A battery charger for fast charging batteries, such as batteries requiring constant current charging, such as lithium ion batteries. The battery charger provides charging voltages across a battery pack having at least one rechargeable cell connected to battery terminals. The battery charger includes a digital to analog converter circuit for controlling a current source for supplying a charging current to the battery pack. The digital to analog converter may provide a constant current or a constant voltage output as a function of the battery characteristics. An analog to digital converter measures a first voltage across the battery pack while the battery pack is being charged and a second voltage across the battery pack while the charging current is interrupted, and a digital processor determines the potential difference between the first voltage and the second voltage to determine a voltage drop across the terminals of the battery pack. A memory stores an optimum voltage level for charging the rechargeable cell, and a digital interface from the processor is used to adjust the setting of the digital to analog converter to provide the optimum voltage level at the rechargeable cell identified from the memory. The battery charger may include dual pockets for charging two battery packs.