The Formulas Want the Radius

Circle formulas run on the radius, arcs and sectors are a share of the whole, and the circle equation hides a sign trap. Watch where points quietly leak: the diameter used where the radius belongs, the arc or sector proportion set up against the wrong whole, and the center signs flipped or r² reported as r.

8 STEPS · 6 QUICK CHECKS · convert to radius first · center signs flip · v1