  Motivated by various geometric problems, we study the nodal set of solutions
to Dirac equations on manifolds, of general form. We prove that such set has
Hausdorff dimension less than or equal to $n-2$, $n$ being the ambient
dimension. We extend this result, previously known only in the smooth case or
in specific cases, working with locally Lipschitz coefficients. Under some
additional, but still quite general, structural assumptions we provide a
stratification result for the nodal set, which appears to be new already in the
smooth case. This is achieved by exploiting the properties of a suitable
Almgren-type frequency function, which is of independent interest.
