linguistic:paraphrasing
Distance moved

The linear distance d {\displaystyle d\,} a screw shaft moves when it is rotated through an angle of α {\displaystyle \alpha \,} degrees is:

where l {\displaystyle l\,} is the lead of the screw.

The distance ratio of a simple machine is defined as the ratio of the distance the applied force moves to the distance the load moves. For a screw it is the ratio of the circular distance d a point on the edge of the shaft moves to the linear distance d the shaft moves. If r is the radius of the shaft, in one turn a point on the screw's rim moves a distance of 2π r, while its shaft moves linearly by the lead distance l. So the distance ratio is