Circle Area Calculator
Calculate the area of a circle from its radius with A = πr², with the diameter and circumference shown alongside.
Last updated: October 2026
Circle area
78.54 square units
Formula below · 1 source (mathworld.wolfram.com) · Updated Oct 2026
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About this calculator
The area of a circle is the space inside it. It depends only on the radius, the distance from the center to the edge.
The formula
A = π × r². Square the radius, then multiply by π (about 3.14159). A circle with radius 5 has area π × 25 = 78.54 square units.
If you have a different measurement
• Diameter d: the radius is d ÷ 2, or use A = π × d² ÷ 4 directly. A 10 cm circle has area 78.54 cm². • Circumference C: the radius is C ÷ (2π), or use A = C² ÷ (4π). The Circle Calculator on this site converts between all four measurements.
Units
The area is in the square of the unit you used for the radius: a radius in feet gives square feet, in meters gives square meters. To convert square inches to square feet divide by 144.
Common mistakes
Using the diameter in place of the radius makes the area four times too big. Forgetting to square the radius gives a number that is not an area at all. Rounding π to 3 understates the area by about 4.5%.
| Radius | Diameter | Area (πr²) |
|---|---|---|
| 1 | 2 | 3.14 |
| 2 | 4 | 12.57 |
| 3 | 6 | 28.27 |
| 5 | 10 | 78.54 |
| 6 | 12 | 113.1 |
| 10 | 20 | 314.16 |
| 12 | 24 | 452.39 |
How to use
Enter the radius. The default radius of 5 gives an area of 78.54 square units, and the drawing shows the matching diameter (10) and circumference (31.42). If you measured across the circle, enter half that distance. For a round patio 12 ft across, enter 6 to get 113.1 sq ft.
Frequently asked questions
What is the formula for the area of a circle?
A = πr², where r is the radius. For a radius of 3 m the area is π × 9 ≈ 28.27 m².
How do I find the area from the diameter?
Divide the diameter by 2 to get the radius and use A = πr², or use A = πd² ÷ 4. A 20-inch circle has an area of about 314.16 square inches.
How many square feet is a circle 10 feet across?
The radius is 5 ft, so the area is π × 25 ≈ 78.54 square feet.
Why is the area in square units?
Area measures a surface, so the unit is the length unit multiplied by itself. A radius in centimeters gives an area in square centimeters.
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Sources & references
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