The circular formula derivation model consists of a disc, a detachable radius rope, a rolling ruler, and a fan-shaped panel. Students measured the circumference by "straightening the radius rope" and found that C ≈ 2 π r. They divided the circle into 16 equal sectors and pieced them together to form an approximate rectangle, observing the length ≈ π r and width ≈ r, thus intuitively deriving the area S=π r ². The model can be rotated, split, and reassembled, supports hands-on experiments, and is suitable for upper primary and middle school classrooms, effectively reducing the abstraction of pi and area formulas.