Using my CAD software, I have determined that if your circle is 5 inches after sewing and turning, your square should be 3.5 inches per side.
ETA: for other sized circles (without using math), draw your circle on a piece of paper and cut it out. Fold it in half, creasing it. Then fold it in half again and crease it. Then draw a line from the end of each crease along the edge of the circle. This should give you the measure you need for your square.