A rechargeable battery charger is provided and is characterized by comprising a supercapacitor comprised of one or more sheets of graphene or a graphene-containing material, a power module adapted to provide a current up to 40 amps to the supercapacitor from a source of alternating current rated at 100 volts or above, an output converter adapted to deliver direct current power from the supercapacitor to an output port for connecting to a battery-powered electrical device, and a control module adapted to control various functions of the rechargeable battery charger automatically and/or for managing and regulating a variable output from the supercapacitor. The rechargeable battery charger is especially useful for recharging portable electrical devices such as smartphones, tablets, laptops or similar hand-held or worn items.