<p>Machining simulations involve the generation of a swept volume. In helical milling, the swept volume becomes particularly complex due to the simultaneous rotational and translational motion of the tool. While three-dimensional representations of the swept volume provide a global view of the process, they often lack the precision needed for evaluating fine geometric details. In practice, two-dimensional cross-sections are frequently used in technical drawings to convey such details. Existing methods for multi-axis machining can obtain complete swept volume but are computationally expensive and limited in accuracy. In contrast, this study focuses on three-axis helical milling, where the cross-section of the swept volume can be formulated analytically. The proposed model provides the cross-sectional profile directly, without constructing the full swept volume, and is applicable to both convex and concave cutter geometries. The model relies on the geometric property that an axisymmetric solid (cutting tool) can be represented as a collection of circular cross-sections. When each of these circles undergoes helical motion, it generates an individual swept volume. The intersection of all such swept volumes with a plane that contains the screw axis of the motion yields a set of boundaries whose envelope forms the cross-section of the cutting tool’s swept volume. An explicit analytical formulation is derived for cutters with spherical and conical geometries, whereas an implicit formulation is necessary for ring torus-shaped cutters. Commercial CAD software is employed to validate the proposed model. Furthermore, the model is applied to a generic form cutter to assess its practical applicability.</p> Graphical abstract <p>Illustration of the swept volume cross-section formation: (top) swept volume and cross-section of a circle moving along a helical path; (bottom left) extension to a general form cutter by accumulation of individual cross-sections; (bottom right) the corresponding three-dimensional view</p> <p></p>