Some time ago a dispersive representation of the scalar Kpi form factor has been proposed. It does not only allow to limit the number of free parameters in the analysis of the experimental K decay data on physically motivated ground, but the main interest is that it allows via the Callan-Treiman low-energy theorem to test the standard model precisely. This asks for a detailed study of the uncertainties of the dispersive representation which will be presented here. In addition, a dispesive representation of the vector form factor together with its uncertainties will be discussed.