Area of a sector of a circle calculator

\[ A = {\theta \over 360} \pi r^2 \] 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: \[ A = {2 {1 \over 2} \over 2} \cdot 16^2 = {2 {1 \over 2} \over 2} \cdot 256 = 320 \]

How to Use the Area of a sector Calculator?

The procedure to use the area of a sector calculator is as follows:

Step 1: Enter the arc length and theta value in the input field

Step 2: Now click the button “Calculate” to get the area of a sector 

Step 3: Finally, the area of a sector will be displayed in the output field

What is Meant by Area of a sector?

In mathematics, the area of a sector is proportional to the arc length. It is also known as the sector area. Generally, the sector is defined as the part of a circle, which is enclosed by the two radii and the intercepted arc. In other words, the sector is the pie-shaped part of the circle. Thus, the

If the perimeter is needed, add together the lengths of

The formula for the area of a sector is (angle / 360) x π x radius2. The figure below illustrates the measurement:

As you can easily see, it is quite similar to that of a circle, but modified to account for the fact that a sector is just a part of a circle. Measuring the diameter is easier in many practical situations, so another convenient way to write the formula is (angle / 360) x π x (diameter / 2)2. The radius can be expressed as either degrees or radians, with our area of a sector calculator accepting only degrees for now (let us know if it would help you if it supported radians as well). π is, of course, the mathematical constant equal to about 3.14159.

    Area of a Sector calculation

You need to measure or know two things: the sector's radius and its angle. If the sector is a quadrant, then the angle is 90°. There are different tools for measuring angles, depending on your particular situation. A protractor can be useful in many cases.

After you have obtained the measurements, just apply the formula above or use our sector calculator as an easier and faster alternative.

    Example: find the area of a sector

As established, the only two measurements needed to calculate the area of a sector are its angle and radius. For example, if the angle is 45° and the radius 10 inches, the area is (45 / 360) x 3.14159 x 102 = 0.125 x 3.14159 x 100 = 39.27 square inches.

Calculate the area of a sector using the central angle and radius below and learn the formula and steps to solve it below.

Central Angle (θ):

Radius (r):

Diameter:

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Results:

Sector Area

Arc Length (s)

Chord Length (a)

Learn how we calculated this below

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How to Calculate Sector Area

A sector is a pie-slice shaped portion of a circle surrounded by two radii edges and bounded by the circle’s outer arc.

To calculate the area of a sector, a simple formula can be used.

Sector Area Formula

The area of a sector can be found using the formula:

sector area = r² × θ / 2

Thus, a sector’s area is equal to the radius r squared times the central angle θ in radians, divided by 2.

How do you calculate the area of a sector of a circle?

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How do you find the area of an arc?