Sector Area Calculator

It's easy to calculate the size of a circle's specific sector using our sector area calculator.

The circumference of a circle's sectors, measured in square miles, is known as the sector area. The origin of a sector comes from the center of a circle. A circle's sector is the area encompassed by the circle's two radii and the arc connecting them. There are many other types of circles, but a semi-circle is the most frequent.

Since a circle has many sectors, its shape has been altered to reflect the reality that each sector is a small fraction of the whole circle. (Angle / 360) x (diameter / 2)² is another simple method to express the formula, however in many practical cases, calculating the diameter is simpler. This calculator offers a lot of additional useful features, like the ability to input radius in degrees. There's no doubt about the mathematical constant which is 3.14159. Let's take a closer look at the formula for calculating a sector's area in radius and degrees below.

Sector area calculation

The sector area of a circle is calculated using the formula shown below;

A = πr² × θ°/360

So,

A = area of the sector

π = 3.14159.

r= radius

θ° = angle at the center calculated in degrees

Sector area calculation is determined by two things; the radius and angle of the sector. The angle is 90° when the sector is quadrant. You may use a variety of instruments to measure angles, depending on the scenario at hand. The use of a protractor is sometimes necessary when calculating the sector area manually, however, this is not the case if you use our tool. Apply the formula above in our sector area calculator, then click the “Calculate Area of Sector” button and enter the circle's radius and the central angle in degrees. The results will be displayed on the sector area calculator according to the values you inputted.

An example is illustrated below,

You have an angle of 45° and 10m is the radius, let’s use the formula above to calculate;

Area = (45 / 360) x 3.14159 x 10² = 0.125 x 3.14159 x 100 = 39.27 square metres.

 

Calculating sector area using degrees

It is time to apply this formula and understand how to calculate an area of a circle sector in degrees by using the example below to illustrate the concept.

Example

A circle is split into three sectors with center angles of 100°, 100°, and 160⁰ formed by the radius accordingly. Let’s calculate the area of the three sectors.

First sector answer

Sector = [θ/360°] × πr² = [100°/360°] × [22/7] × 6² = [5/18] × [22/7 × 36] = 220/7 = 31.43 square units.

As with the previous sector, the second sector makes a similar angle (θ = 100°). The second sector's area is equivalent to the first sector's area. As a result, 31.43 square units make up the second sector's total area.

Third sector
sector = [θ/360°] × πr² = [160°/360°] × [22/7 × 6²] = [4/9 × 22/7 × 36] = 352/7 = 50.28 square units.

 

Calculating the Sector area in radian units

To calculate the area of a sector, whose angle is in radian units, the formula below is used;

Area of a sector = 1/2 × r² × θ

Where θ  = center angle,

r = radius.

Sector area in degrees format = (θ/360⁰) × πr² because it’s a portion of the circle. This means that the radian area of the sector is equal to (θ/2π) × πr². When this formula is further simplified we get the sector area as (θ/2) × r² or (1/2) × r²θ. Below is an example of how we can find the sector area in radian units.

Question; if you are given an angle at the center as 2π/3, and 6 units as the radius, how do you find the sector area?

Answer,

Sector area in radians = (θ/2) × r² so,

The sector area in radians = [2π (3×2)] × 6² = (π/3) × 36 = 12π].

So the sector area in radians = 12π.

 

The importance of sector area calculator in real life

When it comes to pizza measurement, the sector area calculator is very important. Pizza is an example in real life when it comes to calculating the sector area. All the slices of a pizza are shaped like a sector. Let’s use an example where a pizza is cut into 6 pieces with the same measurement, where 7 inches is the radius of the pizza and a sector is equal to a slice. Let’s calculate the area sector of each slice using the area sector formula. Note that because the pizza is cut into six slices that are of equal size, 60⁰ is the sector angle.

So, the pizzas’ slice area = (θ/360°) × πr² = (60°/360°) × (22/7) × 7² = 1/6 × 22 × 7 = 77/3 = 25.67 square units.

 

Summary

To accurately calculate sector area, it is vital to use the sector calculator. Use it for better results.