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.

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.

By AbraCalc Editorial Team · Reviewed by AbraCalc Methodology Review · Last reviewed: 2026-06-25 2 sources

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Cite this tool

APA

AbraCalc. (2026). Arc Length Calculator [Online calculator]. Retrieved from https://abracalc.com/calculator/arc-length-calculator/

BibTeX

@misc{abracalc-arc-length-calculator, author = {AbraCalc}, title = {Arc Length Calculator}, year = {2026}, howpublished = {\url{https://abracalc.com/calculator/arc-length-calculator/}} }

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How to use this tool

Enter radius and central angle in the fields above.
Results update instantly as you type — 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: θ = angle × π/180. Then arc length s = rθ.

Worked example

Quarter circle, radius 5

Common mistakes to avoid

Entering the angle in degrees without converting to radians — 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) — 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.