We compute the leading post-Newtonian and quantum corrections to the Coulomb and Newtonian potentials using the full modern arsenal of on-shell techniques; we employ spinor-helicity variables everywhere, use the Kawai-Lewellen-Tye (KLT) re-lations to derive gravity amplitudes from gauge theory and use unitarity methods to extract the terms needed at one-loop order. We stress that our results are univer-sal and thus will hold in any quantum theory of gravity with the same low-energy degrees of freedom as we are considering. Previous results for the corrections to the same potentials, derived historically using Feynman graphs, are verified explicitly, but our approach presents a huge simplification, since starting points for the compu-tations are compact and tedious index contractions and various complicated integral reductions are eliminated from the onset, streamlining the derivations. We also an-alyze the spin dependence of the results using the KLT factorization, and show how the spinless corrections in the framework are easily seen to be independent of the interacting matter considered.