A start-up possibility determining apparatus that determines an engine-start-up possibility by driving a starter motor by power accumulated in a secondary battery includes a dynamic internal resistance measuring unit that measures an internal resistance of the secondary battery while the engine is being started up by the starter motor, a static internal resistance measuring unit that measures an internal resistance of the secondary battery when the engine is stopped, and a determining unit that determines an engine start-up possibility by the secondary battery, based on a value obtained by a product of a ratio between a first static internal resistance before or after the past engine start-up and a second static internal resistance within a predetermined time since a current time point and the dynamic internal resistance measured by the dynamic internal resistance measuring unit at the time of the engine start-up in the past.