About

CMYK and HSV occupy fundamentally different color spaces. CMYK is subtractive, built for ink on paper. HSV is a cylindrical remap of RGB, designed for human-intuitive color selection. Converting between them requires a two-step transform: CMYK → RGB → HSV. Each step introduces quantization. Because CMYK gamuts are device-dependent (governed by ICC profiles), the conversion here assumes ideal inks with no dot gain or paper absorption. The intermediate RGB values are computed as R = 255 × (1 − C) × (1 − K), then mapped to the HSV cylinder where H ∈ [0°, 360°], S and V ∈ [0, 100]%.

Getting this wrong matters. A mismatched color value in a brand guideline document can cause a print run worth thousands of dollars to reproduce the wrong hue. This tool performs the exact arithmetic without rounding until the final output, preserving maximum precision through the two-stage pipeline. Note: this conversion assumes the standard sRGB color space as the intermediate. Device-specific CMYK profiles (FOGRA39, SWOP) are not modeled here.

Formulas

The conversion proceeds in two stages. First, CMYK to RGB (assuming ideal, uncoated inks in sRGB space):

R = 255 × (1 − C100) × (1 − K100)

G = 255 × (1 − M100) × (1 − K100)

B = 255 × (1 − Y100) × (1 − K100)

Next, the RGB triplet is normalized to [0, 1] and converted to HSV:

V = max(R′, G′, B′)

S =

{

0 if V = 0V − min(R′, G′, B′)V otherwise

H =

{

60 × G′ − B′δ if V = R′60 × (B′ − R′δ + 2) if V = G′60 × (R′ − G′δ + 4) if V = B′

Where δ = V − min(R′, G′, B′). If H < 0, add 360. C = Cyan (0 - 100%), M = Magenta, Y = Yellow, K = Key (Black). H = Hue in degrees, S = Saturation (0 - 100%), V = Value/Brightness (0 - 100%). R′, G′, B′ are channels normalized to [0, 1].

Reference Data

Color Name	C	M	Y	K	H°	S%	V%	HEX
Pure Red	0	100	100	0	0	100	100	#FF0000
Pure Green	100	0	100	0	120	100	100	#00FF00
Pure Blue	100	100	0	0	240	100	100	#0000FF
Pure Yellow	0	0	100	0	60	100	100	#FFFF00
Cyan	100	0	0	0	180	100	100	#00FFFF
Magenta	0	100	0	0	300	100	100	#FF00FF
White	0	0	0	0	0	0	100	#FFFFFF
Black	0	0	0	100	0	0	0	#000000
Navy	100	100	0	50	240	100	50	#000080
Olive	0	0	100	50	60	100	50	#808000
Teal	100	0	0	50	180	100	50	#008080
Maroon	0	100	100	50	0	100	50	#800000
Silver	0	0	0	25	0	0	75	#BFBFBF
Gray 50%	0	0	0	50	0	0	50	#808080
Coral	0	50	69	0	16	69	100	#FF7F50
Salmon	0	52	55	2	6	54	98	#FA8072
Gold	0	16	100	0	51	100	100	#FFD700
Sky Blue	45	18	0	7	197	43	93	#87CEEB
Forest Green	76	0	76	45	120	76	55	#228B22
Chocolate	0	50	86	18	25	86	82	#D2691E

Frequently Asked Questions

CMYK is a subtractive model (ink absorbs light) while HSV is a polar remap of the additive RGB model. There is no direct mathematical mapping between the two spaces. The conversion must pass through RGB because the HSV cylinder is defined as a geometric transformation of the RGB cube. Skipping this step would require a lookup table of infinite size.

The K channel acts as a global darkening multiplier. Every RGB channel is scaled by (1 − K/100). At K = 100, all RGB channels become 0 regardless of C, M, Y values, producing V = 0 (pure black). At K = 50, the maximum possible V is 50%. This is why high-K CMYK colors always map to low-Value HSV results.

Not perfectly. CMYK has a fourth channel (K) that creates infinite CMYK representations for a single RGB color. For example, CMYK(0, 0, 0, 100) and CMYK(100, 100, 100, 0) both yield black (or near-black). When converting back from HSV to CMYK, a GCR (Gray Component Replacement) strategy must be chosen to determine how much K to use. This tool does not perform reverse conversion because the K-channel ambiguity cannot be resolved without a print profile.

Screens emit light (additive, RGB/HSV), while printers absorb light (subtractive, CMYK). The CMYK gamut is smaller than sRGB. Colors like vivid electric blue (H=240, S=100, V=100) cannot be physically reproduced with standard CMYK inks. This tool assumes ideal sRGB-space conversion. For print-accurate results, use an ICC profile (e.g., FOGRA39 for coated European stock) in dedicated software like Adobe Photoshop.

C=0, M=0, Y=0, K=0 maps to RGB(255, 255, 255), which is HSV(0°, 0%, 100%). This represents pure white - no ink on paper. The Hue value of 0° is technically undefined for achromatic colors (S=0) and is conventionally reported as 0.

This tool performs a purely mathematical conversion assuming ideal inks. In reality, dot gain (the spread of ink on porous paper) can increase effective coverage by 15-25%. Uncoated paper absorbs more ink, shifting colors toward darker, less saturated results. Coated stock holds dots tighter. These physical effects are modeled by ICC profiles, not by the simple arithmetic used here. Factor in dot gain manually if targeting a specific press condition.