An implicit method based on high-order differentiation to determine the mean, Gaussian and principal curvatures of implicit surfaces from a three-dimensional scalar field is presented and assessed. The method also determines normal vectors and principal directions. Compared to explicit methods, the implicit approach shows robustness and improved accuracy to measure curvatures of implicit surfaces. This is evaluated on simple cases where curvature is known in closed-form. The method is applied to compute the curvatures of wrinkled flames on large triangular unstructured meshes (namely a 3D isosurface of temperature).