The radius of your spool increased by the diameter of your thread with each complete spool layer. The tricky part is getting your thread to go down in even layers. I used to work for a cable manufacturer and i believe we could achieve +3% tolerance.

Take your internal spool width divided by the thread diameter (which can be found online from thread weight or measured directly if you have a micrometer) to get the number of circumferences per layer. Set up code to say every N turns where N = the above number of circumferences, spool diameter increases by 2*thread diameter. Whatever precision your motor turning the spool has will determine your accuracy (and you’ll need to control it with an arduino or similar). There is also a fit factor. It should just be a simple % that accounts for gaps between the threads on the spool caused by seating issues and overlays. Some sites recommend that a spool will contain 80% of its expected capacity due to imperfect winding so you might start there.

Best suggestion is to start by winding known lengths of thread without any adjustment and finding the error in your program, then just adding a fudge number (average error as a percentage).

Also keep in mind that to achieve “perfect spools” you’ll need to have an ideal fleet angle (angle the thread approaches the spool as seen from above on a horizontal spool) from your sheave (the guide into the spool which oscillates with the thread). It should be between .25 deg and 1.25 deg.

Equation should look like

Rotation amount (deg or rad)/360 deg (2pi rad)* spool diameter*pi

Your loop should increment by your chosen motor precision.

Hope this helps