How to Find the Square Footage of a Circle
Part of Area & Volume
Quick answer
The square footage of a circle is π × radius², where the radius is half the diameter. Measure across the circle (the diameter), halve it for the radius, square that, and multiply by 3.1416. A circle 12 ft across has a 6 ft radius: 3.1416 × 6² = about 113 square feet.
Round patios, fire-pit areas, above-ground pools and planting beds are all circles, and a circle's area doesn't come from length × width. It comes from the radius — the distance from the center to the edge — squared, times pi (π ≈ 3.1416).
The formula
Square feet = π × radius², where radius = diameter ÷ 2 (in feet)
Easiest in three steps: measure the diameter (straight across, through the center) in feet, divide by 2 to get the radius, then multiply the radius by itself and by 3.1416. Measured in inches? Divide by 12 first to get feet.
Worked example — a 12 ft round patio
Diameter 12 ft → radius 6 ft → 6 × 6 = 36 → 36 × 3.1416 = 113.1 ft². So a 12-foot-wide round patio is about 113 square feet — round up to 113 when ordering pavers or concrete and add a waste allowance.
Circle area by diameter
| Diameter | Radius | Square footage |
|---|---|---|
| 4 ft | 2 ft | 12.6 ft² |
| 8 ft | 4 ft | 50.3 ft² |
| 10 ft | 5 ft | 78.5 ft² |
| 12 ft | 6 ft | 113.1 ft² |
| 16 ft | 8 ft | 201.1 ft² |
| 20 ft | 10 ft | 314.2 ft² |
For a half-circle, work out the full circle and divide by 2; for a ring (like a path around a pool), find the big circle's area and subtract the small one. The square footage calculator totals multiple shaped areas so you can add a round section to rectangular rooms.
FAQs
What is the square footage of a 12-foot circle?
About 113 square feet. A 12 ft diameter means a 6 ft radius, and π × 6² = 3.1416 × 36 = 113.1 ft².
Do I use the radius or the diameter?
The formula uses the radius (half the diameter). If you measured straight across the circle, that's the diameter — divide it by 2 before squaring. Squaring the full diameter by mistake gives four times the real area.
How do I find the area of a half or quarter circle?
Find the full circle's area with π × radius², then multiply by 0.5 for a half or 0.25 for a quarter. A 12 ft half-round is about 57 ft².