Radius of a Circle Calculator
Enter one of the following values to calculate the radius of a circle:
Understanding the Radius of a Circle
A circle is a fundamental shape in geometry, defined as the set of all points in a plane that are equidistant from a central point. This equidistant measure is what we call the radius. The radius (often denoted by 'r') is a crucial component in understanding and calculating various properties of a circle, such as its diameter, circumference, and area.
What is the Radius?
The radius of a circle is the distance from its center to any point on its boundary (circumference). It's essentially half the length of the circle's diameter. Understanding the radius is key to many mathematical and real-world applications, from engineering and architecture to art and design.
How to Calculate the Radius
The radius can be calculated if you know the circle's diameter, circumference, or area. Here are the formulas:
1. From Diameter (d)
The diameter is the distance across the circle passing through its center. It's twice the length of the radius. Therefore, if you know the diameter, the radius is simply half of it:
Radius (r) = Diameter (d) / 2
Example: If a circle has a diameter of 20 units, its radius would be 20 / 2 = 10 units.
2. From Circumference (C)
The circumference is the total distance around the circle. The relationship between circumference, radius, and the mathematical constant Pi (π ≈ 3.14159) is given by the formula C = 2πr. To find the radius from the circumference, you can rearrange this formula:
Radius (r) = Circumference (C) / (2 * π)
Example: If a circle has a circumference of 31.4159 units, its radius would be 31.4159 / (2 * 3.14159) = 5 units.
3. From Area (A)
The area of a circle is the space enclosed within its boundary. The formula for the area of a circle is A = πr². To find the radius from the area, you need to rearrange this formula and take the square root:
Radius (r) = √(Area (A) / π)
Example: If a circle has an area of 78.5398 square units, its radius would be √(78.5398 / 3.14159) = √25 = 5 units.
Using the Radius of a Circle Calculator
Our Radius of a Circle Calculator simplifies these calculations for you. Simply enter one of the known values (Diameter, Circumference, or Area) into the corresponding field. The calculator will automatically determine which input you've provided and apply the correct formula to give you the radius. You only need to fill in one field; leave the others blank.
- Diameter: Input the length of the diameter.
- Circumference: Input the total distance around the circle.
- Area: Input the total space enclosed by the circle.
Click "Calculate Radius" to see your result instantly. This tool is perfect for students, engineers, designers, or anyone needing quick and accurate circle radius calculations.