There are many different ways of calculating greyscale, by multiplying the red, green and blue colour values by different fractions. These give different results though, looked at on greyscale-converted complex images side-by-side, those differences can be hard to detect – the clearest way of detecting the differences is on yellows. Alternatively by changing greyscale formulas on Experiments with Colour Filters the difference can be seen on the greyscale panels as the formula is switched.

The results can be applied linearly or with a brightness weighting. (For brightness weighting in graphic form, see Colour Brightness Experiment.) Brightness-weighted results will inevitably be darker by the nature of the curve, as shown graphically on Colour Brightness Experiment.

Brightness weighted

This applies a brightness weighting according to the following formula, where ic = the calculated brightness value and exp the exponent, the function returns a percentage that is then multiplied by 255: var c = ic/255.0; if ( c <= 0.04045 ){ return c/12.92; } else { return Math.pow(((c+0.055)/(1.055)),exp); }

like PS	Approximates to the greyscale calculation formula used by Photoshop. red_value × 0.2235, green_value × 0.7154, blue_value × 0.0611, each in turn passed through the inverse gamma formula: var c = ic/255.0; if ( c <= 0.04045 ){ return c/12.92; } else { return Math.pow(((c+0.055)/(1.055)),2.4); } then the result vi passed through a gamma formula as follows, which returns a percentage that is then multiplied by 255: return vi<=0.0031308 ? vi * 12.92 : 1.055*Math.pow(vi,1.0/2.4)-0.055; See Formulas for Calculating Colour Brightness.
W3C YIQ	YIQ coefficients also known as Digital CCIR601 and suggested in the Web Accessibility Guidelines from the W3C and challenged by me (see Holes in the W3C Colour Readability Guidelines. ) red_value × 0.2125 + green_value × 0.7154 + blue_value × 0.0721
YIQ Sqd	sqrt((0.0.2125 * red_value^2) + (0.7154 * green_value^2) + (0.0721 * blue_value^2))
CIE XYZ	red_value × 0.299 + green_value × 0.587 + blue_value × 0.114
XYZ Sqd	sqrt((0.0.299 * red_value^2) + (0.587 * green_value^2) + (0.587* blue_value^2))
Lightness	½ × (max(R,G,B) + min(R,G,B)), see Puzzling Greys.
Average	(R + G + B) ÷ 3, see Puzzling Greys.