I am a visual/kinesthetic learner. Put simply; I need to see and do in order to learn. When I first started machine embroidery, I had a hard time remembering that the hoop area I saw was not the hoop area I would get to use. Maybe you have also had trouble reconciling the inside of the hoop you see versus the inside area of the hoop you get to use. Let me break it down for you.
The embroidery foot needs room to move around the hoop, thus the allowance of 1/4″ on three sides and the 1.25″ on the top. When you purchase a design or use one from the built in designs on your machine, you will notice the size is never as large as the stated hoop size. This is done to allow you to use the positioning feature on your machine, placing the design exactly where you want it. If you are looking for the most exact measurements, remember to use everything in metric. The conversion to inches leaves a little “fudge factor” just because they are not the same measurement systems. I hope this makes the embroidery hoop a little easier to understand. Happy Sewing!