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# Calculate The Area Of A Circular Segment

Last updated: Saturday, April 29, 2023
Select a type of segment below
Circular Segment
Elliptical Segment

The area of a circular segment is the region bounded by a chord and the arc of a circle. It can be calculated by subtracting the area of the triangle formed by the two radii and the chord from the area of the sector formed by the same two radii and the arc.

The area of a circular segment has practical applications in geometry, physics, and engineering. For example, the segment area can be used to calculate the volume of certain shapes such as a frustum (a truncated cone or pyramid). It can also be used in optics to calculate the area of a lens or mirror, which can help determine their optical properties. Additionally, it has applications in the design of gears and pulleys, as the area of the segment is related to the amount of torque that can be transmitted through the gear or pulley.

The formula for determining the area of a circular segment is defined as:
$$A$$ $$=$$ $$r^2$$ $$\cdot$$ $$\Big(\dfrac{\theta \cdot \pi}{360^\circ}$$ $$-$$ $$\dfrac{\sin(\theta)}{2}\Big)$$
$$A$$: the area of the segment
$$\theta$$: The angle of the sector
$$r$$: the radius of the circle
$$\pi$$: A mathematical constant with an infinite decimal tail
The SI unit of area is: $$square \text{ } meter\text{ }(m^2)$$

## Find $$A$$

Use this calculator to determine the area of a segment when the length of its radius and the angle of the corresponding sector is given.
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The angle of the sector
$$\theta$$
$$degree$$
$$r$$
$$meter$$
$$\pi$$ : A mathematical constant with an infinite decimal tail