Circle Calculator
Input the radius, circumference, or area of a circle, and the tool will compute the other two parameters instantly.
Calculate the Radius, Circumference, and Area of a Circle
Radius
Circumference
Area
Basic Properties of a Circle
A circle has three key attributes: radius (\( r \)), circumference (\( C \)), and area (\( A \)). These attributes are mathematically related as follows:
Circumference and Radius Relation: \( C = 2\pi r \)
Area and Radius Relation: \( A = \pi r^2 \) All calculations for a circle are derived from these two fundamental formulas.
How to Calculate?
If you know one parameter of the circle, here's how you can calculate the others:
If Radius (\( r \)) Is Known
- Circumference: \( C = 2\pi r \)
- Area: \( A = \pi r^2 \)
If Circumference (\( C \)) Is Known
- Radius: \( r = \frac{C}{2\pi} \)
- Area: \( A = \pi \left(\frac{C}{2\pi}\right)^2 = \frac{C^2}{4\pi} \)
If Area (\( A \)) Is Known
- Radius: \( r = \sqrt{\frac{A}{\pi}} \)
- Circumference: \( C = 2\pi \sqrt{\frac{A}{\pi}} = 2 \sqrt{\pi A} \)
Examples
Example 1: Given the radius \( r = 7 \), find the circumference and area of the circle.
Solution:
Circumference:
\( C = 2\pi \times 7 \approx 43.98 \)
Area:
\( A = \pi \times 7^2 \approx 153.94 \)
Result: The circumference is approximately \( 43.98 \), and the area is approximately \( 153.94 \).
Example 2: Given the circumference \( C = 31.42 \), find the radius and area of the circle.
Solution:
Radius:
\( r = \frac{31.42}{2\pi} \approx 5 \)
Area:
\( A = \pi \times 5^2 = 78.54 \)
Result: The radius is \( 5 \), and the area is approximately \( 78.54 \).