Math Playground
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Geometry › Circles

Circles

A perfectly round shape: every point on the boundary is the same distance from the center.

Circle playground

Drag the radius slider — watch every measurement update.

rd = 2r

Radius (r)

80

Diameter (d)

160

Circumference

502.7≈ 2πr

Area

20106≈ πr²

The parts

  • Center — the middle point.
  • Radius (r) — distance from center to the edge.
  • Diameter (d) — straight across, through the center. Always d = 2r.
  • Circumference — the perimeter of a circle.
  • Chord — a straight line joining two points on the edge.
  • Arc — a piece of the edge.
  • Sector — a pizza slice (pie wedge).

The π pattern

Take any circle. Divide its circumference by its diameter. You always get the same number, no matter how big the circle is. That number is π, about 3.14159…

The two formulas

Circumference: C = 2πr  ·  Area: A = πr²

Why π appears in area too

Slice a circle into many thin pizza slices. Re-arrange them tip-up, tip-down, alternating. They almost form a rectangle of width πr (half the circumference) and height r. Area = πr × r = πr².

Quick facts

  • π is irrational — its decimal goes on forever without repeating.
  • π is also transcendental — you can't square the circle with ruler and compass.
  • 22/7 ≈ 3.143 is a popular but inexact approximation.