Area of Circle Calculator: Formula & Examples

This calculator works out the area of a circle from its radius, diameter, or circumference. You enter one known measurement (in any unit), and it returns the area in square units, along with the other two measurements for reference. The calculation uses the standard formula A = πr², and the tool handles the unit conversions for you.

Formula

The area of a circle is given by the formula:

A = π × r²

Where:

• A = area of the circle (square units, e.g., m², ft², cm²)
• Ï€ (pi) ≈ 3.14159, a mathematical constant
• r = radius of the circle (linear units, e.g., m, ft, cm)

If you know the diameter (d) instead of the radius, use A = π × (d/2)². If you know the circumference (C), use A = C² / (4π).

Worked Example

Using the default values from the calculator above (radius = 5 m):

1. Start with the formula: A = π × r²
2. Substitute r = 5 m: A = π × (5)²
3. Square the radius: (5)² = 25
4. Multiply by π: 25 × 3.14159 ≈ 78.54

The area is 78.54 m², which matches the calculator’s output. The circumference is 2 × Ï€ × 5 ≈ 31.42 m, and the diameter is 10 m.

When to Use This Calculator

You might need the area of a circle for many everyday tasks:

• Finding the amount of fabric, grass seed, or paint needed for a circular surface.
• Calculating the cross-sectional area of a pipe or wire (for flow or electrical purposes).
• Determining the size of a circular garden bed, pond, or tablecloth.
• Working out the area of a pizza or cake to compare sizes (a 12-inch pizza has about 113 in², while two 8-inch pizzas total about 100 in²).

The calculator accepts any unit you choose—meters, feet, inches, etc.—and returns the area in that unit squared. Just be consistent: if you enter the radius in inches, the area comes out in square inches.

How to Read the Result

The main output is the area in square units. For example:

• Radius 5 m → area 78.54 m² (about 845 ft²).
• Radius 10 cm → area 314.16 cm² (about 48.7 in²).
• Diameter 2 ft → radius 1 ft → area 3.14 ft².

If you need a different unit, convert the radius first (e.g., 1 m = 3.28084 ft) or convert the final area (1 m² = 10.7639 ft²). The calculator does not convert between units automatically—it only uses the unit you type in.

Common Mistakes and Misconceptions

• Using diameter instead of radius: The formula uses radius. If you have the diameter, halve it first. Using the diameter directly gives an area four times too large.
• Forgetting to square the radius: A common error is multiplying Ï€ × r instead of Ï€ × r². For r=5, π×5 ≈ 15.7, but the correct area is 78.54.
• Unit mix-ups: If you measure the radius in meters and the area in square feet, you must convert. 1 m = 3.28084 ft, so 1 m² = 10.7639 ft².
• Rounding too early: If you round Ï€ to 3.14, the result is slightly off. Use 3.14159 or the calculator’s built-in Ï€ for accuracy.

Limitations of the Formula

The formula A = πr² is exact for a perfect Euclidean circle. In the real world, most “circles� are not perfect—a pond, a table, or a garden bed may have slight irregularities. For such shapes, the formula gives a close approximation, but not an exact measurement. If you need a precise area for an irregular shape, consider using a grid method or a planimeter.

Also, the calculator assumes the radius is positive. A negative radius makes no geometric sense, so the input minimum is set to 0. For extremely large or small circles, the result may be displayed in scientific notation (e.g., 3.14e+6 for 3,140,000 m²).

Frequently Asked Questions

How do I find the area of a circle if I only know the diameter?

Divide the diameter by 2 to get the radius, then use A = πr². For example, a circle with a diameter of 10 cm has a radius of 5 cm, so the area is π × 25 ≈ 78.54 cm².

Can I use this calculator for a semicircle or quarter circle?

Yes. First calculate the full circle area, then multiply by 0.5 for a semicircle or 0.25 for a quarter circle. The calculator gives the full area, so you do the extra step manually.

What is the formula for the area of a circle in terms of circumference?

If you know the circumference C, the area is A = C² / (4π). For example, a circumference of 31.42 m gives an area of (31.42²) / (4π) ≈ 78.54 m².

Why is pi (Ï€) approximately 3.14?

Pi is the ratio of a circle’s circumference to its diameter, and it is an irrational number—its decimal representation never ends or repeats. 3.14 is a common approximation, but 3.14159 is more accurate. The calculator uses the built-in Ï€ value for precision.

Does the area change if I use inches instead of centimeters?

Yes, the numeric value changes because the units are different. A radius of 1 inch gives an area of π in² ≈ 3.14 in², while a radius of 1 cm gives π cm² ≈ 3.14 cm². The actual physical area is the same if the lengths are equal (1 inch = 2.54 cm), but the numbers differ because the units differ.

How do I calculate the area of a circle with a radius in feet and get the answer in square yards?

First compute the area in square feet (A = πr²). Then divide by 9, because 1 square yard = 9 square feet. For example, a radius of 3 ft gives an area of π × 9 ≈ 28.27 ft², which is about 3.14 yd².

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in r | Radius | m | 5 | 0
out area | Area | m² | pi * r^2 | 2
out circ | Circumference | m | 2 * pi * r | 2
out diam | Diameter | m | 2 * r | 2