A quantitative determination of interface (Ks) and volume anisotropy (Ko) constants of MBE and sputtered Co/Pt multilayers is reported. Torque and VSM magnetometry were used to determine the total average anisotropy and the room temperature magnetization of four different series of films with varying Co thickness and nearly constant Pt thickness. All films were characterized with X-ray diffraction and X-ray fluorescence, allowing the determination of the "magnetic" volume with good accuracy. Both Ks and KWf are found to be orientation dependent. We find the following results for MBE films grown on Ag buffered GaAs substrates and highly < 111 > textured films, grown on etched SiNx buffers: (111)Ks =0.92mJ/m 2 , Kveff=-l.l IMJ/m 3 sputtered (110) Ks=0.42mJ/m 2 , Kveff=-l.95MJ/m 3 MBE (001)Ks=0.59mJ/m 2 , Kveff=-5.98MJ/m 3 MBE The [l10]-oriented MBE films show in addition a large (intrinsic) in-plane anisotropy constant K -'-3MJ/m 3 , which is found to be independent of the Co thickness.[100] is the easy and [1I0] the hard in-plane direction.