We provide a graph formula which describes an arbitrary monomial in \(\omega\) classes (also referred to as stable \(\psi\) classes) in terms of a simple family of dual graphs (pinwheel graphs) with edges decorated by rational functions in \(\psi\) classes. We deduce some numerical consequences and in particular a combinatorial formula expressing top intersections of \(\kappa\) classes on \(\overline{\mathcal{M}}_g\) in terms of top intersections of \(\psi\) classes.