How to find the square footage of a circle
To find the square footage of a circle from its radius, square the radius and multiply by π. The formula is area = π × r². From the diameter, use area = π × d² ÷ 4.
Measure from the center of the circle to its edge to get the radius. A 5-foot radius gives π × 5² = π × 25 = 78.5 square feet. A 10-foot radius gives π × 10² = π × 100 = 314 square feet.
Use the same unit for every measurement. A radius measured in feet produces area in square feet. For rectangular or triangular sections beside the circle, use the rectangle calculator or triangle calculator.
Locked circle examples for radius, diameter, and a semicircle.
| Radius or diameter | Area (ft²) | Area (m²) |
|---|---|---|
| Radius 5 ft | 78.5 | 7.3 |
| Radius 10 ft | 314 | 29.2 |
| Diameter 12 ft | 113 | 10.5 |
| Semicircle, radius 10 ft | 157 | 14.6 |
Area of a circle from the diameter
To find area from the diameter, divide the diameter by 2 to get the radius, then apply area = π × r². You can also calculate the area directly with area = π × d² ÷ 4, which is approximately 0.7854 × d².
A circle with a 20-foot diameter has a 10-foot radius. Its area is π × 10², or 314 square feet. The direct calculation gives the same result: 0.7854 × 20² = 314.16 square feet, displayed as 314 square feet.
A 12-foot-diameter circle has a 6-foot radius. Its area is π × 6² = π × 36, displayed as 113 square feet.
Area versus circumference
Area is the space inside a circle and is measured in square feet. Circumference is the distance around the circle and is measured in feet. The area formula is π × r². The circumference formula is 2 × π × r, which also equals π × d.
Do not use circumference as square footage. Circumference can tell you the length of edging or fencing needed around a circular space. Area tells you how much surface a circular patio, rug, garden, or pool covers.
Half circles and circle sections
A semicircle has half the area of a full circle, so its formula is ½ × π × r². A quarter circle has one-fourth of the full circle's area.
A semicircle with a 10-foot radius covers 157 square feet, half of the full circle's 314 square feet. A quarter circle with the same radius covers about 78.5 square feet.
For a plan that combines curved and straight sections, calculate each section separately and add the results. The room calculator handles rectangular floor areas.
Common circular areas
Circular area calculations apply to round patios, pools, rugs, garden beds, and other round surfaces. Measure the radius when the center is accessible. Measure the diameter across the widest point when it is easier to reach both edges.
A circular area of 314 square feet (ft²) equals 29.2 square meters (m²).
Use the square yards calculator for any area.
A 10-foot-radius patio or garden covers 314 square feet. Use that area to estimate surface material or soil coverage. For a round swimming area, continue with the pool calculator.
Circle square footage calculator summary
The Circle Square Footage Calculator finds the area of a circle from the radius or diameter. Use area = π × r², area = π × d² ÷ 4, or the equivalent decimal formula area = 0.7854 × d².
Keep area separate from circumference. Area is measured in square feet, while circumference is measured in feet. A 5-foot radius covers 78.5 square feet, a 10-foot radius covers 314 square feet, and a 12-foot diameter covers 113 square feet.