A comparatively simple but accurate fluid-density measuring device has been developed, based in principle on the measuring method described by Kerl (1987), but due to its fully automatic operation the uncertainty has been considerably reduced (by at least a factor of ten). A permanent magnet suspended from a balance acts on a second permanent magnet within a buoy with overall density rho b, immersed in a fluid of density rho > rho b. When the vessel containing the fluid is automatically moved upwards slowly, the balance readings steadily increase until the buoy lifts off suddenly. The density rho is simply calculated from the weighing value W obtained when the buoy lifts off. With a buoy of Vb=20 cm3, fluid densities were measured in a range from 790 to 1000 kg m-3 (up to viscosities of 20 Pa s) with a relative uncertainty of 1*10-4. This method allows the density to be measured even at high temperatures and pressures, and can also be used for aggressive and opaque fluids.