Arc Length Calculator
How It Works
This arc length calculator uses established formulas to provide accurate results.
The basic rule:
- Arc length = rθ (radians)
- Arc length = 2πr(θ/360) (degrees)
- Sector area = ½r²θ (radians)
- Sector area = πr²(θ/360) (degrees)
Results are estimates. Consult a professional for critical decisions.
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Explore Allday Everyday Math →Frequently Asked Questions
What is the arc length formula?
In radians: arc length = rθ, where r is the radius and θ is the central angle in radians. In degrees: arc length = 2πr(θ/360).
How is arc length related to sector area?
Both depend on the central angle. Arc length = rθ and sector area = ½r²θ (in radians). You can derive sector area as ½ × r × arc length.
What fraction of the circle does my arc represent?
The fraction is θ/360 (in degrees) or θ/(2π) (in radians). For example, a 90° arc is ¼ of the circle.
Can the arc length be longer than the circumference?
If the central angle exceeds 360° (or 2π radians), the arc length will exceed the circumference. This represents wrapping around the circle more than once.