Saturation Luminance Converter

Relative luminance is a measure of how bright a colour appears to the human visual system, and it is deliberately not the average of the three channels. The coefficients 0.2126, 0.7152 and 0.0722 weight green far above red and blue because the eye's photopic sensitivity peaks near 555 nanometres, in the green region of the spectrum. Critically, the weights apply to linear light, not to the stored channel values. An sRGB byte must first be divided by 255 and then linearised: values at or below 0.03928 are divided by 12.92, and higher values are transformed by ((v + 0.055) / 1.055) raised to the power 2.4. Skipping that step is the most common error in hand-rolled contrast checkers, and it typically overstates the luminance of dark colours. Contrast ratio follows as (L1 + 0.05) / (L2 + 0.05) with L1 the lighter of the two. The 0.05 term models about 5 percent ambient screen flare, which is why the scale runs from 1:1 to a maximum of 21:1 rather than to infinity. WCAG 2.1 sets 4.5:1 as the Level AA threshold for body text, 3:1 for large text at 18 point or 14 point bold and above, 3:1 for user interface components and meaningful graphics, and 7:1 for Level AAA body text. Saturation is a separate axis and behaves differently between models: HSL saturation is measured relative to the achievable chroma at the current lightness, so it peaks at L = 50 percent, while HSV saturation measures the distance from the brightest channel. Neither is perceptually uniform, so two colours with identical saturation numbers can differ sharply in apparent vividness, and palettes intended to feel evenly spaced are better built in CIELAB or OKLCH.

The weighting of the three channels descends from colorimetry rather than computing. The Commission Internationale de l'Eclairage adopted the photopic luminous efficiency function V(lambda) in 1924 and built it into the 1931 CIE XYZ system, where the Y component is defined as luminance by construction. Any set of RGB primaries therefore inherits its luminance coefficients from where those primaries sit in XYZ space. The older NTSC primaries of 1953 produced the familiar 0.299, 0.587 and 0.114 values still seen in video luma equations, while the modern figures of 0.2126, 0.7152 and 0.0722 come from the ITU-R BT.709 primaries standardised in 1990 for HDTV. Those same BT.709 primaries were adopted for sRGB, proposed by Hewlett-Packard and Microsoft in 1996 and published as IEC 61966-2-1 in 1999, which also fixed the piecewise transfer function with its 12.92 linear segment and 2.4 exponent. Accessibility work then borrowed the colorimetry. WCAG 1.0, published by the W3C in 1999, offered only a rough brightness and colour difference formula; WCAG 2.0, which became a Recommendation in December 2008, replaced it with the relative luminance definition and the (L1 + 0.05) / (L2 + 0.05) ratio used here, and WCAG 2.1 in June 2018 extended the same machinery to non-text contrast. Regulatory adoption followed: the United States Section 508 refresh of 2017 and the European standard EN 301 549 both reference WCAG Level AA, which is why a 4.5:1 result now carries legal as well as design consequences.