A procedure to predict the state of charge of a lithium ion cell using experimental data (cell potential versus time), as it becomes available, is presented. The procedure is based on the physics of the system and provides a realistic estimate of the state of charge of the cell as a function of time, for a given set of properties of the electrodes. An electrochemical cell model is used to obtain an extended Kalman filter (EKF) for estimating the state of charge (SOC) of a lithium ion cell in which the negative electrode is the limiting electrode. The method could also be used for a cell in which the positive electrode is limiting.