The spin injection technique has been adapted to a thin-film geometry. Measurements of the spin-coupled voltage V(s) as a function of film thickness d result in a determination of the spin diffusion length delta(s) = square-root D-T1 with D the electron diffusion constant in polycrystalline gold films. The conduction electron spin relaxation time T, is found to be 4.6 +/- 2.5 x 10(-11) s, for the temperature range 4 K<T<70 K. The magnitude of V(s) is large enough to suggest device applications. In a three-terminal trilayer device, an electric current I(e) biasing a thin permalloy film injects spin-polarized electrons into gold films of thickness 100 nm less-than-or-equal-to d less-than-or-equal-to 5.1 mum, and induces a nonequilibrium magnetization M. A second permalloy film detects the bipolar, spin-coupled voltage eV(s) = betaM/chi, where beta is the Bohr magneton, X the Pauli susceptibility and e the electron charge. The sign of V(s) depends on the relative orientation of the magnetizations of the permalloy films. In the thin limit, d < delta(s), the magnitude of the spin-coupled impedance Z(s) = V(s)/I(e) scales inversely with d. In the thick limit, d > delta(s), Z(s) is exponentially diminished.