Here is the link to the spreadsheet I wrote to do the calculations (no signup required): https://www.patreon.com/posts/41672326
The pitch of the screw and circumference of the circle on the diameter make two sides of a right-angled triangle. Solving the hypotenuse with Pythagoras gives the the length of the helical path at this diameter, knowing the ratio of the inner and outer diameters allows you to calculate the radii of the annular ring that fits both helical paths.