Radius of a Circle Calculator

The radius is the fundamental distance from the exact center of a circle to any point on its outer boundary. Depending on your starting data, three primary geometric formulas govern this calculation:

1. From Diameter: The radius is simply half of the diameter. The formula is radius = diameter / 2.

2. From Circumference: Because circumference equals 2 multiplied by pi (π) and the radius, you isolate the radius by dividing the circumference by 2 times pi. The formula is radius = circumference / (2 * π).

3. From Area: Since the area of a circle is pi times the radius squared, you find the radius by taking the square root of the area divided by pi. The formula is radius = square_root(area / π).

Let us walk through a practical scenario where you are given a circle with a total surface area of 113.1 square units, and you need to determine its radius.

Step 1: Divide the given area by the mathematical constant pi (approximately 3.14159). 113.1 / 3.14159 = 36.0.

Step 2: Take the principal square root of that quotient to find the final radius dimension. The square root of 36.0 is 6. Therefore, the radius of the circle is exactly 6 units.

Always double-check which boundary measurement you are using, as confusing diameter with radius is the most common cause of calculation errors. When working with pi, utilize at least two decimal places (3.14) for everyday estimates, or use your calculator's native pi button for engineering-grade precision. Finally, remember that units matter—if your area is in square inches, your resulting radius will be in linear inches.