  Given a surface $S$ in a 3D contact sub-Riemannian manifold $M$, we
investigate the metric structure induced on $S$ by $M$, in the sense of length
spaces. First, we define a coefficient $\widehat K$ at characteristic points
that determines locally the characteristic foliation of $S$. Next, we identify
some global conditions for the induced distance to be finite. In particular, we
prove that the induced distance is finite for surfaces with the topology of a
sphere embedded in a tight coorientable distribution, with isolated
characteristic points.
