Circle Square Footage Calculator

The square footage of a circle is pi times the radius squared. The one number you need is the radius, which is the distance from the center to the edge. If all you have is the diameter, the distance all the way across, cut it in half first. Enter your measurement below, and the sections that follow show how to get it right on a real round patio, pool, or garden.

The formula

For any circle:

Area = π × r²

Here r is the radius and π (pi) is about 3.14159. "r squared" just means the radius times itself. Measure the radius in feet and the answer comes out in square feet. So a circle with a 5 foot radius covers 3.14159 × 5 × 5 = 78.5 square feet.

If you'd rather not carry all the decimals, 3.14 is close enough for most jobs. The difference between 3.14 and 3.14159 on a 10 foot radius circle is under a fifth of a square foot.

Getting the radius from a diameter

Most round things are easier to measure across than from the center, because finding the exact center of a patio or pool by eye is tough. The distance straight across through the middle is the diameter. The radius is half of it.

Radius = diameter ÷ 2

A 16 foot wide circle has an 8 foot radius. A 12 foot round rug has a 6 foot radius. Measure the widest straight line across the circle, divide by two, and you have your radius.

Diameter to area reference table

If you know the width across, this table skips the arithmetic. Every row uses the full pi value, rounded to the nearest tenth of a square foot.

Diameter	Radius	Area (sq ft)
8 ft	4 ft	50.3
10 ft	5 ft	78.5
12 ft	6 ft	113.1
15 ft	7.5 ft	176.7
18 ft	9 ft	254.5
20 ft	10 ft	314.2
24 ft	12 ft	452.4

Notice how fast the area climbs. Doubling the width from 12 feet to 24 feet doesn't double the area, it quadruples it, from about 113 square feet to about 452. That's the squaring at work, and it's why a slightly bigger round pool or patio eats so much more material than you'd guess.

Measuring a round space in practice

Finding dead center is the hard part. The reliable move is to measure the diameter instead: stretch a tape across the circle and slide it until you find the longest straight-line distance across. That longest line passes through the center, and it's the diameter. Halve it for the radius.

For a big circle like a patio or an above-ground pool, take the diameter in two directions, roughly at right angles, and average them. Real-world circles are never perfect, and averaging two diameters smooths out the lumps before you square anything.

When you can only reach the diameter

Sometimes you can't get to the middle at all. A round pool is full of water, a fountain has a base in the center, or a raised bed is planted solid. You don't need the center. Run your tape flat across the top of the circle, edge to edge, and hunt for the longest reading by pivoting one end slightly. The longest straight span across any circle always goes through the center, so that single measurement is your diameter. Halve it and you're done, no center point required.

If even a full crossing is blocked, measure the distance around the outside instead. The circumference is pi times the diameter, so diameter equals circumference divided by pi. Wrap a tape around a round planter, get 37.7 feet, divide by 3.14159, and the diameter is about 12 feet. From there it's an 6 foot radius and roughly 113 square feet.

Half circles and quarter circles

Plenty of real shapes are only part of a circle: a semicircular patio off a straight wall, a rounded garden bed in a corner, a fan-shaped landing.

Half circle (semicircle): Area = (π × r²) ÷ 2.
Quarter circle: Area = (π × r²) ÷ 4.

Work out the full circle first, then take the fraction you actually have.

Half-circle example. A semicircular patio bumps out from a straight house wall and reaches 10 feet from the wall at its deepest point. That 10 feet is the radius. Full circle is 3.14159 × 10 × 10 = 314.2 square feet, so the half circle is 314.2 ÷ 2 = 157.1 square feet.

Quarter-circle example. A rounded flower bed tucks into the 90 degree corner where two fences meet, curving out 6 feet along each fence. Those 6 feet are the radius. Full circle is 3.14159 × 6 × 6 = 113.1 square feet, and a quarter of that is 113.1 ÷ 4 = 28.3 square feet. One two-cubic-foot bag of mulch spread three inches deep covers about eight square feet, so that little corner bed needs roughly four bags.

Ring and border area (annulus)

A ring is a circle with a smaller circle punched out of the middle. Think of a paver border around a round pool, a walkway ringing a fountain, or a doughnut of grass between two circles. The shape has a name, an annulus, and its own tidy formula:

Ring area = π × (R² − r²)

R is the outer radius and r is the inner radius. You work out the big circle, work out the hole, and subtract.

Border example. A round above-ground pool is 16 feet across, and you're laying a paver ring that extends the whole thing out to 20 feet across. Outer radius R = 20 ÷ 2 = 10 feet. Inner radius r = 16 ÷ 2 = 8 feet. Ring area = 3.14159 × (10² − 8²) = 3.14159 × (100 − 64) = 3.14159 × 36 = 113.1 square feet of pavers. You never need to measure the ring directly, which is good, because measuring a curved band with a tape is a nightmare.

Worked example: a 16 foot patio

You're pouring a round patio that measures 16 feet across.

Diameter is 16 ft, so radius = 16 ÷ 2 = 8 ft.
Square the radius: 8 × 8 = 64.
Multiply by pi: 3.14159 × 64 = 201 square feet (201.06 to be exact).

So a 16 foot round patio is about 201 square feet. That's the number you take to the materials counter. If you're ordering pavers rated at a certain coverage, or concrete by the cubic yard, start from 201 square feet and add a little for cutting and spillage. For a poured slab, our concrete calculator turns the area and thickness into cubic yards; for the surrounding yard, the lawn calculator handles the grass.

Round patios waste more material than square ones because you're cutting curved edges out of rectangular pavers, so a 10 percent cushion is sensible here.

Worked example: a round pool footprint

Say you're buying a 24 foot round above-ground pool and want to know how much ground it covers, both to clear a level pad and to price the liner.

Diameter is 24 ft, so radius = 24 ÷ 2 = 12 ft.
Square it: 12 × 12 = 144.
Times pi: 3.14159 × 144 = 452 square feet.

That footprint is why a 24 foot pool needs so much flat, compacted ground. Compare it to the 18 foot model at about 254 square feet and the jump is nearly 200 extra square feet for six feet of width. Pool sizes are always quoted as the diameter, so read "24 foot round" as 24 feet across, never 24 feet from center to edge.

Where circle square footage comes up

Round patios and concrete pads. The classic case, and the reason a 16 foot patio question shows up so often. Area sets your paver count or concrete volume.

Above-ground pools. A round pool's footprint, and the deck or liner area, both come from π r². Pool sizes are usually given as the diameter, so halve it first.

Circular gardens and flower beds. Mulch, soil, and edging all scale with the bed's area. A round bed's square footage tells you how many bags of mulch to buy, at roughly eight square feet per two-cubic-foot bag spread three inches deep.

Round rugs and tables. Rugs are sized by diameter. A "9 foot round" rug has a 4.5 foot radius and covers about 63.6 square feet, which helps when you're checking it fits a room.

Sprinkler and irrigation coverage. A sprinkler throws a circle. Its radius squared times pi tells you the area one head waters, which feeds into layout spacing.

Common mistakes

Squaring the diameter instead of the radius. The biggest error by far. Plugging the diameter into π r² gives you four times the real area. Always halve the diameter to get the radius first.

Forgetting to square the radius. π times r is the circumference math's cousin, not the area. Area needs the radius times itself, then times pi.

Confusing radius and diameter in a listed size. Pools, rugs, and tables are almost always sold by diameter. Read the size as the full width across, not the center-to-edge distance.

Subtracting diameters instead of areas on a ring. For a border, subtract the two areas, not the two widths. The formula π × (R² − r²) does the squaring before the subtraction for a reason.

Skipping the waste factor on curved cuts. Circles carved out of square material leave more offcuts than straight layouts. Add roughly 10 percent for pavers and tile on a round shape.

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 the distance from the center to the edge, in feet, and squared means times itself. A circle with an 8 foot radius is 3.14159 × 8 × 8 = about 201 square feet.

How do I find the radius if I only know the diameter?

Divide the diameter by two. The diameter is the full distance across the circle through the center, and the radius is half of that. A 16 foot diameter gives an 8 foot radius.

How many square feet is a 16 foot round patio?

About 201 square feet. The radius is 8 feet, and 3.14159 × 8 × 8 = 201.06 square feet. Add roughly 10 percent for cutting waste when ordering pavers for a curved edge.

How many square feet is a 24 foot round pool?

About 452 square feet. The radius is 12 feet, so 3.14159 × 12 × 12 = 452.39 square feet. Use that footprint to size the pad you level and the liner you order.

How do I calculate a half circle or quarter circle?

Find the full circle's area with pi times the radius squared, then divide by two for a half circle or by four for a quarter circle. A semicircle with a 10 foot radius is (3.14159 × 100) ÷ 2 = about 157 square feet.

How do I find the area of a round border or ring?

Use the annulus formula: pi times the outer radius squared minus the inner radius squared, or π × (R² − r²). For a paver ring going from a 16 foot pool out to 20 feet across, that's 3.14159 × (100 − 64) = about 113 square feet.

What if I can't reach across the circle to measure it?

Measure around the outside instead. The circumference is pi times the diameter, so divide the distance around by 3.14159 to get the diameter, then halve that for the radius. A planter measuring 37.7 feet around is about 12 feet across.

What value of pi should I use?

3.14159 is plenty precise for any building or landscaping job, and 3.14 is fine for a quick estimate. The gap between them is a fraction of a square foot even on a large circle.

For any other shape or a whole project at once, start from the main square footage calculator.

Circle Square Footage Calculator