Nonlocal measurements are performed on a multiterminal device to in situ determine the spin-diffusion length and in combination with resistivity measurements also the spin-relaxation time in Al films. By varying the thickness of Al we determine the contribution to spin relaxation from surface scattering. From the temperature dependence of the spin-diffusion length it is established that the spin relaxation is impurity dominated at low temperature. A comparison of the spin- and momentum-relaxation lengths for different thicknesses reveals that the spin-flip scattering at the surfaces is weak compared to that within the bulk of the Al films.