Portable device for displaying battery charge information and battery charge information display system

Charge information based upon predictions is displayed even when a portable device and an in-vehicle device cannot communicate with each other, to give benefits to a user. During charging of a battery, charge characteristic data on the battery is transmitted from the in-vehicle device to the portable device. In the portable device, when charge information cannot be received from the in-vehicle device after pressing of a charge inquiry button to inquire of the in-vehicle device about a battery remaining amount and time before completion of charging, a battery predicted remaining amount and predicted time before completion of charging are calculated using previously obtained charge characteristic data, and these information is displayed in a display section.