Disclosed is a battery state of charge (SOC) determining method and a battery managing apparatus that acquires a stochastic reduced order model (SROM) and a mean using battery conservation equations acquired based on a stochastic Pseudo 2-dimensional electrochemical thermal (P2D-ECT) model, measures state information, and assimilates the state information with the SROM and the mean to determine an accurate SOC at a relatively low calculation cost.