Circle Calculator
Area, circumference, diameter
About This Calculator
A circle is the set of all points equidistant from a center point. Its fundamental properties — radius, diameter, circumference, and area — all relate through the constant pi (≈ 3.14159). Circles appear throughout engineering, physics, and design.
Formula
Circumference = 2*pi*r = pi*d
Area = pi*r^2
Arc length = r*theta (theta in radians); Sector area = (1/2)*r^2*theta
Example Calculation
Circle with radius 7
- Circumference = 2 * pi * 7 = 2 * 3.14159 * 7 = 43.98
- Area = pi * 7^2 = 3.14159 * 49 = 153.94
Circumference = 43.98 units; Area = 153.94 sq units
Circle Measurements by Radius
| Radius | Diameter | Circumference | Area |
|---|---|---|---|
| 1 | 2 | 6.28 | 3.14 |
| 2 | 4 | 12.57 | 12.57 |
| 3 | 6 | 18.85 | 28.27 |
| 5 | 10 | 31.42 | 78.54 |
| 7 | 14 | 43.98 | 153.94 |
| 10 | 20 | 62.83 | 314.16 |
| 15 | 30 | 94.25 | 706.86 |
| 20 | 40 | 125.66 | 1256.64 |
Frequently Asked Questions
What is the difference between circumference and perimeter?
Perimeter is the general term for the total boundary length of any 2D shape. Circumference is the specific term for the perimeter of a circle or ellipse.
How do I find the radius from the area?
Rearrange Area = pi*r^2 to get r = sqrt(Area / pi). For example, if area = 50, then r = sqrt(50 / 3.14159) = sqrt(15.92) ≈ 3.99.
What is a radian?
A radian is the angle subtended at the center of a circle by an arc equal in length to the radius. A full circle = 2*pi radians = 360 degrees. 1 radian ≈ 57.3 degrees.