Formula to determine perceived brightness of RGB color

I'm looking for some kind of formula or algorithm to determine the brightness of a color given the RGB values. I know it can't be as simple as adding the RGB values together and having higher sums be brighter, but I'm kind of at a loss as to where to start.

The method could vary depending on your needs. Here are 3 ways to calculate Luminance:

• Luminance (standard for certain colour spaces): (0.2126*R + 0.7152*G + 0.0722*B) source

• Luminance (perceived option 1): (0.299*R + 0.587*G + 0.114*B) source

• Luminance (perceived option 2, slower to calculate): sqrt( 0.241*R^2 + 0.691*G^2 + 0.068*B^2 ) → sqrt( 0.299*R^2 + 0.587*G^2 + 0.114*B^2 ) (thanks to @MatthewHerbst) source

^{_{[Edit: added examples using named css colors sorted with each method.]}}