CMYK conversions based on Photoshop's color profiles. Based on https://github.com/at-import/color-schemer/blob/master/stylesheets/color-schemer/_cmyk.scss

_cmyk_function.scss

// CMYK conversion function:

// [1] Coated_FOGRA27
// [2] Coated_FOGRA39
// [3] Coated_GRACoL_2006
// [4] Japan_Color_2001_Coated
// [5] Japan_Color_2001_Uncoated
// [6] Japan_Color_2002_Newspaper
// [7] Japan_Color_2003_Web_Coated
// [8] Japan_Web_Coated
// [9] US_Sheetfed_Coated_v2
// [10] US_Sheetfed_Uncoated_v2
// [11] US_Web_Coated_v2
// [12] US_Web_Uncoated_v2
// [13] Uncoated_FOGRA29
// [14] Web_Coated_FOGRA28
// [15] Web_Coated_SWOP_2006_Grade_3_Paper
// [16] Web_Coated_SWOP_2006_Grade_5_Paper
// [17] Euroscale_Coated_v2
// [18] Euroscale_Unoated_v2
// [19] Legacy_Photoshop_Default_CMYK

$profiles: (
    Coated_FOGRA27: (
        C: rgb(0, 158, 224),
        M: rgb(226, 0, 122),
        Y: rgb(255, 237, 0),
        K: rgb(26, 23, 27)
    ),
    Coated_FOGRA39: (
        C: rgb(0, 159, 227),
        M: rgb(230, 0, 126),
        Y: rgb(255, 237, 0),
        K: rgb(29, 29, 27)
    ),
    Coated_GRACoL_2006: (
        C: rgb(0, 159, 227),
        M: rgb(229, 0, 120),
        Y: rgb(255, 237, 0),
        K: rgb(27, 27, 26)
    ),
    Japan_Color_2001_Coated: (
        C: rgb(0, 161, 233),
        M: rgb(228, 0, 127),
        Y: rgb(255, 241, 0),
        K: rgb(35, 25, 22)
    ),
    Japan_Color_2001_Uncoated: (
        C: rgb(0, 157, 226),
        M: rgb(230, 49, 131),
        Y: rgb(255, 245, 15),
        K: rgb(68, 63, 53)
    ),
    Japan_Color_2002_Newspaper: (
        C: rgb(0, 183, 244),
        M: rgb(246, 86, 160),
        Y: rgb(255, 243, 38),
        K: rgb(32, 19, 0)
    ),
    Japan_Color_2003_Web_Coated: (
        C: rgb(0, 155, 228),
        M: rgb(232, 0, 128),
        Y: rgb(255, 240, 0),
        K: rgb(25, 20, 15)
    ),
    Japan_Web_Coated: (
        C: rgb(0, 156, 222),
        M: rgb(218, 0, 128),
        Y: rgb(255, 239, 0),
        K: rgb(31, 20, 15)
    ),
    US_Sheetfed_Coated_v2: (
        C: rgb(0, 163, 230),
        M: rgb(227, 33, 126),
        Y: rgb(255, 237, 0),
        K: rgb(28, 27, 26)
    ),
    US_Sheetfed_Uncoated_v2: (
        C: rgb(0, 162, 227),
        M: rgb(220, 23, 111),
        Y: rgb(255, 236, 0),
        K: rgb(32, 34, 29)
    ),
    US_Web_Coated_v2: (
        C: rgb(0, 174, 239),
        M: rgb(236, 0, 140),
        Y: rgb(255, 242, 0),
        K: rgb(35, 31, 32)
    ),
    US_Web_Uncoated_v2: (
        C: rgb(0, 162, 227),
        M: rgb(220, 23, 111),
        Y: rgb(255, 236, 0),
        K: rgb(32, 34, 29)
    ),
    Uncoated_FOGRA29: (
        C: rgb(0, 157, 222),
        M: rgb(228, 46, 135),
        Y: rgb(255, 232, 0),
        K: rgb(46, 32, 20)
    ),
    Web_Coated_FOGRA28: (
        C: rgb(0, 165, 232),
        M: rgb(227, 0, 124),
        Y: rgb(255, 233, 0),
        K: rgb(27, 24, 25)
    ),
    Web_Coated_SWOP_2006_Grade_3_Paper: (
        C: rgb(0, 170, 234),
        M: rgb(233, 0, 131),
        Y: rgb(255, 242, 0),
        K: rgb(36, 36, 37)
    ),
    Web_Coated_SWOP_2006_Grade_5_Paper: (
        C: rgb(0, 174, 240),
        M: rgb(236, 4, 140),
        Y: rgb(255, 242, 0),
        K: rgb(40, 37, 39)
    ),
    Euroscale_Coated_v2: (
        C: rgb(0, 166, 235),
        M: rgb(229, 0, 131),
        Y: rgb(255, 237, 0),
        K: rgb(27, 28, 32)
    ),
    Euroscale_Uncoated_v2: (
        C: rgb(0, 185, 243),
        M: rgb(232, 42, 140),
        Y: rgb(255, 240, 13),
        K: rgb(56, 58, 59)
    ),
    Legacy_Photoshop_Default_CMYK: (
        C: rgb(0, 168, 236),
        M: rgb(227, 0, 123),
        Y: rgb(248, 244, 0),
        K: rgb(0, 0, 0)
    )
);

@function C($profile, $Cy: 'C') {
    @return map-get(map-get($profiles, $profile), $Cy);
}
@function M($profile, $Ma: 'M') {
    @return map-get(map-get($profiles, $profile), $Ma);
}
@function Y($profile, $Ye: 'Y') {
    @return map-get(map-get($profiles, $profile), $Ye);
}
@function K($profile, $Bl: 'K') {
    @return map-get(map-get($profiles, $profile), $Bl);
}

@function cmyk($cyan, $magenta, $yellow, $black, $profile: false) {
    @if map-has-key($profiles, $profile) {
        $cyan    : mix(C($profile, $Cy: 'C'), white, $cyan);
        $magenta : mix(M($profile, $Ma: 'M'), white, $magenta);
        $yellow  : mix(Y($profile, $Ye: 'Y'), white, $yellow);
        $black   : mix(K($profile, $Bl: 'K'), white, $black); 
    } @else {
        $cyan    : mix(cyan, white, $cyan);
        $magenta : mix(magenta, white, $magenta);
        $yellow  : mix(yellow, white, $yellow);
        $black   : mix(black, white, $black); 
    }

    $color: white - invert($cyan) - invert($magenta) - invert($yellow) - invert($black);
    @return $color;
}

// EXAMPLE:

// $profile: 'US_Web_Coated_v2';

// .element {
//     background-color: cmyk(75, 5, 40, 0, $profile);
//     .child {
//         background-color: cmyk(24, 0, 5, 0);
//     }
//     .child-red {
//         background-color: cmyk(0, 95, 100, 0, Japan_Color_2002_Newspaper);
//     }
// }