Area of a Circular Segment
Area of a Circular Segment
\[A = \frac{r^2}{2}\left(\theta-\sin\theta\right)\]
Variables
A = circular segment area (m²)
r = radius (m)
theta = central angle (rad)
Description
What is this formula?
This formula calculates the area of a circular segment using the radius and the central angle measured in radians. A circular segment is the region bounded by a chord and its corresponding arc.
When to use it
Use this formula when the area enclosed between a chord and an arc of a circle needs to be determined.
Example
If the radius is 5 m and the central angle is 1.8 rad:
A = (5²/2)(1.8 - sin(1.8)) = 10.128 m²
Applications
- Geometry and trigonometry
- Engineering and design
- Structural and architectural calculations
- CAD and technical drawing
- Circular tank and pipe analysis
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