Subtractive mixing versus additive mixing
RGB, hex, HSL, and HSV all describe additive color — light sources that start from black (no light) and add red, green, and blue light together to produce brighter colors, ending at white when all three are at maximum. Ink on paper works the opposite way: it starts from white paper (which reflects all light) and subtracts wavelengths by absorbing them, getting darker as more ink is added. CMYK — cyan, magenta, yellow, and key (black) — is built around that subtractive process, which is why converting between an additive model like RGB and a subtractive one like CMYK requires a genuinely different formula, not just a relabeling of the same three channels.
Why there's a fourth channel: the "K" in CMYK
In principle, mixing cyan, magenta, and yellow ink in equal, sufficient amounts produces black — but in practice, real inks aren't perfectly pure, and mixing three inks to approximate black is more expensive, slower to dry, and produces a muddier, less consistent black than using a fourth, dedicated black ink directly. The K channel (black, sometimes explained as "key" to avoid confusion with blue) exists for that practical printing reason, not because the color math strictly requires a fourth dimension — CMY alone can represent every color CMYK can, just less efficiently and less accurately on real printing equipment.
How the conversion works
Converting RGB to CMYK starts by finding K: the amount of black needed is based on whichever RGB channel is largest — a pixel that's already quite dark (all channels low) needs a lot of black ink, and pure white (all channels at maximum) needs none. Once K is set, the C, M, and Y values are calculated from each RGB channel relative to that black amount, effectively factoring out the "how dark is this overall" component first, then describing the remaining color as a mix of the three ink colors. For#3B82F6, that works out to cmyk(76%, 47%, 0%, 4%) — high cyan and moderate magenta (consistent with a blue that leans slightly toward purple), no yellow at all (yellow is blue's opposite on the subtractive color wheel), and only a small amount of black, since this color isn't especially dark.
Why this conversion is approximate
The formula used here — and used by most simple RGB-to-CMYK converters — is a "naive" or device-independent conversion: it computes CMYK values mathematically from RGB without accounting for how a specific printer, ink set, or paper stock actually reproduces color. Real print production uses an ICC color profile specific to the printer and paper combination, which can shift the resulting CMYK values significantly from the naive calculation, because real ink doesn't behave with perfect mathematical purity the way this formula assumes. This tool is useful for a rough preview of how a screen color might translate to print, or for general CMYK arithmetic, but a print production workflow that needs accurate color matching should still go through proper color-profile-aware software before final output.
A note on percentages versus other CMYK notations
This tool expresses each CMYK channel as a percentage from 0 to 100, which is the most common developer-facing notation and the one used by CSS's experimental device-cmyk() function. Print software and some design tools instead express CMYK values as 0–255 integers or as 0–1 decimals, matching the same conventions RGB sometimes uses. The underlying proportions are identical regardless of notation — 76% is the same amount of cyan whether written as 76, 194 (out of 255), or 0.76 — so converting between these display conventions is a straightforward rescaling, not a color change.
When to reach for CMYK at all
CMYK is only relevant when the destination is physical, ink-based printing — packaging, brochures, business cards, anything produced on an offset or digital press. Anything destined for a screen (web pages, apps, digital images) should stay in RGB or hex throughout, since converting to CMYK and back introduces the rounding and gamut differences described above for no benefit — CMYK's ink-based color space also can't represent every color RGB can (certain bright, saturated colors visible on screen have no exact ink equivalent), which is part of why colors sometimes look duller in print than they did on screen even with accurate color management.