sRGB

sRGB specifies a red-green-blue colour encoding. Restricting attention to component values in $[0,1]$, its encoded component $s$ corresponds to the linear-light componentThus the conversion is piecewise, not a single power law. The reverse conversion used here isThese conventional rounded thresholds are used by the W3C conversion routines; they give a tiny mismatch at the join rather than a mathematically exact pair of inverses everywhere.^[ref][ref]

For an eight-bit neutral grayscale code $q$, use $s=q/255$ in all three components. Its relative luminance is then $D(s)$. For example, $D(0.5)\approx 0.21404$, whereas $E(0.5)\approx 0.73536$. This is why averaging encoded values and averaging linear light give different answers. sRGB is a specified interpretation; merely calling a raster image grayscale does not imply it uses sRGB.

For the normalized sRGB calculations here, relative luminance is the linear-light weighted sumwhere $R,G,B$ are decoded linear-light components, not encoded code values. This is the sRGB calculation specified in W3C's WCAG 2.2 definition of relative luminance. It places reference black at 0 and reference white at 1; it does not by itself specify an absolute display light level.^[ref]

For a neutral sRGB shade, $R=G=B=l$, and the weights sum to 1, so $Y=l$. For a coloured pixel, relative luminance can be encoded as a neutral sRGB shade with all three encoded components $E(Y)$. This preserves the specified $Y$ while discarding colour differences; it is one precisely defined grayscale conversion, not a unique way to turn all colour images into grayscale.