For obvious reasons this conversion method is called the arithmetic mean method. There is also a geometric mean method (it basically sucks and uses (R*G*B)^1/3 - so if R,G, or B are 0 you get black).

Proportional sum of the colors.

This algorithm is simple but the basis of it is much more complex. The formula looks like:

Y = .30 * R + .59 * G + .11 * B.
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The percentages here relate to how perceptive the eye is to a given color.

"The formula used in the GIMP is Y = 0.3R + 0.59G + 0.11B; this result is known as luminance. The weights used to compute luminance are related to the monitor's phosphors. The explanation for these weights is due to the fact that for equal amounts of color the eye is most sensitive to green, then red, and then blue. This means that for equal amounts of green and blue light the green will, nevertheless, seem much brighter. Thus, the image obtained by the normal averaging of an image's three color components produces a grayscale brightness that is not perceptually equivalent to the brightness of the original color image. The weighted sum that defines Y, however, does." - READ FULL TEXT, SEE PRETTY EXAMPLE PICTURES at http://gimp-savvy.com/BOOK/index.html?node54.html