We have measured the quadratic Zeeman coefficient for the 1 S0 ↔ 3 P0 optical clock transition in 27 Al + , C2 = −71.944(24) MHz/T 2 , and the unperturbed hyperfine splitting of the 25 Mg + 2 S 1/2 ground electronic state, ∆W/h = 1 788 762 752.85(13) Hz, with improved uncertainties. Both constants are relevant to the evaluation of the 27 Al + quantum-logic clock systematic uncertainty. The measurement of C2 is in agreement with a previous measurement and a new calculation at the 1 σ level. The measurement of ∆W is in good agreement with a recent measurement and differs from a previously published result by approximately 2σ. With the improved value for ∆W , we deduce an improved value for the nuclear-to-electronic g-factor ratio gI /gJ = 9.299 308 313(60) × 10 −5 and the nuclear g-factor for the 25 Mg nucleus gI = 1.861 957 82(28) × 10 −4 . Using the values of C2 and ∆W presented here, we derive a quadratic Zeeman shift of the 27 Al + quantum-logic clock of ∆ν/ν = −(9241.8 ± 3.7) × 10 −19 , for a bias magnetic field of B ≈ 0.12 mT.