Arc Length Calculator
Calculate the arc length of a circle sector from the radius and central angle in degrees. Uses the formula arc length = radius x angle in radians. Useful for geometry and engineering tasks.
How to use this tool
- Enter radius and central angle in the fields above.
- Results update instantly as you type โ or click Calculate.
- Read your arc length and the full breakdown beneath it.
Formula
s = r * theta (theta in radians = angle_deg * pi/180)
How it works
Convert the angle to radians: ฮธ = angle ร ฯ/180. Then arc length s = rฮธ.
Worked example
Quarter circle, radius 5
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- 9
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- 5
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- 7
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Common mistakes to avoid
- Entering the angle in degrees without converting to radians โ the formula s = r * theta requires theta in radians; multiply degrees by pi/180 first (the calculator does this automatically if configured for degrees input).
- Confusing arc length (a distance along the curve) with chord length (the straight line between the two endpoints of the arc) โ they are different and chord length requires a separate formula.
- Using the diameter instead of the radius, doubling the computed arc length.
Key terms
Frequently asked questions
- How do I convert a degree angle to radians for the arc length formula?
- Multiply degrees by pi/180. For example, 90 degrees = 90 * pi/180 = pi/2 radians approximately 1.5708 radians. Then s = r * (pi/2).
- What is the difference between arc length and the chord length?
- Arc length s = r*theta is the curved distance along the circle between two points. Chord length is the straight-line distance: chord = 2*r*sin(theta/2). For small angles they are nearly equal; for large angles the arc is significantly longer.
- Can arc length equal the radius?
- Yes, exactly when theta = 1 radian (about 57.3 degrees). This is actually the definition of a radian: the angle for which the arc length equals the radius.