Radius Formulas | List of Radius Formulas You Should Know - BYJUS

In a circle, the distance between the fixed point, the center, and any point on the boundary, the circumference, is always constant. This constant distance is known as the radius of the circle. In this article we will learn about the different formulas used to find the radius of a circle when the diameter, the circumference, and area are given....Read MoreRead Less

### What is the Radius of a Circle?

The radius of a circle is the distance between the fixed point(center) and any point on the circumference of the circle.

The radius can be easily calculated by considering half the length of the diameter of a circle.

### Formula to Find the Radius of a Circle

Formula for the Radius of a Circle, When the Diameter is Given:

Diameter = 2 $$\times$$ Radius

D = 2r

Hence, Radius, r = $$\frac{D}{2}$$

Formula for the Radius of a Circle, When the Circumference is Given:

Circumference C = 2 $$\times$$ π $$\times$$ Radius

C = 2πr

r = $$\frac{C}{2\pi}$$

Formula for the Radius of a Circle, When the Area is Given:

Area = π $$\times~\text{Radius}^2$$

A = π$$r^2$$

r = $$\sqrt{\frac{A}{\pi}}$$

### Solved Examples

Example 1: Find the radius of a circle if its diameter is 44 meters.

Solution:

The diameter of the circle is provided as, D= 44 m.

Radius of the circle is calculated by the formula,

Radius, r = $$\frac{D}{2}$$

= $$\frac{44}{2}$$

= 22 m

So, the radius of the circle is 22 meters.

Example 2: Find the radius of the circle, if the circumference is 66 inches.[Use π = $$\frac{22}{7}$$].

Solution:

The circumference of the circle is,  C = 66 in.

Radius of the circle is calculated using the formula,

r = $$\frac{C}{2\pi}$$

r = $$\frac{66\times 7}{22\times 2}$$

r = $$\frac{21}{2}$$

r = 10.5 in

So, the radius of the circle is 10.5 inches.

Example 3: Find the radius of the circle, if its area is 154 square yards.

Solution:

The area A of the given circle is stated as 154 square yards.

Radius of a circle is obtained by applying the formula,

r = $$\sqrt{\frac{A}{\pi}}$$

r = $$\sqrt{\frac{154\times 7}{22}}$$

r = $$\sqrt{7\times 7}$$

r = $$\sqrt{7^2}$$

r = 7 in.

So, the radius of the circle is 7 inches.

Example 4: Jacob has ordered pizza. After the pizza was delivered he read that the pizza has an area of 49 square centimeters. Now he wants to calculate the length of the boundary of the pizza. Can you help him?(Use = $$\frac{22}{7}$$)

Solution:

Area of the pizza is stated in the question as, A = 49$$\pi cm^2$$

Radius of the circle is calculated by the formula,

r = $$\sqrt{\frac{A}{\pi}}$$

r = $$\sqrt{\frac{49\pi}{\pi}}$$

r = $$\sqrt{49}$$

r = 7 cm

Hence, the radius of the pizza is 7 centimeters.

Circumference of the pizza, C = 2πr

C = $$2\times \frac{22}{7}\times 7$$

C = 22 $$\times$$ 2

C = 44 cm

So, the length of the boundary of the pizza is 44 centimeters.