Circle Segment 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.

A segment of a circle is a part of a circle limited by an arc and a chord pulling it together.

A circle segment is a region bounded by an arc and a chord of a circle. The area of a circle segment is the area of the corresponding sector minus the area of the triangle formed by the radii and the chord. To find the area of a circle segment, you need to know the radius of the circle and the length of the chord. This circle segment area calculator makes it easy to find the area of a circle segment.

Circle Segment Area Formulas

There are two formulas that can be used to find the area of a circle segment. The first formula uses the central angle of the segment, while the second formula uses the length of the chord and the radius of the circle. The formulas are:

• S = \dfrac{R^2}{2}\left(\pi \dfrac{\alpha^o}{180^o}-sin(\alpha)\right)
• S = \dfrac{R^2}{2}(\alpha - sin(\alpha))

How to Use the Circle Segment Area Calculator

Using this calculator is easy. Just follow these steps:

1. Enter the radius of the circle in the first box.
2. Enter the central angle in the second box.
3. Our calculator will automatically give you the answer.

Circle Segment Area Example

For example, let's say you have a circle with a radius of 5 units and a chord length of 8 units. To find the area of the corresponding circle segment, use the following steps:

1. Enter the value 8 in the `Radius` box.
2. Enter the value 60 in the `Central angle` box.
3. You will get the area of the circle segment, which is 2.2647 units².

Conclusion

Calculating the area of a circle segment is important in many fields, including mathematics, engineering, and physics. With this easy-to-use circle segment area calculator and formulas, you can quickly find the area of any circle segment. Try it out for yourself!