In the talk, I will introduce a distance-like function on the zero section of the cotangent bundle using symplectic embeddings of standard balls inside an open neighborhood of the zero section. I will provide some examples which illustrate the properties of such a function. The main result that I will present is a relationship between the length structure associated to the introduced distance and the usual Riemannian length. Time permitting, I will explain a connection with the strong Viterbo conjecture for certain domains.