We have investigated the magnetic structure of thin [001] oriented Cr films using neutron and X-ray diffraction experiments to measure their spin density waves and the strain waves, respectively. For epitaxial Cr films with thicknesses between 1000 and 4000 A grown on Nb films on sapphire substrates, we provide phase diagrams including incommensurate transverse and longitudinal spin-density waves (SDW) as well as commensurate antiferromagnetic spin structures. The results show that for Cr(001) on Nb a single domain SDW prevails with a wave vector Q perpendicular to the surface. At low temperatures the SDW is longitudinal and becomes mostly transverse between 150 and 250 K, higher than in bulk Cr where the spin-flip transition occurs at 123 K. Furthermore, the magnitude of Q is increased as compared to bulk Cr. These effects decrease with increasing film thickness. With neutron scattering we have also observed a commensurate antiferromagnetic phase with spins pointing out of the plane. The commensurate phase occurs at a temperature between 250 and 305 K and persists up to at least 340 K, far above the bulk Neel temperature of 311 K for the incommensurate phase.