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.
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This calculator finds the area of a sector when the radius (or diameter) and the angle are known.
A sector is a section (or part) of a circle.
Sectors have central angles and radius values which we can use to find the area.
In the image above you can see the light brown sector of the circle (called a minor sector) with a central angle of θ°
There is also a larger white sector (called a major sector) which has a central angle of (360 - θ)°
Sectors can have any central angle of up to 360°
The central angle can also be measured in radians - when it is measured in radians, the angle can be any value up to 2π radians.
When the central angle is measured in radians, the formula for the area is slightly different.
The area of a sector of a circle where the central angle is in degrees is: \[ A = {\theta \over 360} \pi r^2 \]
The area of a sector of a circle where the central angle is in radians is: \[ A = {\theta \over 2} r^2 \]
where θ is the central angle and r is the radius of the circle.
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: \[ A = 36.1 \; cm^2 \; to \; 1 \; decimal \; place \]
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: \[ A = 45.4 \; in^2 \; to \; 1 \; decimal \; place \]
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: \[ A = 223.6 \; cm^2 \; to \; 1 \; decimal \; place \]
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: \[ A = 320 \; m^2 \]
We have created some worksheets to help you practice this skill.
The first and second sheets involve working out the area of different sectors where the angle is measured in degrees.
Sheet 3 involves finding the area of different sectors where the angle is measured in radians.
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