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It is not always to choose the right color and contrast for your website. There are many factors involved in the process. However i usually check on the color matcher for this purpose. When ever there is a problem for me to find the complementary color, i use this tool. Also as a professional, if a client is insisting on creating the site to make it readable for the color blind users, you have to go through all the possibilities. Look at some of the restaurant website designs i have created, it usually have the range of colors that is readable for any user even the color blind ones.
I personally have a mild colorblindness issue, and certainly too much or too little contrast can cause readability issues. You have to also keep in mind that there are a wide variety of displays, lighting conditions, user settings, etc., so you will never be perfect for 100% of viewers. Even so, I like to use a tool that measures color and brightness differential. It's been around for years, so it's not the slickest, but it works.
As someone who is cursed with color-blindness, this is a question near to my heart.
About 8% of men are color blind to some degree, while it's rare among women (well under 1%), so if you have a popular website, it will be visited every day by people who have problems with some colors. (I have trouble discerning some browns from greens and some blues from purples.)
I found a site for designers called Color Laboratory that "allows you to select colors and see how they appear next to one another, and in various foreground/background combinations." More importantly, it also allows you to "see those colors as they might appear to color-blind users."
Also, this site offers some advice to web designers trying to accommodate the color-challenged.
Thanks for thinking about us, AppDevGuy!