# Sector Area Calculator

Get easy calculation with Sector Area Calculator your go-to tool for effortlessly calculating the area of sectors! Sectors are fundamental components of circles, and understanding their area is crucial in geometry. Whether you're a student exploring geometric concepts or someone seeking a quick solution for practical applications, our Sector Area Calculator is designed with simplicity and accuracy in mind.

### What is a sector ?

A sector is a portion of a circle enclosed by two radii and an arc. Understanding the area of a sector is essential in geometry and real-world scenarios where circular shapes play a role.aces.

### Why calculate the sector area ?

Calculating the sector area is vital in various fields such as engineering, physics, and architecture. It provides insights into proportions, helping in design an

### Formula

The formula for calculating the area of a sector is straightforward:

`${\text{Sector Area}}_{}=\frac{{\text{Central Angle}}_{}}{{\text{360}}_{}}×\pi {r}^{2}$`

where:

π is the mathematical constant (approximately 3.14159)

r is the radius of the circle

Central Angle is the angle subtended by the sector at the center of the circle.

### Examples:

Example 1:

Consider a circle with a radius of 8 units and a central angle of 60 degrees.

Using the formula:

`${\text{Sector Area}}_{}=\frac{{\text{Central Angle}}_{}}{{\text{360}}_{}}×\pi ×{r}^{2}$`

`${\text{Sector Area}}_{}=\frac{{\text{60}}_{}}{{\text{360}}_{}}×\pi ×{8}^{2}$`

`${\text{Sector Area}}_{}=\frac{{\text{1}}_{}}{{\text{6}}_{}}×\pi ×{\mathrm{64}}^{}$`

`${\text{Sector Area}}_{}=\mathrm{33.5103}\phantom{\rule{0.2em}{0ex}}\text{units²}$`

Example 2:

For a circle with a radius of 12 units and a central angle of 120 degrees.

Using the formula:

`${\text{Sector Area}}_{}=\frac{{\text{Central Angle}}_{}}{{\text{360}}_{}}×\pi ×{r}^{2}$`

`${\text{Sector Area}}_{}=\frac{{\text{120}}_{}}{{\text{360}}_{}}×\pi ×{\mathrm{12}}^{2}$`

`${\text{Sector Area}}_{}=\frac{{\text{1}}_{}}{{\text{3}}_{}}×\pi ×{\mathrm{144}}^{}$`

`${\text{Sector Area}}_{}=\mathrm{150.7964}\phantom{\rule{0.2em}{0ex}}\text{units²}$`

Example 3:

Let's explore a scenario where the central angle is the full circle 360 degrees and radius is 10 units.

Using the formula:

`${\text{Sector Area}}_{}=\frac{{\text{Central Angle}}_{}}{{\text{360}}_{}}×\pi ×{r}^{2}$`

`${\text{Sector Area}}_{}=\pi ×{\mathrm{10}}^{2}$`

`${\text{Sector Area}}_{}=\frac{}{}×\pi ×{\mathrm{100}}^{}$`

`${\text{Sector Area}}_{}=\mathrm{134.16}\phantom{\rule{0.2em}{0ex}}\text{units²}$`