Sector Perimeter Calculator

Introduction

Welcome to our Sector Perimeter Calculator! Now, you can quickly calculate the Perimeter of the Sector with high precision. A sector is a portion of a circle formed by an arc on the circle and the arc’s endpoints being connected to the center of the circle.

The simplest example of the sector certainly has to be a slice of a pizza or a slice of a cake, as seen from the top.

How to use the Sector Perimeter Calculator?

Using the Sector Perimeter Calculator, you can calculate the perimeter of the sector by inputting the circle’s radius value and the angle formed by the arc at the center of the circle.

The variables in the calculator include

Radius (r) The distance from the center to the circle.

Angle (θ) The angle made by the arc at the circle’s center.

Perimeter (P) We can calculate the perimeter of the circle using the following formula.

What is the Sector of the Circle?

A sector is a two-dimensional shape formed by an arc on the circle along with the radii, which are lines connecting the ends of the arc to the center of the circle.

The size of a sector is often described using the measure of the central angle formed by the two radii. The central angle is the included angle formed at the center of the circle, measured in degrees.

The semi-circle i.e. the sector with the central angle of 180 degrees, will have the largest possible area when compared to sectors with the same radius.

Moreover, some real-life examples of the sector include slices of pizza or cake.

The smaller area is called the minor sector when the arc forms a sector. Whereas, the larger area is called the major sector.

How is the Perimeter of the Sector Calculated?

We can calculate the Perimeter of the Sector by summing up two lengths of the sides as well as the arc length of the sector.

We can calculate the perimeter of the sector by using the following formula.

\begin{aligned} \text{Perimeter (P)} &= 2 \times \text{Radius + Arc Length}\\[10pt] &= 2 \times r + \bigg(\normalsize \dfrac{θ}{360} \times 2 \times \pi \times r\bigg) \\[10pt] \end{aligned}

Where,

r = Radius of the circle

θ = Angle made by the arc at the center of the circle

Examples

Given a Sector formed by an arc on a circle which makes an angle of 45 degrees at the center and the circle’s radius is 7cm. What is the Perimeter of the sector?

We can calculate the perimeter of the sector using the following formula.