Abstract: A method for providing state of charge (SOC) estimations is disclosed. The method may comprise: receiving a battery having a nominated capacity; measuring an initial SOC of the battery; discharging the battery and measuring a sequence of time-based discharge characteristics; measuring a total operating time and a total consumed capacity; providing a set of relationship equations derived from a circuit-based battery model having a variable capacitor; utilizing a computing module to perform data fitting of the set of relationship equations based on: the initial SOC, the nominated capacity, the total operating time, the total consumed capacity, and the sequence of discharge characteristics, the computing module being configured for determining values for a plurality of parameters of the set of relationship equations through said data fitting; and obtaining a remaining capacity estimation equation based on the set of relationship equations after the values for the plurality of parameters are determined.