RGB to CMYK: The Formula + Why Printed Colors Look Different

Additive versus subtractive

Screens make color by adding light. Start with a black screen, add red, green, and blue light, and at full strength you get white. That is the additive model, and it is why RGB values run 0 (no light) to 255 (full light) per channel.

Paper works in reverse. Start with white paper and add ink, which absorbs light. Cyan ink absorbs red light, magenta absorbs green, yellow absorbs blue. Adding all three inks should make black, but real inks are imperfect, so the result is a muddy brown. That is why the K channel exists: key black is a dedicated black ink that gives clean darks, sharp text, and lower total ink coverage. CMYK is the subtractive model: four ink percentages, each 0 to 100.

The formula, step by step

First, normalize the RGB channels to the 0 to 1 range by dividing each by 255. Then apply these formulas:

• K = 1 - max(R, G, B)
• C = (1 - R - K) / (1 - K)
• M = (1 - G - K) / (1 - K)
• Y = (1 - B - K) / (1 - K)

Worked example with rgb(255, 87, 51), the orange-red from our other guides. Normalize: R = 255 / 255 = 1, G = 87 / 255 = 0.3412, B = 51 / 255 = 0.2.

• K = 1 - max(1, 0.3412, 0.2) = 1 - 1 = 0
• C = (1 - 1 - 0) / (1 - 0) = 0 / 1 = 0%
• M = (1 - 0.3412 - 0) / 1 = 0.6588 = 65.9%
• Y = (1 - 0.2 - 0) / 1 = 0.8 = 80%

The result is C0 M65.9 Y80 K0: no cyan, no black, heavy magenta and yellow. Sanity check: magenta plus yellow ink makes red-orange on paper, which is exactly the color we started with.

A second example with black in it

Take the steel blue rgb(46, 134, 193). Normalize: R = 46 / 255 = 0.1804, G = 134 / 255 = 0.5255, B = 193 / 255 = 0.7569.

• K = 1 - 0.7569 = 24.3%
• C = (1 - 0.1804 - 0.2431) / (1 - 0.2431) = 0.5765 / 0.7569 = 76.2%
• M = (1 - 0.5255 - 0.2431) / 0.7569 = 0.2314 / 0.7569 = 30.6%
• Y = (1 - 0.7569 - 0.2431) / 0.7569 = 0 / 0.7569 = 0%

So rgb(46, 134, 193) is C76.2 M30.6 Y0 K24.3. Notice how the black channel absorbed the shared darkness instead of laying down all three colors, which is exactly what K is for: it keeps total ink coverage manageable.

The edges: white, black, and rich black

White is rgb(255, 255, 255): all channels at 1, so K = 0 and every numerator is 0, giving C0 M0 Y0 K0, which is just blank paper. Pure black is rgb(0, 0, 0): all channels 0, so K = 1 - 0 = 1, giving C0 M0 Y0 K100.

Printers rarely use plain K100 for large black areas, because a single black ink looks flat and slightly gray. Rich black adds the other inks under the black: a common recipe is C60 M40 Y40 K100. That totals 200 percent ink coverage, which most coated stocks handle fine. Ask your printer for their preferred rich black before a big job, because the safe total varies by paper.

Why prints look darker and duller

Even with perfect math, a print never matches the screen exactly. The RGB gamut, the range of colors the system can express, is wider than the CMYK gamut. Bright neons, vivid cyans, and electric greens exist on screen but have no ink equivalent; the conversion clips them to the nearest printable color, which always reads duller. Paper also absorbs light instead of emitting it, so everything loses the backlit glow.

Three habits close the gap. First, soft-proof: Photoshop and InDesign can preview your design through the printer's color profile before you commit. Second, convert early: do the RGB to CMYK conversion yourself in the design tool, so you see the dulling while you can still adjust. Third, talk to the printer about ICC profiles, because the exact conversion depends on the press, the ink, and the paper, and their profile beats any generic formula.

For brand colors where the print match must be exact rather than approximate, see our hex to Pantone guide: spot-color inks are the professional answer when CMYK is not consistent enough.