A vehicle is disclosed that includes a battery and a controller programmed to calculate a battery voltage characteristic from previously measured charge and discharge data. The battery voltage characteristic is based on differences between the previously measured values when state of charge falls in a range in which the differences are approximately equal. Outside of the range, the charge and discharge voltage data are corrected based on a square root of time to obtain the battery voltage characteristic. The characterization may be performed with a high-rate continuous charge and discharge cycle. Also disclosed is an apparatus for generating the battery characteristic that includes a bi-directional power supply. The battery voltage characteristic is obtained based on the differences of the charge and discharge voltage data and corrected data based on the square root of time. A method is also disclosed based on the same.