Circular Segment Area Calculator
A circular segment is a region of a circle cut off from the rest of the circle by a chord. It's the area between the chord and the arc. Use this calculator to find the area of such a segment by providing the circle's radius and the central angle subtended by the arc.
Enter the radius of the circle (e.g., 10)
Enter the central angle in degrees (e.g., 60)
A circular segment is a region of a circle cut off from the rest of the circle by a chord. It's the area between the chord and the arc. Use this calculator to find the area of such a segment by providing the circle's radius and the central angle subtended by the arc.
The area of a circular segment is calculated using the formula: Area = r² * (θ - sin(θ)) / 2 Where: 'r' is the radius of the circle. 'θ' (theta) is the central angle in radians.
Imagine a circle with a radius of 10 cm. If a chord cuts off a segment with a central angle of 60 degrees, what is the area of that segment? First, convert 60 degrees to radians: 60 * (π / 180) = π/3 radians. Then, apply the formula: Area = 10² * (π/3 - sin(π/3)) / 2 Area = 100 * (1.0472 - 0.8660) / 2 Area = 100 * (0.1812) / 2 Area = 9.06 cm² Our calculator will do this for you in seconds!
A circular segment is the area of a circle that is 'cut off' from the rest of the circle by a chord. It's the region bounded by the chord and the arc it subtends. Think of it as a slice of pizza (a sector) with the triangle part removed.
A circular sector is a region bounded by two radii and the arc between them, like a slice of pizza. A circular segment, on the other hand, is the region bounded by a chord and the arc it subtends. You can find the area of a segment by subtracting the area of the triangle formed by the two radii and the chord from the area of the corresponding sector.
The standard formula for the area of a circular segment, Area = r² * (θ - sin(θ)) / 2, requires the angle θ to be in radians for the 'θ - sin(θ)' part to work correctly. If you use degrees directly, the result will be incorrect. Our calculator handles the conversion for you, so you can input degrees directly.
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