Geometry

Area and Circumference of a Circle: Formulas and Examples

Learn the circle area and circumference formulas with two worked examples and the most common mistakes.

The formulas

Circumference is a length around the edge. Area is the space inside, so it has squared units.

Example 1

A circle has radius 5. Find C and A.

  1. C = 2π(5) = 10π
  2. A = π(5)² = 25π
C = 10π, A = 25π

Example 2

A circle has diameter 12. Find its area.

  1. Radius = 12 / 2 = 6
  2. A = π(6)² = 36π
36π ≈ 113.1

Common mistake

A = π(12)² when the diameter is 12

Always halve the diameter to get the radius first.

Square only the r, not the π: πr², not (πr)².

Want more Geometry practice?

The free Geometry study guide has quizzes, flashcards and practice exams. 100% free, no sign-up needed.

Open the Geometry guide