Calculate arc length, sector area, and chord length with support for degrees and radians
Max: 360°
Arc = (θ/360) × 2πr
Where θ is in degrees and r is radius
Example: (90/360) × 2π × 10 = 15.71 units
Arc = r × θ
Where θ is in radians - the simplest formula!
Example: 10 × 1.571 = 15.71 units
Area = (1/2) × r² × θ (radians)
Or: Area = (θ/360) × πr² (degrees)
Example: (1/2) × 10² × 1.571 = 78.54 square units
Chord = 2r × sin(θ/2)
Straight-line distance between arc endpoints
Example: 2 × 10 × sin(0.7855) = 14.14 units
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Arc length is the distance along the curved line of a circle between two points. Calculate it using: Arc = (θ/360) × 2πr for degrees, or Arc = rθ for radians, where r is radius and θ is the central angle. For example, with radius 5 and angle 60°: Arc = (60/360) × 2π × 5 = 5.24 units.
Degrees and radians are two ways to measure angles. A full circle is 360° or 2π radians. To convert: degrees to radians multiply by π/180, radians to degrees multiply by 180/π. For example, 90° = π/2 radians ≈ 1.571 radians. Radians are often used in calculus and physics.
The sector area formula is: Area = (1/2) × r × arc length, or Area = (θ/360) × πr² for degrees. For a radius of 10 and arc length of 15.71, the area is (1/2) × 10 × 15.71 = 78.54 square units. This works because the sector is a fraction of the full circle.
Chord length is the straight-line distance between the endpoints of an arc, while arc length is the curved distance. Calculate chord using: Chord = 2r × sin(θ/2), where θ is in radians. The chord is always shorter than the arc except when the arc is a straight line (180°).
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