Circle Square Footage Calculator
Calculate the area of a circle using the formula π × radius². Useful for round patios, pools, garden beds, and circular construction projects.
Circle Area Calculator
The formula and quick examples
Circle area = π × radius². π (pi) ≈ 3.14159. Multiply π by the radius squared.
Quick examples: a 10-ft diameter circle has a 5-ft radius and an area of 78.5 sq ft. A 20-ft diameter circle has a 10-ft radius and an area of 314 sq ft. A 30-ft diameter has a 15-ft radius and an area of 707 sq ft.
Doubling the diameter quadruples the area. A 20-ft circle has 4× the area of a 10-ft circle, not 2×.
Measuring a real circle
In the field, measure diameter (across the widest part of the circle through the center) - it's easier than measuring radius. Then divide by 2 for the radius.
For a circular patio: measure across at multiple angles to confirm it's actually a circle (not slightly oval). If diameters vary by more than a few inches, treat it as an ellipse - approximate with two semicircle ends or just average the diameter.
Where circle area calculations come up
Round patios and concrete pads: a 12-ft-diameter circular patio = π × 6² = 113 sq ft. Above-ground pools (round): a 24-ft pool = 452 sq ft. Garden beds, tree rings, fire pit pads, hot tub pads, gazebo footprints, spiral stair landings.
The formula is π × r². Measure across the widest point of the circle to get the diameter, divide by 2 to get the radius, then square it and multiply by π (3.14159).
If the center is inaccessible (a tree, a pond), measure the circumference with a flexible tape, divide by π to get diameter, then divide by 2 for radius.
Common circle sizes in square feet
Reference table: 4 ft = 12.6 sq ft. 6 ft = 28 sq ft. 8 ft = 50 sq ft. 10 ft = 79 sq ft. 12 ft = 113 sq ft. 15 ft = 177 sq ft. 18 ft = 254 sq ft. 20 ft = 314 sq ft. 24 ft = 452 sq ft. 30 ft = 707 sq ft.
For semicircles, divide the full circle area by 2. For quarter circles, divide by 4. For three-quarter circles, multiply by 0.75.
Measuring imperfect circles
Real-world circles are rarely perfect. To check whether your shape is actually circular: mark the apparent center and measure to the edge at 4-8 points around the perimeter. If all measurements fall within 5% of each other, treat as a circle. If they vary more, treat the shape as an irregular polygon — segment it into rectangles and triangles, calculate each, and sum.
For elliptical or oval shapes (longer in one direction): use π × long-radius × short-radius. A 16 × 32 ft oval pool = π × 16 × 8 = 402 sq ft.
Pro tips
Measure diameter, not radius
The center of a circle isn't marked in the real world. Measure across (diameter) and divide by 2.
Half a circle uses half the formula
A semicircle area = (π × r²) ÷ 2. A quarter circle = (π × r²) ÷ 4. Useful for round-end patios and garden beds.
Annulus = ring shape
For a ring (donut shape), area = π × (R² - r²) where R is the outer radius and r is the inner. Use the Annulus mode on the multi-shape calculator.
Use 3.14159 for >1% accuracy
Using 3.14 introduces ~0.05% error. For most projects that's fine. For large patios or pools, use 3.14159 or the calculator's built-in π.