Calculate arc length, sector area, chord length, and the full circumference of a circle from radius and central angle.
Last updated: June 2026 | By Patchworkr Team
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Radius needs a real number.
Arc length is the distance along the curved edge of a circle. It is not the straight line between two points on the circle.
The key relationship is s = r * theta, where theta must be in radians.
That same angle also determines sector area and chord length, so the three values are linked.
For a radius of 10 and a central angle of 60 deg, the angle in radians is pi / 3.
The curved distance is about 10.47 units, which is exactly one sixth of the full circumference of a radius-10 circle.
Why do I need radians?
The arc length formula uses radians because they connect angle directly to radius.
Can the angle be larger than 360 deg?
Yes, but the arc wraps around the circle more than once. The formula still works.
What if the radius is blank?
Blank input is invalid, so the calculator shows an error until you enter a value.
Does the chord length always stay shorter than the arc?
Yes. The straight chord is always shorter than or equal to the curved arc.
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