Circle Area Calculator

A = π × r²

Area scales with the square of radius. Doubling the radius quadruples the area. A 16-inch pizza has four times the surface of an 8-inch pizza, not twice. That fact alone is worth knowing before you order.

A few real-world circle areas to anchor your intuition:

(A boxing ring, despite the name, is a square. It has been since the 1830s, when ropes on four posts replaced the roped-off circle drawn on the ground, and the old name simply stuck. Do not reach for π on that one.)

If you only know the diameter: r = d/2, then plug into A = π × r². Or skip a step: A = π × d² / 4.

If you only know the circumference: r = C / (2π), then A = π × r² works out to A = C² / (4π).

Worked example: fabric for a round tablecloth

You want a tablecloth that drapes 12 in below the edge of a 60-in diameter round table. Total cloth diameter = 60 + 2 × 12 = 84 in (radius 42 in). Area = π × 42² ≈ 5,542 sq in ≈ 38.5 sq ft. From standard 60-in width fabric, you need at least two cuts and a seam down the middle, or a wide bolt to get a single piece.

Why a 14-inch pizza is 36% bigger than a 12-inch:

12-inch pizza: π × 6² = 113 sq in. 14-inch pizza: π × 7² = 154 sq in.

Two inches of diameter, a sixth more across, and you get over a third more pizza. This is why the upsell is usually worth it and why two friends holding a 12 and a 14 are eating noticeably different amounts.

Quick reference values:

• Radius 1: area π ≈ 3.14
• Radius 2: area 4π ≈ 12.57
• Radius 3: area 9π ≈ 28.27
• Radius 5: area 25π ≈ 78.54
• Radius 10: area 100π ≈ 314.16

Memorize a few of these and you can sanity-check any circle area in your head.