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A circular cylinder of radius $R$ has principal curvatures $0$ and $\pm 1/R$, according to orientation. Hence $K=0$ and $|H|=1/(2R)$.

This is the circular generating-curve case of a Cylinder; the curvature formulas here refer to its lateral surface.

A cylinder is generated by translating a plane curve along parallel lines transverse to its plane. A circular cylinder uses a circle as its generating plane curve; it is right when the generators are perpendicular to that plane. The term can denote the lateral surface or, for a bounded portion with end caps, the enclosed solid. The circular cylinder curvature formulas describe the smooth lateral surface.