Arc Length Calculator
Arc length and chord, with the radian conversion shown.
Work out Arc Length. Arc length and chord, with the radian conversion shown. Shows the working, not just the answer.
Arc length (units)
10.472
1.0472 radians · chord 10 units
Arc length is simply rθ once the angle is in radians, which is the entire reason radians exist as a unit — they are defined so that this formula has no conversion factor in it. The arc always exceeds the chord, and the gap widens with the angle: 0.472 units here.
How the Arc Length Calculator works
Arc length is simply rθ once the angle is in radians, which is the whole reason radians exist as a unit — they are defined so this formula carries no conversion factor. Degrees need dividing by 180 and multiplying by π first, and this page shows that step.
Also known as: arc length formula · length of an arc calculator · chord length calculator · arc of a circle
Frequently asked questions
How do I calculate arc length?
Multiply the radius by the angle in radians. For degrees, convert first: a 60° arc on a radius of 10 is 10 × (60π⁄180) = 10.47 units.
Why do radians make the formula simpler?
Because a radian is defined as the angle whose arc equals the radius. That definition makes arc length exactly rθ, with no constant to remember.
How long is the chord?
2r sin(θ⁄2). It is always shorter than the arc, since a straight line is the shortest path between two points.
What fraction of the circle is my arc?
The angle divided by 360. A 60° arc is one sixth of the circumference.
Put this calculator on your own site
Free to use, on any site, commercial or not. Paste this where you want it to appear. It is a plain iframe, so it works in WordPress, Squarespace, Wix, Webflow, Ghost and anything else that accepts HTML.
<iframe src="https://www.thecalclibrary.com/embed/arc-length-calculator" width="100%" height="640" style="border:1px solid #e2e8f0;border-radius:12px" loading="lazy" title="Arc Length Calculator"></iframe>The only condition is that the credit line stays visible. It sits inside the frame, so you do not have to do anything to keep it.
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