Pressure relief device for a battery housing, which device is designed to compensate for a pressure difference between an internal pressure of the battery housing and an ambient pressure of the battery housing, which difference occurs as a result of a thermal runaway from at least one battery cell, the pressure relief device comprising: - a separating element for separating an inner region of the battery housing from an outer region of the battery housing, the separating element being designed such that it stretches and deforms when a predeterminable pressure difference occurs between the internal pressure of the battery housing and the ambient pressure of the battery housing, - a retaining element for the separating element in order to mechanically fasten the separating element to the battery housing, and - a planar element which, in an installed state, is arranged on the side of the separating element facing the inner region of the battery housing in parallel with the separating element, characterized in that the planar element a) is mechanically coupled to the retaining element by means of a plastically or elastically deformable projection and has a rectilinear recess which extends within the planar element from a predeterminable distance from the projection transversely to a tilting axis A provided by the projection and centrally with respect to a straight line B through the planar element and ends at a predeterminable distance from the closed edge of the planar element that is opposite the projection; or b) is mechanically coupled to the retaining element by means of a first and a second plastically or elastically deformable projection, the two projections (8, 8') being arranged opposite one another and centrally with respect to a straight line B extending through the middle point of the planar element, and has a rectilinearly extending recess, the longitudinal axis of which aligns with the straight line B and which extends within the planar element from a predeterminable distance from the first projection as far as to a predeterminable distance from the second projection. - a separating element for separating an inner region of the battery housing from an outer region of the battery housing, the separating element being designed such that it stretches and deforms when a predeterminable pressure difference occurs between the internal pressure of the battery housing and the ambient pressure of the battery housing, - a retaining element for the separating element in order to mechanically fasten the separating element to the battery housing, and - a planar element which, in an installed state, is arranged on the side of the separating element facing the inner region of the battery housing in parallel with the separating element, characterized in that the planar element a) is mechanically coupled to the retaining element by means of a plastically or elastically deformable projection and has a rectilinear recess which extends within the planar element from a predeterminable distance from the projection transversely to a tilting axis A provided by the projection and centrally with respect to a straight line B through the planar element and ends at a predeterminable distance from the closed edge of the planar element that is opposite the projection; or b) is mechanically coupled to the retaining element by means of a first and a second plastically or elastically deformable projection, the two projections (8, 8') being arranged opposite one another and centrally with respect to a straight line B extending through the middle point of the planar element, and has a rectilinearly extending recess, the longitudinal axis of which aligns with the straight line B and which extends within the planar element from a predeterminable distance from the first projection as far as to a predeterminable distance from the second projection. a) is mechanically coupled to the retaining element by means of a plastically or elastically deformable projection and has a rectilinear recess which extends within the planar element from a predeterminable distance from the projection transversely to a tilting axis A provided by the projection and centrally with respect to a straight line B through the planar element and ends at a predeterminable distance from the closed edge of the planar element that is opposite the projection; or b) is mechanically coupled to the retaining element by means of a first and a second plastically or elastically deformable projection, the two projections (8, 8') being arranged opposite one another and centrally with respect to a straight line B extending through the middle point of the planar element, and has a rectilinearly extending recess, the longitudinal axis of which aligns with the straight line B and which extends within the planar element from a predeterminable distance from the first projection as far as to a predeterminable distance from the second projection.