Square footage of a circle calculator

What is the square footage of a circle?

The square footage of a circle is simply its area expressed in square feet. It tells you how much flat surface a round shape covers — a patio, a rug, a garden bed, a pool, or a planting circle. Because so many real-world projects in the United States are priced and measured in feet, knowing the area of a circle directly in ft² makes ordering material and estimating cost far easier.

This calculator works from a single measurement. Enter the radius or the diameter of the circle, and it returns the area. You can supply the input in feet, inches, meters, or other length units, and read the result in square feet, square meters, square inches, and so on — the conversion happens automatically.

How does the calculator work?

A circle is fully described by one length, so a single value is enough to find its area. The calculator uses the radius internally:

• If you enter the radius directly, it is used as-is.
• If you enter the diameter, the radius is found from $r = \frac{d}{2}$.

The area is then computed and converted into the unit you selected for the result. Entering the area instead works in reverse, giving you the radius and diameter that would produce it.

Formulas

Area from the radius:

Area from the diameter:

Here $r$ is the radius, $d$ is the diameter, and $\pi \approx 3.14159$. When the lengths are measured in feet, the area comes out in square feet.

Examples

Example 1: Square footage from the radius

A circular patio has a radius of 10 ft. Its square footage is:

Example 2: A larger circle

For a circle with a radius of 13.1 ft:

Example 3: Square footage from the diameter

A round pool measures 20 ft across, so its diameter is 20 ft. The radius is 10 ft, and the area is:

Practical notes

• Radius vs. diameter: Measuring across the widest point gives the diameter, which is often easier in the field than locating the exact center for a radius. The calculator accepts either.
• Mixed units: You can enter a measurement in inches or meters and still read the square footage in ft² — useful when a plan and a tape measure disagree on units.
• Material allowance: When buying flooring, turf, or paint, add a margin for cuts and waste on top of the calculated square footage.

Frequently asked questions

How do I find the square footage of a circle?

Square the radius and multiply by $\pi$: $A = \pi r^2$. If you only have the diameter, halve it first to get the radius, or use $A = \frac{\pi d^2}{4}$ directly. With the length in feet, the answer is in square feet.

What is the square footage of a 10-foot-radius circle?

$A = \pi \times 10^2 \approx 314.16 \ \text{ft}^2$.

I only know the diameter — can I still use this?

Yes. Enter the diameter and the calculator finds the radius and the area for you.

Why is the result slightly different from a hand calculation?

The calculator uses a high-precision value of $\pi$, whereas a quick hand estimate may round $\pi$ to 3.14. The difference is small but grows with larger circles.