Cylindrical battery and battery module

The utility model discloses a cylindrical battery and a battery module. The cylindrical battery comprises a battery shell, an inner core accommodated in the battery shell, a positive terminal arrangedat the axial right end of the battery shell and insulated and separated from the battery shell, and a negative terminal arranged at the axial left end of the battery shell and insulated and separatedfrom the battery shell, wherein the negative terminal protrudes leftwards out of the left end surface of the battery shell; an insulating space ring and a conductive cap are further included. The insulating space ring consists of an insulating circular ring sleeve which is arranged outside the axial left end of the battery shell in an abutting and sleeving manner, and a circle of annular inner flange which protrudes inwards in the radial direction from a circular opening edge at the axial left end of the circular ring sleeve; the conductive cap is composed of a conductive circular ring sleevesleeving the circular ring