Circle Sector Area Calculator

Area is a numerical characteristic of a two-dimensional (flat or curved) geometric figure, informally speaking, showing the size of this figure. Historically, the calculation of the area was called quadrature. A figure having an area is called quadratic. Find the area of more than 22 shapes (triangle, square, pentagon, etc.) using our amazing calculator.

Sector — in geometry is a part of a circle bounded by an arc and two radii connecting the ends of the curve with the center of the circle.

A circle sector is a portion of a circle enclosed by two radii and an arc. Finding the area of a circle sector is an important skill in geometry. This calculator and formula make it easy to find the area of your circle sector.

Circle Sector Area Formula

The formula for finding the area of a circle sector is:

S = \pi *R^2* \dfrac{\alpha^o}{360^o}

Where S is the area, α is the central angle of the sector in degrees, π is pi (3.14), and R is the radius of the circle.

How to Use the Circle Sector Area Calculator

Our circle sector area calculator makes it easy to find the area of your sector. To use the calculator:

1. Select the method you want to use to calculate the area (through the corner or through the arc length).
2. Enter the required values, such as the radius and central angle or arc length, in the corresponding input boxes.
3. That's all, our calculator will instantly do all calculations and provide the answer with formula.

How to Find Circle Sector Area

You can find the area of a circle sector using two different methods:

Method 1: Through the Corner of the Sector

If you know the radius and the central angle of the sector in degrees, you can use the following formula to find the area:

S = \pi *R^2* \dfrac{\alpha^o}{360^o}

Where α is the central angle of the sector in degrees, π is pi (3.14), and R is the radius of the circle.

Method 2: Through the Arc Length of the Sector

If you know the radius and the length of the arc that forms the sector, you can use the following formula to find the area:

S = \dfrac{1}{2}*l*R

Where l is the length of the arc and R is the radius of the circle.

Circle Sector Area Examples

Here are some examples of finding the area of a circle sector using the formulas:

Example 1

Find the area of a circle sector with a radius of 5 cm and a central angle of 60 degrees.

S = \pi *R^2* \dfrac{\alpha^o}{360^o}

S = \pi *5^2* \dfrac{60^o}{360^o}

S = 4.14 cm^2

Example 2

Find the area of a circle sector with a radius of 7 cm and an arc length of 4 cm.

S = \dfrac{1}{2}*l*R

S = \dfrac{1}{2}*4*7

S = 14 cm^2

Conclusion

Calculating the area of a circle sector is an important skill in geometry. Our circle sector area calculator and formulas make it easy to find the area of your sector. Try it out for yourself and see how easy it can be!