# Area of a Sector Calculator

Welcome to our Area of a Sector Calculator page.

We explain how to find the area of a sector and provide a quick calculator to work it out for you step-by-step.

There are also some worked examples and worksheets to help you practice this skill.

### Area of a Sector Calculator

Area of a Sector Calculator

### Area of a Sector Examples

#### Area of a Sector Example 1

Find the area of the sector below to 1 decimal place.

The sector has a central angle of 115° and a radius of 6 cm.

The area of a sector:

$A = {\theta \over 360} \pi r^2$ where A is the area, θ is the central angle and r is the radius of the circle.

So if we substitute the values of the angle and radius into this equation, we get: $A = {115 \over 360} \pi \cdot 6^2 = {115 \over 360} \pi \cdot 36 = {23 \over 2} \pi$

This gives us a final answer of: $A = 36.1 \; cm^2 \; to \; 1 \; decimal \; place$

#### Area of a Sector Example 2

Find the area of the sector below to 1 decimal place.

The sector has a central angle of 72° and a radius of 8 ½ in.

The area of a sector:

$A = {\theta \over 360} \pi r^2$ where A is the area, θ is the central angle and r is the radius of the circle.

So if we substitute the values of the angle and radius into this equation, we get: $A = {72 \over 360} \pi \cdot (8 {1 \over 2})^2 = {72 \over 360} \pi \cdot {289 \over 4} = {289 \over 20} \pi$

This gives us a final answer of: $A = 45.4 \; in^2 \; to \; 1 \; decimal \; place$

#### Area of a Sector Example 3

Find the area of the sector below, giving your answer to 1 decimal places.

The sector has a central angle of 278° and a radius of 9.6 cm.

The area of a sector:

$A = {\theta \over 360} \pi r^2$ where A is the area, θ is the central angle and r is the radius of the circle.

So if we substitute the values of the angle and radius into this equation, we get: $A = {278 \over 360} \pi \cdot (9.6)^2 = {278 \over 360} \pi \cdot 92.16 = 71.168 \pi$

This gives us a final answer of: $A = 223.6 \; cm^2 \; to \; 1 \; decimal \; place$

#### Area of a Sector Example 4

Find the area of the sector below, where the angle is in radians.

The sector has a central angle of 2 ½ radians and a radius of 16 m.

The area of a sector, where the angle is in radians, is:

$A = {\theta \over 2} r^2$ where A is the area, θ is the central angle and r is the radius of the circle.

So if we substitute the values of the angle and radius into this equation, we get: $A = {2 {1 \over 2} \over 2} \cdot 16^2 = {2 {1 \over 2} \over 2} \cdot 256 = 320$

This gives us a final answer of: $A = 320 \; m^2$

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