In extensions of the gauge group rank of the Standard Model (SM), one wishes to ascribe an additional
charge under the additional $u(1)$ subgroup to the chiral fermions.
Such charges are constrained by anomaly cancellation conditions.
We consider models with SM fermions plus SM singlets (which could play the role of right-handed neutrinos, for example).
We discuss methods of solution of the anomaly cancellation conditions using geometric methods, arriving at an analytic solution for SM chiral fermion charges.