Using recently established results on the superconformal moduli space and their relation to the geometry of N = 2 SUGRA, we give an explicit formula for the Kähler potential for the chiral multiplets associated to deformation of the Kähler class [(1, 1) forms]. The formula holds for all compactifications on (2, 2) systems and it requires only topological informations about the internal superconformal theory (i.e. the intersection numbers). The metric turns out to be the unique Kähler metric which is conformal to the one proposed by Strominger some time ago. From this fact we infer that the cone in H 2 (K, R ) consisting of Kähler classes coincides with a class of convex cones whose remarkable geometrical properties were already noticed in the contexts of N = 2 supergravity and Jordan algebras. Our formula gives a closed expression for this Kähler cone.