  We prove the coarea formula for sufficiently smooth contact mappings of
Carnot manifolds. In particular, we investigate level surfaces of these
mappings, and compare Riemannian and sub-Riemannian measures on them. Our main
tool is the sharp asymptotic behavior of the Riemannian measure of the
intersection of a tangent plane to a level surface and a sub-Riemannian ball.
This calculation in particular implies that the sub-Riemannian measure of the
set of characteristic points (i.\,e., the points at which the sub-Riemannian
differential is degenerate) equals zero on almost every level set.
