We characterize the geometry of a path in a sub-Riemannian manifoldusing two metric invariants, the entropy and the complexity.The entropy of a subset A of a metric space is the minimum number ofballs of a given radius ε needed to cover A.It allows one to compute the Hausdorff dimension in some cases andto bound it from above in general.We define the complexity of a path in a sub-Riemannian manifold as theinfimum of the lengths of all trajectories contained in anε-neighborhood of the path, having the same extremities as thepath.The concept of complexity for paths was first developed to model thealgorithmic complexity of the nonholonomic motion planning problem inrobotics. In this paper, our aim is to estimate the entropy, Hausdorff dimension andcomplexity for a path in a general sub-Riemannian manifold.We construct first a norm $\| \cdot \|_{\varepsilon}$ on the tangent spacethat depends on a parameter ε > 0.Our main result states then that the entropy of a path is equivalent to theintegral of this ε-norm along the path.As a corollary we obtain upper and lower bounds for the Hausdorffdimension of a path.Our second main result is that complexity and entropy are equivalentfor generic paths.We give also a computable sufficient condition on the path for thisequivalence to happen.