On this page you can see how readable text in one colour is, over a background of a different colour. A small barchart gives you a programmatically-calculated guess.

Working this out depends on which formula is used for calculating how bright a given colour is, readability is a feature of relative brightness, those who say that the hue has anything to do with it, well they’re only very marginally correct, see my page Equivalent Colour Brightnesses. There are different ways of calculating brightness of a colour, the best options are those where Gamma is checked. This applies only to the leftmost four options: DCs, sRGB, YIQ and CIE XYZ, Gamma is meaningless on the rightmost two. Read more on Formulas for Calculating Pixel Brightness.