Calculate the area and circumference of a circle from its diameter or radius. Switch between US and metric input units and see results in both systems. This calculator models a flat, complete circle. It does not estimate material quantities, depth, waste or installation costs.
Circle area and circumference
Enter a decimal number with no unit symbols. Switching systems clears the measurement to prevent it being read in a different unit.
Circle formulas
Let r be the radius and d be the diameter. Diameter = 2 × radius. Radius = diameter ÷ 2.
- Area = π × r², or π × d² ÷ 4.
- Circumference = 2 × π × r, or π × d.
The calculator uses the JavaScript value of π for the arithmetic, then rounds its displayed results to at most six decimal places. Area uses squared units, such as square feet. Circumference uses length units, such as feet. A circumference value is not an area.
US and metric conversion
NIST states that one inch is exactly 25.4 millimeters and gives the equivalent yard as 0.9144 meters, with 36 inches per yard.1 The calculator therefore uses 0.0254 meter per inch, 0.3048 meter per foot and 0.9144 meter per yard. For area, the length conversion factor is squared: square feet = square meters ÷ (0.3048 × 0.3048).
Circle area chart by diameter
These are calculated geometric values, rounded to four decimal places, not product coverage or recommended sizes.
| Diameter | Radius | Area | Circumference |
|---|---|---|---|
| 2 ft | 1 ft | 3.1416 sq ft | 6.2832 ft |
| 4 ft | 2 ft | 12.5664 sq ft | 12.5664 ft |
| 6 ft | 3 ft | 28.2743 sq ft | 18.8496 ft |
| 8 ft | 4 ft | 50.2655 sq ft | 25.1327 ft |
| 10 ft | 5 ft | 78.5398 sq ft | 31.4159 ft |
| 12 ft | 6 ft | 113.0973 sq ft | 37.6991 ft |
| 16 ft | 8 ft | 201.0619 sq ft | 50.2655 ft |
| 20 ft | 10 ft | 314.1593 sq ft | 62.8319 ft |
Checked examples
- 10-foot diameter: radius = 5 ft. Area = π × 25 ≈ 78.539816 sq ft. Circumference = π × 10 ≈ 31.415927 ft.
- Equivalent metric input: 10 ft = 3.048 m. Entering a 3.048 m diameter produces the same circle: about 7.296588 sq m and 78.539816 sq ft.
- 2-meter radius: diameter = 4 m. Area = π × 4 ≈ 12.566371 sq m. Circumference = 4 × π ≈ 12.566371 m. The numbers happen to match; their units and meanings do not.
- 12-inch diameter: diameter = 1 ft and radius = 0.5 ft. Area ≈ 0.785398 sq ft and circumference ≈ 3.141593 ft.
Diameter is not radius
A 10-foot diameter circle has a 5-foot radius. A 10-foot radius circle has a 20-foot diameter and four times the area. Select the measurement type before calculating; the tool clears its result if the type changes.
What the result does not include
The output is a mathematical area and boundary length. It does not convert area into a purchase order or account for overlap, gaps, cuts, material thickness or product yield. An irregular outline is not automatically a circle. This tool does not set structural dimensions or establish a construction plan.
For rectangular areas, use the square footage calculator. To convert a fractional-inch measurement before entering a decimal, use the fraction to decimal inches calculator.
Source and method
1 NIST: SI Units – Length, checked November 3, 2026. The source supports the unit conversion factor. Circle formulas, chart values and examples are arithmetic for this calculator.