1-Y'\}<math>

or substituting in

- <math>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\}<math>

### Converting RGB to CMYK

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

Converting now

- <math>t_{RGB} = \{R, G, B\}<math>

converting to CMY

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

and then to CMYK:

- if <math>\min\{C', M', Y'\} = 1<math>
- then
- <math>t_{CMYK} = \{0, 0, 0, 1\}<math>

- else
- <math>K = \min\{C', M', Y'\}<math>
- <math>t_{CMYK} = \left\{ \frac{C' – K}{1 – K}, \frac{M' – K}{1 – K}, \frac{Y' – K}{1 – K}, K \right\}<math>

## See also

- Color model
- RGB color model commonly used for color monitors
- HSV color space
- HLS color space
- RYB color model the traditional color model used by artists.
- YUV for PAL television
- YIQ for NTSC television

## External links

- A song about YMCK, to the tune of 'YMCA'
- List CMYK values for hundreds of colors
- List named colors and their RGB value
- Convert CMYK to RGB and back

Categories: Color space | Printing