The radius of a circle is a fundamental measurement that extends from the center of the circle to any point on its circumference. Understanding the significance of the radius is essential to numerous geometric calculations and applications. Whether you're a student learning about circles or someone seeking quick calculations, our Radius of a Circle Calculator is designed to assist you in effortlessly determining this fundamental circle measurement.

What is the definition of the radius of a circle ?

The radius of a circle is the distance from its center to any point on the circumference. It is represented by the symbol 'r' in mathematical formulas.

How is the radius of a circle different from the diameter ?

The radius of a circle is half the length of the diameter. Mathematically, the diameter is equal to twice the radius (d = 2r).

Why is finding the radius important ?

Calculating the radius is essential for various mathematical and real-world applications, including geometry, physics, engineering, and design.

Formula

The formula to calculate the radius of a circle is:

`${\text{Radius}}_{}=\frac{{\text{circumference}}_{}}{{\text{2π}}_{}}$`

where

• Radius is the distance from the center to any point on the circumference
• Circumference is the distance from the center to any point on the circumference
• π is a mathematical constant approximately equal to 3.14159.

Examples:

Example 1:

Circumference : 20 units

`${\text{Radius}}_{}=\frac{{\text{20}}_{}}{{\text{2π}}_{}}$`

Example 2:

Circumference : 50 cm

`${\text{Radius}}_{}=\frac{{\text{50}}_{}}{{\text{2π}}_{}}$`

Example 3:

Circumference : 36 units

`${\text{Radius}}_{}=\frac{{\text{36}}_{}}{{\text{2π}}_{}}$`