How to Calculate the Square Footage of a Circle

The square footage of a circle is π × radius² — pi times the radius, squared. The one mistake nearly everyone makes is using the diameter, which is the measurement you actually take with a tape, as if it were the radius. It isn’t. Halve the diameter first, and the rest is easy.

This guide covers the formula, why you measure across and then halve, a ready-made diameter-to-square-feet table, and how to handle half-circles and sectors. The circle calculator does it from a single measurement.

Pi times the radius, squared

The radius is the distance from the center of the circle to its edge. Square it — multiply it by itself — and multiply by pi (about 3.14159):

area = π × radius²

A circle with a 5-foot radius is π × 5² = 3.14159 × 25 = about 78.5 square feet. That’s the whole calculation. The only real work is getting the radius, because circles don’t have a corner to measure from.

Measure the diameter, then halve it

Finding the exact center of a patio or a round rug to measure the radius is fiddly, so don’t. Measure the diameter instead — the widest distance straight across the circle, passing through the middle — and divide by two to get the radius.

So a round patio 14 feet across has a radius of 7 feet, giving π × 7² = about 154 square feet. Measure across in a couple of directions and use the largest reading, since it’s easy to cut a chord slightly off the true diameter.

Diameter to square feet

If you already know the diameter, here are the common ones worked out:

Diameter	Radius	Square feet
10 ft	5 ft	78.5
12 ft	6 ft	113.1
16 ft	8 ft	201.1
20 ft	10 ft	314.2
24 ft	12 ft	452.4
30 ft	15 ft	706.9

Notice how fast the area grows: doubling the diameter from 10 to 20 feet doesn’t double the area, it quadruples it, from 78.5 to 314 square feet. That’s the squaring at work, and it’s why a slightly bigger circle needs a lot more material than it looks.

Part of a circle: semicircles and sectors

Not every round space is a full circle:

• A semicircle (half a circle, like a rounded patio end) is just half the area: work out the full circle and divide by two.
• A quarter circle (a rounded corner) is a quarter of the area.
• A sector (any pie slice) is (angle ÷ 360) × π × radius². A 90-degree sector is a quarter; a 45-degree sector is an eighth.

The sector calculator handles any angle, which is useful for curved bay windows, cul-de-sac lots and fan-shaped patios.

Round spaces in practice

The circle formula covers more than patios — above-ground pools, round rugs, garden beds, fire-pit surrounds and tank footprints all use it. For a ring or border, like the deck around a round pool, work out the big circle and subtract the small one: the area left is the ring. And when a room has one curved end, treat it as a rectangle plus a semicircle and add the two.

The mistakes to avoid

1. Using the diameter as the radius. The radius is half the diameter — skip the halving and your area comes out four times too big.
2. Forgetting to square the radius. It’s radius × radius × pi, not radius × pi.
3. Rounding pi to 3. Use 3.14 at least; 3.14159 for anything you’re ordering material against.
4. Confusing circumference with area. The distance around the circle isn’t its square footage — see the FAQ if that’s all you have.

Frequently asked questions

How do you calculate the square footage of a circle?

Multiply pi (about 3.14159) by the radius squared. The radius is half the distance across the circle, so measure the diameter and halve it first. A circle 12 feet across has a 6-foot radius, giving π × 6² = about 113 square feet.

How many square feet is a 20-foot diameter circle?

About 314 square feet. A 20-foot diameter means a 10-foot radius, and π × 10² = 3.14159 × 100 = 314.2 square feet. If you’d used 20 as the radius by mistake, you’d have got over 1,250 — which is the classic four-times-too-big error.

Do you use the radius or the diameter to find the area?

The radius — but you usually measure the diameter and halve it, since the diameter (straight across) is far easier to tape than the radius (center to edge). Just remember to do the halving; plugging the diameter straight into the formula overstates the area fourfold.

How do you find the square footage of half a circle?

Work out the full circle with π × radius², then divide by two. A semicircular patio built on a 16-foot straight edge has an 8-foot radius, so the full circle would be about 201 square feet and the half is roughly 100.5.

What if I only know the circumference of the circle?

You can still get the area. Divide the circumference by 2π (about 6.283) to find the radius, then use π × radius². For example, a circle with a 31.4-foot circumference has a radius of about 5 feet, giving roughly 78.5 square feet.

The short version

A circle’s square footage comes down to the radius and remembering to square it.

• Area = pi × radius², with the radius in feet.
• Measure the diameter (straight across) and halve it to get the radius.
• Half-circles and sectors are simple fractions of the full area.
• Don’t use the diameter as the radius, and don’t round pi down to 3.

Enter one measurement in the circle calculator, or an angle and radius in the sector calculator, and either returns the area in square feet, square yards and square meters.