A general mathematical form for contact angles on surfaces is suggested, offering fundamental new insights into describing wettability phenomena, which may be of considerable relevance to many fields of science. It was found that the Young equation -although physically well understood on ideal surfaces -is not unique, but a special case of a more general fundamental equation based on complex contact angles, comprising wettability on both ideal and non-ideal surfaces. The novel mathematical form predicts the existence of imaginary contact angles on all nonideal surfaces, implying two dimensions of wettabilty and necessitating the experimental determination of real and imaginary contact angles. It could be demonstrated that the new equation can be successfully applied to experimental physical and biomedical data in the hydrophilic and hydrophobic range, with novel information gained on non-ideality in the form of complex and imaginary contact angles.