Luminance & Contrast Mathematics

1. Relative Luminance Formula

Relative luminance ($L$) measures the perceived brightness of a color. It is calculated by applying weighting coefficients to the linearized red ($R_s$), green ($G_s$), and blue ($B_s$) channels to match human eye sensitivity:

2. Channel sRGB Linearization

Web colors are compressed in sRGB space. To perform linear physical operations, each color channel $C_{\text{rgb}} \in [0, 1]$ (derived from dividing the 0–255 value by 255) must be converted to linear light values $C_s$:

3. Final Contrast Ratio

The contrast ratio is calculated by comparing the relative luminance values of the lighter color ($L_{\text{light}}$) and the darker color ($L_{\text{dark}}$), adding a constant offset ($0.05$) to account for ambient light striking the display screen:

This results in ratios ranging from 1.0:1 (identical colors, zero contrast) to 21.0:1 (pure black vs pure white).