A new method for accurately converting vibrating tube periods of oscillation in density values is presented. This method is based on the fundamental requirement of the non-dependence on pressure of the vibration period of the cell under vacuum. An analytical method permits to correctly evaluate the evacuated vibrating tube periods of the Anton Paar cells namely the high pressure cells, 512 and 512P, as a function of temperature. It is further shown that the previously experimental method for the determination of this parameter is not suitable for obtaining reliable density values. A new simple calibration procedure is described and tested over wide ranges of temperature, T = (283.15 to 323.15) K and pressure, P = (0.1 to 60) MPa. New recommended density values for n-alkanes (C-6, C-7, C-8, and C-10) and tetrachloromethane, calculated by the proposed method, are given and compared with literature values in terms of mutual uncertainties. (C) 2010 Elsevier Ltd. All rights reserved.