Motivated by a recent experiment [Nature 442, 176 (2006)], we present a quantitative microscopic theory to investigate the inverse spin-Hall effect with spin injection into aluminum considering both intrinsic and extrinsic spin-orbit couplings using the orthogonalized-plane-wave method. Our theoretical results are in good agreement with the experimental data. It is also clear that the magnitude of the anomalous Hall resistivity is mainly due to contributions from extrinsic skew scattering, while its spatial variation is determined by the intrinsic spin-orbit coupling. [7,8,9,10].The SO coupling mechanism can also lead to a reciprocal SHE effect, the "inverse spin-Hall effect" (ISHE), which was predicted by Hirsch [2]. When a purely longitudinal spin current is applied, the electrons with opposite spins, flowing in opposing longitudinal directions, move toward the same transverse side of the sample due to SO interaction, resulting in charge accumulation. Recently, Valenzuela and Tinkham presented a first clear ISHE observation [11]. By a nonlocal spin injection into metallic aluminum through a ferromagnetic/nonmagnetic contact (the configuration is illustrated in Fig. 1), they observed a finite Hall resistivity of order of milli-Ohms over a spin-diffusion length of the order of µm.It is well known that spin [12] and charge[13] relaxations in aluminum are strongly influenced by bandstructure anomalies which arise mainly from several accidental degeneracy points (near W points) in the Brillouin zone (BZ). Therefore, in an analysis of the ISHE by spin injection in aluminum, the momentum dependence of the scattering should be taken into account. Earlier work by Zhang analyzing the SHE in the presence of spin diffusion treated only momentum-independent relaxation [14]. In this Letter, we provides a realistic, quantitative theory for ISHE by spin injection in aluminum considering the momentum dependencies of the scattering rates and of the side-jump and skew scattering contributions to the anomalous Hall current (AHC). Both the intrinsic and extrinsic SO couplings are taken into account and the electronic bands and states are determined by the orthogonalized-plane-wave (OPW) method. The resulting Hall resistivities are in good agreement with the experimental data. It is also clear that, with spin injection into aluminum, the spatial variation of AHC is determined by the intrinsic SO coupling while its magnitude is mainly due to contributions from the extrinsic skew scattering.In general, the SO interaction induced by ionic fields, i.e. the intrinsic SO coupling, may affect both the energy bands and the states of electrons in solids. However, in aluminum, its effect on the electronic band structure can be ignored. Hence, in our treatment, the energy band structure of electrons is determined by the standard OPW method in the absence of SO interaction, while the electronic Bloch states are a mixture of spin up and spin down species: ψ (µ) np (r) = G a (µ) np (G)|µ > +b (µ) np (G)|μ > exp[i(p − G) · r], with µ = 1, 2 repr...