Calculate the properties of circular segments with ease using our Segment of Circle Calculator.
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A circular segment is a region bounded by an arc and a chord within a circle. It is essentially a slice of the circle between two points on the circumference connected by a straight line. The area of a circular segment can be calculated by subtracting the area of an isosceles triangle from the area of a sector. The central angle of the segment determines the shape and size of the segment.
- Area of shaded part = r2 * (a – sin(a)) / 2
- arc length of shaded part = r * a
- The perimeter of the segment = r * a + chord length
( Note: unit of arc angle is radian )
Properties of Circular Segments
Before we dive into the calculations, let’s explore some key properties of circular segments:
- Chord: The chord is the straight line connecting the two endpoints of the circular segment.
- Arc: The arc is the curved portion of the circle that bounds the segment.
- Central Angle: The central angle is the angle subtended by the segment at the center of the circle.
- Segment Height: The segment height is the perpendicular distance between the chord and the center of the circle.
- Radius: The radius is the distance between the center of the circle and any point on its circumference.
The Complete Circular Arc Calculator
To simplify the process of calculating the area of a circular segment, we have developed the Segment of Circle Calculator. This calculator allows you to input the radius and central angle of the segment and provides you with the area of the segment instantly. Let’s take a closer look at how to use this calculator effectively.
Using the Segment of Circle Calculator
The Segment of Circle Calculator is an intuitive tool that streamlines the calculation process. Follow these steps to calculate the area of a circular segment:
- Input: Enter the radius of the circle and the central angle of the segment in degrees.
- Calculate: Click the “Calculate” button to obtain the area of the segment instantly.
- Results: The calculator will display the area of the segment in square units.
It’s that simple! The Segment of Circle Calculator saves you time and effort, allowing you to focus on understanding the concepts and applications of circular segments. Let’s explore some examples to see the calculator in action.
Examples: Calculating the Area of Circular Segments
To illustrate the usage of the Segment of Circle Calculator, let’s consider a few examples:
Example 1: Small Circular Segment
Suppose we have a circle with a radius of 5 units and a central angle of 60 degrees. Using the Segment of Circle Calculator, we find that the area of the segment is approximately 3.82 square units.
Example 2: Large Circular Segment
Consider a circle with a radius of 10 units and a central angle of 120 degrees. By inputting these values into the calculator, we determine that the area of the segment is approximately 17.77 square units.
Example 3: Full Circle
In the case of a full circle, where the central angle is 360 degrees, the segment becomes the entire circle itself. The area of the segment is then equal to the area of the entire circle, which can be calculated using the formula A = πr^2, where r is the radius of the circle.
Formulas for Calculating Circular Segment Areas
While the Segment of Circle Calculator simplifies the calculation process, it’s essential to understand the underlying formulas. Here are the formulas for calculating circular segment areas:
- Area of Circular Segment: A = (R^2 / 2) * (θ – sin(θ)), where R is the radius of the circle and θ is the central angle in radians.
- Area of Circular Segment (Alternative): A = (R^2 / 2) * ((π / 180) * θ – sin((π / 180) * θ)), where R is the radius of the circle and θ is the central angle in degrees.
These formulas allow you to calculate the area of a circular segment manually if needed. However, we recommend using the Segment of Circle Calculator for convenience and accuracy.
Remember that circular segments play a crucial role in geometry and have numerous real-world applications. By utilizing the calculator and understanding the underlying formulas, you can confidently solve problems related to circular segments.