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Showing content from https://www.w3.org/TR/2008/REC-WCAG20-20081211/relative-luminance.xml below:

MathML version of the relative luminance definition

the relative brightness of any point in a colorspace, normalized to 0 for darkest black and 1 for lightest white

Note 1: For the sRGB colorspace, the relative luminance of a color is defined as L = 0.2126 × R + 0.7152 × G + 0.0722 × B where R, G and B are defined as:

• If R s R G B ≤ 0.03928 then R = R s R G B 12.92 else R = ( R s R G B + 0.055 1.055 ) 2.4

• If G s R G B ≤ 0.03928 then G = G s R G B 12.92 else G = ( G s R G B + 0.055 1.055 ) 2.4

• If B s R G B ≤ 0.03928 then B = B s R G B 12.92 else B = ( B s R G B + 0.055 1.055 ) 2.4

and R s R G B , G s R G B , and B s R G B are defined as:

• R s R G B = R 8 b i t 255
• G s R G B = G 8 b i t 255
• B s R G B = B 8 b i t 255

(Formula taken from [sRGB] and [IEC-4WD].)

Note 2: Almost all systems used today to view Web content assume sRGB encoding. Unless it is known that another color space will be used to process and display the content, authors should evaluate using sRGB colorspace. If using other color spaces, see Understanding Success Criterion 1.4.3.

Note 3: If dithering occurs after delivery, then the source color value is used. For colors that are dithered at the source, the average values of the colors that are dithered should be used (average R, average G, and average B).

Note 4: Tools are available that automatically do the calculations when testing contrast and flash.

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