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Circle Calculator
Find area, circumference, diameter, and radius from any known value. Enter radius, diameter, circumference, or area — and get all four instantly.
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Circle Calculator
Circle Formulas
All four circle measurements are derived from a single value — the radius. Once you know the radius, everything else follows directly from these standard formulas.
Core Formulas (r = radius, d = diameter)
Diameter = 2 × r
Circumference = 2 × π × r = π × d
Area = π × r²
Deriving radius from other inputs:
From diameter: r = d ÷ 2
From circumference: r = C ÷ (2π)
From area: r = √(A ÷ π)
Diameter = 2 × r
Circumference = 2 × π × r = π × d
Area = π × r²
Deriving radius from other inputs:
From diameter: r = d ÷ 2
From circumference: r = C ÷ (2π)
From area: r = √(A ÷ π)
Circle Area Reference Table
| Diameter (ft) | Radius (ft) | Area (sq ft) | Circumference (ft) |
|---|---|---|---|
| 2 | 1 | 3.14 | 6.28 |
| 4 | 2 | 12.57 | 12.57 |
| 6 | 3 | 28.27 | 18.85 |
| 8 | 4 | 50.27 | 25.13 |
| 10 | 5 | 78.54 | 31.42 |
| 12 | 6 | 113.10 | 37.70 |
| 16 | 8 | 201.06 | 50.27 |
| 20 | 10 | 314.16 | 62.83 |
| 24 | 12 | 452.39 | 75.40 |
| 30 | 15 | 706.86 | 94.25 |
Construction Uses for Circle Calculations
- Round patios and slabs: Use area to calculate square footage for concrete, pavers, or tile orders.
- Circular pools and ponds: Area determines liner size and water volume; circumference determines coping material.
- Column forms: A 12-inch diameter column has an area of 0.785 sq ft — multiply by height for concrete volume.
- Circular garden beds: Area for soil and mulch orders; circumference for edging material.
- Curved driveways: Use circumference of partial arcs to calculate paving area and edging lengths.
- Pipe sizing: Cross-sectional area of a pipe determines flow capacity in plumbing and drainage design.
? Frequently Asked Questions
How do I calculate the area of a circle?
The area of a circle equals π × r², where r is the radius (half the diameter) and π ≈ 3.14159. For example, a circle with a 10-foot diameter has a radius of 5 feet and an area of π × 5² = 78.54 square feet. Our calculator accepts radius, diameter, circumference, or area as input and derives all other values.
What is the circumference of a circle?
Circumference is the distance around the outside edge of a circle. It equals 2 × π × r, or equivalently π × diameter. A 10-foot diameter circle has a circumference of π × 10 = 31.42 feet. In construction, circumference is used when calculating fencing around a circular garden, edging around a circular patio, or forming material around a curved pour.
What is the difference between radius and diameter?
The diameter is the full width of a circle measured through its center. The radius is half the diameter — it is the distance from the center point to the edge. When measuring a circular area in the field (like a round pond or patio), it is usually easier to measure the diameter, then divide by 2 to get the radius for calculations.
How do I find the area of a circle if I only know the circumference?
First derive the radius from the circumference: r = circumference ÷ (2 × π). Then calculate area = π × r². For example, if circumference = 62.83 feet, then r = 62.83 ÷ 6.2832 = 10 feet, and area = π × 100 = 314.16 sq ft. Our calculator handles this automatically — just select "Circumference" as your input type.
How is the circle calculator used in construction?
Circle calculations are common in construction for round patios, circular driveways, round columns, curved formwork, circular pools, and curved landscape beds. The area tells you how much material (concrete, pavers, sod) you need. The circumference tells you how much edging, forming, or border material you need around the perimeter.
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💡 Pro Tips
- ✅ In the field, measure the diameter (easiest) then divide by 2 for radius
- ✅ Area grows with the square of radius — doubling radius = 4× the area
- ✅ For volume, multiply area by depth in the same unit
- ✅ π ≈ 3.14159 for all standard calculations