Screens produce color by emitting light (additive RGB). Printers produce color by laying down ink that absorbs light (subtractive CMYK). These two systems work in opposite directions — mixing all RGB colors creates white, while mixing all CMYK inks creates near-black.
HEX to CMYK conversion first decodes the hexadecimal string into R, G, B channels, then mathematically converts those additive values into subtractive C, M, Y, K percentages. The formula finds the Key (black) value first — K = 1 - max(R'/255, G'/255, B'/255) — then derives each ink channel relative to K.
This mathematical conversion assumes ideal inks and white paper. Real printing introduces variables like ink absorption, dot gain, and paper color. Professional workflows apply ICC profiles to account for these factors, but the mathematical conversion is the essential starting point.