The sweep differential equation (SDE) method is based upon analyzing and computing the boundary of the cutter swept volume in 5-axis NC milling. The points on the boundary of the cutter swept volume are shown to be a subset of the union of (1) the grazing points of the cutter for the entire sweep, (2) the ingress points of the cutter at the beginning of the sweep, and (3) the egress points of the cutter at the end of the sweep. The grazing points at each time instant are computed from a tangency function which describes the relationship between the sweep vector and the outward surface normals for all the points on the boundary of the cutter. An algorithm is developed and a software program is written for the computation and display of the tool swept volumes for a typical 5-axis NC milling machine. An example is given to demonstrate the algorithm in computing the swept volume of a ball-end cutter.