A rotational Crofton formula is derived relating the flagged intrinsic volumes of a compact set of positive reach with the flagged intrinsic volumes measured on sections passing through a fixed point. In particular cases, the flagged intrinsic volumes defined in the present paper are identical to the classical intrinsic volumes. The tight connection between our main result and other recent rotational integral formulae involving intrinsic volumes is pointed out.

Keywords: Crofton formula; Geometric measure theory; Grassmann manifold; Integral geometry; Intrinsic volume; Rotational integral; Set with positive reach; Unit normal bundle