# Perimeter of a Circle Formula

The perimeter of a circle formula is used to find the perimeter of a circle. The perimeter of a circle is its boundary or the complete arc length of the periphery of a circle. The term that denotes the perimeter of a circle is called its circumference. Hence the perimeter of a circle tells us about the circumference of a circle, therefore it is also known as the circumference of a circle formula. Let us learn more about the perimeter of the circle formula along with solved examples.

## What Is the Perimeter of a Circle Formula??

The perimeter of a circle formula has three components, 2 constants and one variable which is the radius of the circle. The formula to calculate the perimeter of a circle or circumference formula can be given as:

### Perimeter of Circle Formula

Perimeter of a circle = 2 π r = π D units

where,

- r = radius of the circle
- D = diameter of the circle.

## Examples on Perimeter of Circle Formula

Let us solve some interesting problems using the perimeter of circle formula.

**Example 1:** Using the perimeter of a circle formula, calculate the circumference of the circle with a diameter of 7 in (Use the value of π as 22/7)?

**Solution:**

To find: Perimeter of a circle

Given: Diameter of circle = 7 in

Using perimeter of a circle formula,

The perimeter of a circle = π D

Perimeter or circumference = 22/7 × 7

= 22 in

**Answer:** Perimeter of circle or circumference = 22 in.

**Example 2:** Using the perimeter of a circle formula, find the radius of the circle having a circumference of 110 in.

**Solution: **

To find: Radius of circle

Given: Circumference = 110 in

Using perimeter of a circle formula,

The perimeter of the circle or circumference = 2 π r

2 π r = 110

2 × 22/7 × r = 110

r = 110 × 7 / 44

r = 17.5

**Answer:** Radius of circle = 17.5 in.

**Example 3:** The radius of a circle is 7 in. Using the perimeter of a circle formula, calculate the circumference of the circle.

**Solution:**

To find: Perimeter of circle

Given: r = 7 in

The perimeter of circle formula = 2 π r

C = 2 × (22/7) × (7)

**Answer: **The circumference of a circle is 44 inches.

## FAQs on Perimeter of Circle Formula

### What Is the Perimeter of Circle Formula For a Semi-Circle?

Semi-circle means half of the full circle. It includes half of the circumference and the diameter of the circle. Hence if the perimeter of the circle formula is 2 π r, then the perimeter of the semi-circle is 1/2 (2πr) + d = (π r + d) units.

### What Is the Perimeter of Circle Formula When Diameter Is Given?

We know that the perimeter of circle formula = 2 π r and D = 2r. If the diameter is given, then the perimeter of circle formula = π d, where d is diameter and π is constant with value (3.14 or 22/7).

### What Is the Perimeter of Circle Formula When Radius Is Given?

The perimeter of circle formula when the radius is given is 2πr units, where r is radius and π is constant with value (3.14 or 22/7).

### How To Calculate Radius Using Perimeter of Circle Formula?

The perimeter of circle formula = 2πr units. If we know the value of the circumference or the perimeter of a circle, then by substituting the value in formula we can calculate radius. Therefore, R = (perimeter of circle)/ 2π.

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