We report an empirical relation between quark mass ratios and CKM mixing angles:sin θij =pmin(mi, mj )/ max(mi, mj ). Using PDG 2024 quark masses, this relationreproduces the three CKM mixing angles with deviations of 0.6%, 1.4%, and 4.1%,without adjustable parameters. A permutation analysis over the 36 charge-preservingassignments shows that the natural mass ordering provides the best agreement withexperimental data (p = 0.056). The relation implies the testable constraint sin θ12 ×sin θ23 =pmumd/mcms = 9.22 × 10−3, compatible with PDG 2024 at the 2% level.The law is compatible with a Froggatt-Nielsen interpretation. A conjecture for theCP-violating phase gives |sin δCP | = mW /mZ, yielding δCP = 298.13◦, testable by theDUNE experiment (2028—2030). The observed relation may represent a new empiricalflavor law analogous to the historical Balmer formula in atomic spectroscopy.0.050.100.150.200.25θ12 θ23 θ13PDG 2024