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I have an image with green background, lets say #5F7642.
I need to add small text in red color over that background. The problem is, usual red colors pretty much fade in with the background. I need some version of red, which will stand out as much as possible.
Is there some better way than just trial and error to find such color? Is there some formula I could use, to compute the red color, which is as much different from #5F7642, as possible?
There isn't a formula, but there are some well-tested design guidelines.
Two colors that have similar (greyscale) tonal values will not have sufficient contrast to be easily read.
Colors which are opposite one another on the color wheel (complementary colors such as red and green, to take your example) tend to "glare" when placed in immediate proximity, so require some slight isolation between them, such as a white outline around lettering or small shapes.
Red and green are actually a special case. Not only are they complementaries, but the eye focuses differently on one than the other. (Next time you visit an optometrist, notice that one of the first tests she will perform is a red/green comparison.) They also happen to be very similar in tonal value when fully saturated.
What you would need to do in this case is to separate them as widely as possible in tonal value by making one very dark and the other light, and leaving one saturated while greatly desaturating the other.
