Circumference is the perimeter of a circle. It's the total length of the boundary if you "unrolled" the circle into a straight line.
Formulas
- C = 2πr (using radius)
- C = πd (using diameter)
Relationship to Area
Area = πr², so if you know circumference: r = C/(2π), then Area = C²/(4π).
Real-World Example
A bicycle wheel with 26-inch diameter: C = π × 26 ≈ 81.7 inches. Each revolution covers about 6.8 feet.
Arc Length: Circumference's Building Block
An arc (a portion of a circle's edge) has length equal to (angle/360°) × circumference. A 90° arc on a circle with a 10-inch circumference measures 2.5 inches — this relationship is the basis for designing gears, pulleys, and curved architectural elements.
Circumference in Everyday Measurement
Tire size, pipe fittings, and ring sizing all rely on circumference-to-diameter conversion. A bicycle's odometer, for instance, calculates distance traveled by multiplying wheel circumference by the number of wheel rotations detected by a sensor.