RGB Converter

Data Source and Methodology

This tool uses standard, industry-accepted mathematical formulas for converting between digital color spaces. The conversions are not based on subjective perception but on deterministic algorithms commonly used in computer graphics, web design, and print media.

AuthoritativeDataSource: The algorithms are based on the colorimetric principles and standards defined by the International Commission on Illumination (CIE), which form the basis for modern digital color models like sRGB.

All calculations are based strictly on these established formulas to ensure accuracy and consistency.

The Formulas Explained

Here are the core formulas used by the converter to transform RGB values.

RGB to Hexadecimal

This is a base conversion. Each RGB value (0-255) is converted to its 2-digit hexadecimal (base-16) equivalent and concatenated.

$$ \text{Hex} = \# + \text{toHex}(R) + \text{toHex}(G) + \text{toHex}(B) $$

Where $\text{toHex}(v)$ converts a decimal value $v$ to its two-digit hex string (e.g., $255 \rightarrow \text{"FF"}$, $99 \rightarrow \text{"63"}$).

RGB to HSL (Hue, Saturation, Lightness)

1. Normalize RGB: Convert R, G, B values from 0-255 to 0-1.

$$ R' = R/255, \quad G' = G/255, \quad B' = B/255 $$

2. Find Min/Max: Find the maximum and minimum of these new values.

$$ C_{max} = \max(R', G', B'), \quad C_{min} = \min(R', G', B') $$

$$ \Delta = C_{max} - C_{min} $$

3. Calculate Lightness (L):

$$ L = \frac{C_{max} + C_{min}}{2} $$

4. Calculate Saturation (S):

$$ S = \begin{cases} 0 & \text{if } \Delta = 0 \\ \frac{\Delta}{1 - |2L - 1|} & \text{if } \Delta \neq 0 \end{cases} $$

5. Calculate Hue (H):

$$ H = \begin{cases} 0 & \text{if } \Delta = 0 \\ 60^\circ \times \left( \frac{G' - B'}{\Delta} \mod 6 \right) & \text{if } C_{max} = R' \\ 60^\circ \times \left( \frac{B' - R'}{\Delta} + 2 \right) & \text{if } C_{max} = G' \\ 60^\circ \times \left( \frac{R' - G'}{\Delta} + 4 \right) & \text{if } C_{max} = B' \end{cases} $$

The final H, S, L values are typically represented as (0-360°, 0-100%, 0-100%).

RGB to CMYK (Cyan, Magenta, Yellow, Key)

1. Normalize RGB: (Same as HSL)

$$ R' = R/255, \quad G' = G/255, \quad B' = B/255 $$

2. Calculate Key (K): The Key (black) value is calculated first.

$$ K = 1 - \max(R', G', B') $$

3. Calculate C, M, Y:

$$ C = \frac{1 - R' - K}{1 - K}, \quad M = \frac{1 - G' - K}{1 - K}, \quad Y = \frac{1 - B' - K}{1 - K} $$

If $K = 1$ (pure black), then $C = M = Y = 0$. The final values are expressed as percentages (0-100%).

Glossary of Variables

RGB (Red, Green, Blue)

An additive color model where red, green, and blue light are combined in various proportions to produce other colors. Used for digital displays. Each value ranges from 0 to 255.

Hex (Hexadecimal)

A six-digit, base-16 representation of an RGB color. It pairs three 2-digit codes (#RRGGBB) representing the Red, Green, and Blue values.

HSL (Hue, Saturation, Lightness)

A cylindrical color model designed to be more intuitive. Hue is the color's position on the color wheel (0-360°). Saturation is the color's intensity (0-100%). Lightness is its brightness (0% is black, 100% is white).

CMYK (Cyan, Magenta, Yellow, Key)

A subtractive color model used in color printing. It works by absorbing light on a white background (like paper). Key (K) stands for black, which is used for depth and true black tones.

How It Works: A Step-by-Step Example

Let's convert the color 'React Blue', a bright, sky blue.

• Input: RGB(97, 218, 251)

1. Convert to Hex

• Red: $97 \rightarrow \text{"61"}$
• Green: $218 \rightarrow \text{"DA"}$
• Blue: $251 \rightarrow \text{"FB"}$
• Final Hex: `#61DAFB`

2. Convert to HSL

• $R' = 97/255 = 0.38$, $G' = 218/255 = 0.85$, $B' = 251/255 = 0.98$
• $C_{max} = 0.98$ (B'), $C_{min} = 0.38$ (R')
• $\Delta = 0.98 - 0.38 = 0.6$
• $L = (0.98 + 0.38) / 2 = 0.68 \rightarrow \mathbf{68\%}$
• $S = 0.6 / (1 - |(2 \times 0.68) - 1|) = 0.6 / 0.64 = 0.9375 \rightarrow \mathbf{94\%}$
• $H = 60 \times ((0.38 - 0.85) / 0.6 + 4) = 60 \times (-0.783 + 4) = 193.02 \rightarrow \mathbf{193^\circ}$
• Final HSL: `hsl(193, 94%, 68%)`

3. Convert to CMYK

• $R' = 0.38$, $G' = 0.85$, $B' = 0.98$
• $K = 1 - \max(0.38, 0.85, 0.98) = 1 - 0.98 = 0.02 \rightarrow \mathbf{2\%}$
• $C = (1 - 0.38 - 0.02) / (1 - 0.02) = 0.6 / 0.98 = 0.612 \rightarrow \mathbf{61\%}$
• $M = (1 - 0.85 - 0.02) / (1 - 0.02) = 0.13 / 0.98 = 0.133 \rightarrow \mathbf{13\%}$
• $Y = (1 - 0.98 - 0.02) / (1 - 0.02) = 0 / 0.98 = 0 \rightarrow \mathbf{0\%}$
• Final CMYK: `cmyk(61%, 13%, 0%, 2%)`

Frequently Asked Questions (FAQ)