Calculate the area and circumference of a circle. Enter the diameter or radius to size round patios, tabletops, rugs, or gardens.
Usage Tip
Measure the diameter across the widest point through the center and divide by two for the radius — it is easier and more accurate than guessing the center.
Circumference = π × diameter
Radius = diameter ÷ 2
π (pi) is about 3.14159.
For a ring or donut shape, find the outer and inner circle areas and subtract.
Round materials are often sold as squares or by the linear foot of a roll — add waste for the corners you cut off.
How to Calculate Circle Area
The area of a circle is pi times the radius squared. The radius is the distance from the center to the edge – half the diameter. If you only know the diameter or the distance around (circumference), the calculator above converts for you, then turns the area into concrete, mulch, gravel, or sod.
Radius vs Diameter
The radius goes from the center to the edge; the diameter goes all the way across through the center and is exactly twice the radius. People most often measure the diameter (across a patio, table, or pool) because the center is hard to find – so the calculator defaults to diameter input. Just halve it to get the radius for the area formula.
Quick-Reference Area Chart
| Diameter | Radius | Area | Circumference |
|---|---|---|---|
| 4 ft | 2 ft | 12.57 sq ft | 12.57 ft |
| 6 ft | 3 ft | 28.27 sq ft | 18.85 ft |
| 8 ft | 4 ft | 50.27 sq ft | 25.13 ft |
| 10 ft | 5 ft | 78.54 sq ft | 31.42 ft |
| 12 ft | 6 ft | 113.10 sq ft | 37.70 ft |
| 16 ft | 8 ft | 201.06 sq ft | 50.27 ft |
| 20 ft | 10 ft | 314.16 sq ft | 62.83 ft |
Circle Applications
Round shapes turn up everywhere in DIY and landscaping: concrete pads for sheds and hot tubs, fire-pit patios, circular garden beds and tree rings, above-ground pools, round dining tables, and grain or water tanks. In almost every case the area is just the first step toward how much material to buy.
Concrete Slab Examples
Concrete volume = area × thickness, converted to cubic yards (divide cubic feet by 27). For a 4 inch slab:
| Diameter | Area | 4 in slab |
|---|---|---|
| 6 ft | 28.27 sq ft | 0.35 cu yd |
| 8 ft | 50.27 sq ft | 0.62 cu yd |
| 10 ft | 78.54 sq ft | 0.97 cu yd |
| 12 ft | 113.10 sq ft | 1.40 cu yd |
Mulch & Circular Garden Examples
Mulch and soil are sold by the cubic yard or in 2 cubic foot bags. For a circular bed at 3 inch depth:
| Diameter | Area | Mulch (3 in) | 2 cu ft bags |
|---|---|---|---|
| 6 ft | 28.27 sq ft | 0.26 cu yd | 4 bags |
| 8 ft | 50.27 sq ft | 0.47 cu yd | 7 bags |
| 10 ft | 78.54 sq ft | 0.73 cu yd | 10 bags |
A circular garden or tree ring uses the same math; subtract the trunk or inner circle if it is a ring rather than a full disc.
Round Patio & Pool Examples
For a round paver patio, the circle area is the surface to cover – divide by the coverage of your paver or by 1 for poured concrete. For an above-ground pool, the area is the water surface; multiply by average depth and 7.48 to get gallons. A 15 ft pool at 4 ft deep holds roughly 5,300 gallons.
Round Table Sizing
Circle area and circumference also size round tables. A 48 in round seats 4–6, a 60 in round seats 6–8, and a 72 in round seats 8–10 – budget about 24 inches of circumference per place setting. Use the circumference output above to plan a tablecloth drop or seating.
Common Mistakes
- Squaring the diameter instead of the radius (area uses r, not d).
- Forgetting to halve the diameter to get the radius.
- Mixing units – measure and calculate in the same unit.
- Skipping waste on mulch, gravel, and concrete.
- Using the full circle for a ring or donut shape.
Frequently Asked Questions
How do I calculate the area of a circle?
Square the radius and multiply by pi (about 3.1416). If you have the diameter, halve it first. A 10 ft diameter circle has a 5 ft radius and an area of 78.54 sq ft.
What is the formula for circle area?
Area = πr². From diameter it is π(d/2)², and circumference is πd.
What is the difference between radius and diameter?
The diameter crosses the whole circle through the center; the radius is half of it, from center to edge.
How much concrete do I need for a round slab?
Area × thickness ÷ 27 for cubic yards. An 8 ft circle at 4 inches is about 0.62 cubic yards.
How much mulch for a circular bed?
Area × depth ÷ 27 for cubic yards. A 6 ft bed at 3 inches needs about 0.26 cubic yards, or roughly four 2 cubic foot bags.
How do I find area from circumference?
Divide the circumference by 2π to get the radius, then use πr². The calculator above does this in its circumference mode.
Related Area Calculators
Note: results use pi (3.1416) and are rounded for display, so totals may differ slightly from hand calculations. Add a waste factor for mulch, gravel, and concrete, and round material orders up. Coverage and bag sizes vary by product. General DIY guidance, not a professional estimate.