Converting CMYK (Cyan, Magenta, Yellow, Key/Black) to HSV (Hue, Saturation, Value) involves a multi-step process because CMYK is a subtractive color model used in printing, while HSV is an additive model commonly used for digital graphics.
Here's how to convert CMYK to HSV:
Steps to Convert CMYK to HSV:
Convert CMYK to RGB: Since HSV is closely related to RGB, we first need to convert the CMYK values into RGB values using the following formulas:
𝑅
=
255
×
(
1
−
𝐶
)
×
(
1
−
𝐾
)
R=255×(1−C)×(1−K)
𝐺
=
255
×
(
1
−
𝑀
)
×
(
1
−
𝐾
)
G=255×(1−M)×(1−K)
𝐵
=
255
×
(
1
−
𝑌
)
×
(
1
−
𝐾
)
B=255×(1−Y)×(1−K)
Where C, M, Y, K are the CMYK values as decimals (i.e., 50% becomes 0.5, etc.).
Convert RGB to HSV: After obtaining the RGB values, we convert them to HSV. The formulas for the HSV conversion are as follows:
H (Hue) is the angle around the color wheel (0° to 360°).
S (Saturation) is the intensity of the color (0 to 100%).
V (Value) is the brightness of the color (0 to 100%).
The conversion is done with the following steps:
Normalize the RGB values by dividing each by 255 (i.e., R' = R / 255, G' = G / 255, B' = B / 255).
Find Cmax, Cmin, and delta:
Cmax = max(R', G', B')
Cmin = min(R', G', B')
delta = Cmax - Cmin
Value (V) = Cmax
Saturation (S) = (Cmax - Cmin) / Cmax (if Cmax is not 0)
Hue (H) is calculated based on the dominant color component:
If Cmax = R', then H = 60° × ((G' - B') / delta)
If Cmax = G', then H = 60° × ((B' - R') / delta + 2)
If Cmax = B', then H = 60° × ((R' - G') / delta + 4)
If H is negative, add 360° to get the positive hue value.
Example Conversion:
Example 1: CMYK(0%, 100%, 100%, 0%)
CMYK = (0%, 100%, 100%, 0%)
C = 0.0, M = 1.0, Y = 1.0, K = 0.0
Step 1: Convert CMYK to RGB:
R = 255 × (1 - 0.0) × (1 - 0.0) = 255
G = 255 × (1 - 1.0) × (1 - 0.0) = 0
B = 255 × (1 - 1.0) × (1 - 0.0) = 0
RGB = (255, 0, 0)
Step 2: Convert RGB to HSV:
Normalize RGB: R' = 1.0, G' = 0.0, B' = 0.0
Cmax = max(1.0, 0.0, 0.0) = 1.0
Cmin = min(1.0, 0.0, 0.0) = 0.0
delta = Cmax - Cmin = 1.0
V = Cmax = 1.0
S = (Cmax - Cmin) / Cmax = 1.0
H = 60° × ((G' - B') / delta) = 60° × ((0.0 - 0.0) / 1.0) = 0°
HSV = (0°, 100%, 100%) — This is pure red.
Example 2: CMYK(60%, 40%, 0%, 20%)
CMYK = (60%, 40%, 0%, 20%)
C = 0.6, M = 0.4, Y = 0.0, K = 0.2
Step 1: Convert CMYK to RGB:
R = 255 × (1 - 0.6) × (1 - 0.2) = 255 × 0.4 × 0.8 = 81.6 ≈ 82
G = 255 × (1 - 0.4) × (1 - 0.2) = 255 × 0.6 × 0.8 = 122.4 ≈ 122
B = 255 × (1 - 0.0) × (1 - 0.2) = 255 × 1.0 × 0.8 = 204
RGB = (82, 122, 204)
Step 2: Convert RGB to HSV:
Normalize RGB: R' = 82 / 255 = 0.321, G' = 122 / 255 = 0.478, B' = 204 / 255 = 0.8
Cmax = max(0.321, 0.478, 0.8) = 0.8
Cmin = min(0.321, 0.478, 0.8) = 0.321
delta = Cmax - Cmin = 0.8 - 0.321 = 0.479
V = Cmax = 0.8
S = (Cmax - Cmin) / Cmax = (0.8 - 0.321) / 0.8 = 0.59875 ≈ 59.88%
H = 60° × ((G' - B') / delta) = 60° × ((0.478 - 0.8) / 0.479) = 60° × (-0.322 / 0.479) ≈ 60° × -0.673 ≈ -40.38°
Since H is negative, we add 360° to get H = 319.62°.
HSV = (319.62°, 59.88%, 80%) — A bluish color.
Example 3: CMYK(100%, 0%, 0%, 0%)
CMYK = (100%, 0%, 0%, 0%)
C = 1.0, M = 0.0, Y = 0.0, K = 0.0
Step 1: Convert CMYK to RGB:
R = 255 × (1 - 1.0) × (1 - 0.0) = 0
G = 255 × (1 - 0.0) × (1 - 0.0) = 255
B = 255 × (1 - 0.0) × (1 - 0.0) = 255
RGB = (0, 255, 255)
Step 2: Convert RGB to HSV:
Normalize RGB: R' = 0 / 255 = 0.0, G' = 255 / 255 = 1.0, B' = 255 / 255 = 1.0
Cmax = max(0.0, 1.0, 1.0) = 1.0
Cmin = min(0.0, 1.0, 1.0) = 0.0
delta = Cmax - Cmin = 1.0
V = Cmax = 1.0
S = (Cmax - Cmin) / Cmax = 1.0
H = 60° × ((G' - B') / delta) = 60° × ((1.0 - 1.0) / 1.0) = 0°
HSV = (180°, 100%, 100%) — This is pure cyan.
CMYK to HSV Conversion Tools:
To save time and avoid manual calculation, you can use online converters:
RapidTables CMYK to RGB to HSV
ColorHexa CMYK to HSV
Summary:
First, convert CMYK to RGB using the formulas.
Then convert RGB to HSV using the standard RGB to HSV conversion method.
HSV represents color in terms of Hue (color), Saturation (intensity), and Value (brightness).