Introduction to Area of a Sector
Area of a sector is the number of square in order to fill a sector of a circle. The area of sector is proportional to the central angle.
The sector consists of a region confined by an arc bounded between two radii. If its central angle is bigger, the area of the sector will also be larger accordingly.
Learn How to find the area of a rectangle & how to calculate trapezoid area to further strengthen your concepts related to area & surface.
Area of Sector formula in Central Angle
Area of sector is used to measure the central angle (θ) in degrees. As, the area of a circle=r2 and the angle of a full circle = 360°
Thus, the formula of the area of a sector of a circle is:
$$\frac{\text{Area of Sector}}{\text{Area of Circle}}\;=\;\frac{Central\;Angle}{360°}$$
$$\frac{Area\;of\;Sector}{πr^2}\;=\;\frac{0}{360°}$$
$$\text{Area of Sector}\;=\;\frac{0}{360°} * πr^2 $$
By using this formula we can find third values if the other two values are given.
Area of Sector formula in Radian
To measure the angle of a circle in radians, the area of a sector of a circle is
$$\frac{Area\;of\;Sector}{Area\;of\;Circle}\;=\;\frac{Central\;Angle}{2π}$$
$$\frac{Area\;of\;Sector}{πr^2}\;=\;\frac{θ}{2π}$$
$$\text{Area of Sector}\;=\;\frac{θ}{2π} * πr^2 $$
$$\text{Area of Sector}\;=\;\frac{1}{2} * θr^2 $$
Click on to learn more about similar math concepts of cubic feet & pythagorean theorem.
Semicircle Area formula
To know the area of the half of a circle, this formula will be applicable.
$$\text{Semicircle area}\;=\;\frac{πr^2}{2} $$
Divide the area of the circle by 2.
Quadrant Area formula
To know the area of a quarter of a circle, this formula will be applied.
$$\text{Quadrant area}\;=\;\frac{πr^2}{4} $$
Use our Quadratic formula calculator & Distance formula calculator to learn other math related formulas & their calculations.
How to find the area of the shaded region?
In the first figure, shaded area covers half the circle. So the area will be ½ multiplied by πr2. In the 2nd figure, the area of the shaded part will be ¼ πr2.
In the last figure the angle is 30 degrees so area of the sector will be 30/360. In this equation, πr2 is the area of the circle whereas 30/360 tells us how much of the circle is covered.
The area of sector will be θ/360° * πr2. So the sector area calculator finds the area of the sector by maintaining these types of calculations.
This is how we can find the area of the shaded region. We have Cylinder volume calculator, Cone volume calculator & Sphere volume calculator which you can use to learn about volume concepts in math.
What is Area of Sector Calculator?
Sometimes it becomes difficult to get sector area manually on paper. Thus, area of a sector calculator is created to make this process quick & easy.
Our area of a sector calculator can be used to find sector area of a pizza, dress, land or whatever you want. Apart from that it is helpful in mathematical geometry problems etc.
How to use Area of a Sector Calculator?
Our area of a sector calculator is flexible and reliable. You can get your required area of the section by just putting radius value and angle. Click on "Calculate" button to get results instantly.
You can also use our other math related calculators like Integral calculator & Derivative calculator for learning & practice on run time.
Hopefully you've liked our sector area calculator. Please provide your valuable feedback so that we could improve further.