Area of a Circle Calculator
Calculate the area, circumference, and diameter of a circle from its radius, diameter, or circumference. See also Area of Ellipse Calculator and Area of Sector Calculator.
How to Calculate the Area of a Circle
To find the area of a circle, measure the radius — the distance from the center to any point on the edge. Square the radius and multiply by π (pi ≈ 3.14159). If you know the diameter instead, divide it by 2 to get the radius first. If you know the circumference, divide by 2π to find the radius. This calculator handles all three input types automatically.
Circle Area Formula
A = π × r²
A = π × (d/2)² = π × d² / 4
A = C² / (4π)
Circumference: C = 2πr
Diameter: d = 2r
Example
Find the area of a circle with radius 5:
A = π × r²
A = π × 5²
A = π × 25
A ≈ 78.5398 square units
Circle Area Conversion Table
| Radius | Area | Circumference | Diameter |
|---|---|---|---|
| 1 | 3.1416 | 6.2832 | 2 |
| 2 | 12.5664 | 12.5664 | 4 |
| 3 | 28.2743 | 18.8496 | 6 |
| 4 | 50.2655 | 25.1327 | 8 |
| 5 | 78.5398 | 31.4159 | 10 |
| 6 | 113.0973 | 37.6991 | 12 |
| 7 | 153.9380 | 43.9823 | 14 |
| 8 | 201.0619 | 50.2655 | 16 |
| 9 | 254.4690 | 56.5487 | 18 |
| 10 | 314.1593 | 62.8319 | 20 |
| 15 | 706.8583 | 94.2478 | 30 |
| 20 | 1256.6371 | 125.6637 | 40 |
| 25 | 1963.4954 | 157.0796 | 50 |
| 50 | 7853.9816 | 314.1593 | 100 |
| 100 | 31415.9265 | 628.3185 | 200 |
Frequently Asked Questions
What is the area of a circle?
The area of a circle is the total space enclosed within its boundary (circumference). It is measured in square units and calculated using the formula A = πr², where r is the radius.
How do I find the area if I only know the diameter?
Divide the diameter by 2 to get the radius, then use A = πr². Alternatively, use A = πd²/4 directly. For example, a circle with diameter 10 has area = π × 25 ≈ 78.54.
What is the value of π (pi)?
Pi (π) is approximately 3.14159265358979. It is the ratio of a circle's circumference to its diameter and is an irrational number — its decimal representation never ends or repeats.
Can I calculate the area from the circumference?
Yes. From the circumference C, find the radius as r = C/(2π), then compute A = πr². This simplifies to A = C²/(4π).
What units is the area in?
The area is in square units of whatever unit the radius is in. If the radius is in centimeters, the area is in square centimeters (cm²). If in meters, the area is in square meters (m²).