Every circle is one number wearing four outfits. Radius, diameter, circumference and area all encode the same size — so this calculator makes all four fields live: edit any one, the rest follow.
The four conversions
Radius 5: diameter 10, circumference 2π·5 ≈ 31.42, area π·25 ≈ 78.54. Going backwards works because each formula inverts cleanly — from area, r = √(A/π); from circumference, r = C/2π. There's no "solve" button because there's nothing to solve: one measurement is the circle.
π, briefly and honestly
π is what you get when you divide any circle's circumference by its diameter — about 3.14159, irrational, never repeating. Archimedes trapped it between 3 10⁄71 and 3 1⁄7 with polygons two millennia ago; your browser carries it to 15+ digits, more than NASA needs for interplanetary navigation.
The square law worth internalizing
Area rides the square of the radius. Double the radius → 4× the area; that innocent-looking 12-inch pizza has 78% more food than the 9-inch (113 in² vs 64). The same law governs pipe capacity, cable cross-sections, and why a small increase in trunk diameter means a lot more tree.
Where this math gets used
Fencing a round garden bed is a circumference problem; seeding it is an area problem; fitting it through a gate is a diameter problem — same circle, three questions. For the volume of round things (tanks, pipes, planters), cylinder and sphere formulas take over in the volume calculator, and irregular flat areas are the area converter's territory. Triangles, circles' angular cousins, get solved in the triangle calculator.
Values sync at 6-decimal precision; area in square units of whatever you measure with.