An apparatus for determining a differential voltage curve of a battery includes a constant current unit, a sensing unit outputting a sensing signal indicating a voltage and a current of the battery, and a control unit determining a control history indicating the voltage and a remaining capacity of the battery based on the sensing signal. The control unit outputs a first request message when the remaining capacity is outside of a first range of interest, and a second request message when the remaining capacity is within the first range of interest. The constant current unit discharges the battery with a constant current of a first current rate in response to the first request message, and discharges the battery with a constant current of a second current rate in response to the second request message. The control unit determines the differential voltage curve when the remaining capacity reaches a threshold.