Area of A Sector Calculator

Area of A Sector Calculator

Please provide any two values, and the calculator will calculate the sector area, central angle, radius, diameter, arc length, and chord length of any circle sector.

Note: Enter values in any two of the input fields to proceed.

Central angle

deg ▾

Radius

cm ▾

Diameter

cm ▾

Sector area (A)

cm² ▾

Arc length (L)

cm ▾

Chord length (c)

in ▾

An online area of a sector calculator is specifically programmed to find the area of the sector, the arc length, and chord length of a circle sector. This free calculator generates accurate outputs so you may not feel any difficulty during your calculations. But before we move further, let us make sure that you need to memorize some crucial terms which are as follows. Stay Focused!

What Is A Sector Of The Circle?

In the context of geometry:

“A specific figure that is bounded by an arc connecting with one end of two radii separately is called sector of a circle”

area of sector

In the following figure:

The curved line represents the arc of the sector
The two straight lines connected at right angle($\alpha$)to each other are called radii.
If we convert the arc into the straight line, we will be getting a chord of the circle.

The area of sector calculator finds all of the above mentioned values in a span of time to save your precious time.

Important Formulas:

Here we will be discussing some formulas that are used to find these geometrical terms. These include:

Area Of Sector Formula:

You can easily determine the area of a sector of a circle with the help of sector area formula given below:

$$ \text{Area Of Sector} = \alpha * r^{2} * 2 $$

Where:

$\alpha$ = angle of a sector

r = radius of the sector

Arc Length Formula:

You can use the following formula to determine the length of any arc of the sector:

$$ \text{Arc Length} = \theta * r $$

Chord Length Formula:

Below is the most optimized formula to determine the chord length of the sector of a circle.

$$ \text{Chord Length} = 2*r*sin\frac{\theta}{2} $$

Here if you ever get stuck during calculations of these quantities, try using the free online area of a sector calculator. You will always get accurate answers regarding each term that you wish to find.

How To Find The Area Of A Sector Of A Circle?

Let us solve a couple of examples to help you in better understanding of the concept.

Example # 01:

The radius of a circle sector is 3cm. The internal radii angle is $45\text^{o}$. How to find area of a sector?

Solution:

First we need to convert angle given in degrees to radians:

$$ \theta_{rad} = \frac{\text{Angle In Degrees} * π}{180} $$

$$ \theta_{rad} = \frac{45\text^{o} * 3.14}{180} $$

$$ \theta_{rad} = \frac{141.3}{180} $$

$$ \theta_{rad} = 0.785rad $$

Now using the area of a sector of a circle formula:

$$ \text{Area Of Sector} = \alpha * r^{2} * 2 $$

Putting the value given in the statement:

$$ \text{Area Of Sector} = 0.785 * \left(3\right)^{2} * 2 $$

$$ \text{Area Of Sector} = 0.785 * 9 * 2 $$

$$ \text{Area Of Sector} = 14.13 $$

$$ \text{Area Of Sector} = 14.13 cm^{2} $$

You can also get the same results with a free area of sector calculator in a glimpse of an eye to make your calculations more easy.

Example # 02:

What is the arc length of a circle constructed by radius of 4cm and angle of $90^\text{o}$?

Solution:

We know that:

$$ \theta_{rad} = \frac{\text{Angle In Degrees} * π}{180} $$

$$ \theta_{rad} = \frac{90^\text{o} * 3.14}{180} $$

$$ \theta_{rad} = \frac{3.14}{2} $$

$$ \theta_{rad} = 1.57rad $$

$$ \text{Arc Length} = 1.57rad * 4cm $$

$$ \text{Arc Length} = 6.28cm $$