The recent precise measurements of the e+e−→ KS KL and e+e−→ K+K− cross sections and the hadronic spectral function of the τ−→ K−KS ντ decay are used to extract the isoscalar and isovector electromagnetic kaon form factors and their relative phase in a model independent way. The experimental results are compared with a fit based on the vector-meson-dominance model.