Arc Length Calculator
Calculate the arc length of a circle from its radius and central angle. Also finds the sector area and chord length.
Last reviewed by the Radiatus Cloud team
Find the arc length, sector area and chord length of a circle from radius and angle.
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Calculate arc length and more
An arc is a portion of the circumference of a circle, and its length depends on the radius and the central angle it subtends. The arc length equals the radius multiplied by the angle measured in radians. This calculator converts a degree angle to radians automatically, then returns the arc length along with the area of the corresponding sector, the slice of the circle, and the length of the chord that joins the two ends of the arc.
For reference it also shows the full circumference, so you can see what fraction of the whole circle your arc represents.
Where arc length is needed
Arc length appears in engineering, construction and design whenever curved parts are measured, from pipes and roads to gears and clock faces. Students use it in trigonometry and geometry, and it is the basis for understanding radian measure. The sector area is needed for pie charts, pizza slices and any pie-shaped region, while the chord length matters in surveying and structural work.
The chord uses the sine of half the angle, so it is always shorter than the arc it cuts across. Make sure the radius is positive and choose the correct angle unit. All calculation runs locally in your browser.
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Frequently Asked Questions
What is the arc length formula?
Arc length equals the radius times the central angle in radians. For a degree angle, convert it to radians first, which the tool does automatically.
What is the difference between arc and chord?
The arc is the curved distance along the circle, while the chord is the straight line joining the two endpoints. The chord is always shorter.
How do I find the sector area?
The sector area is half the radius squared times the angle in radians. It is the area of the pie-shaped region bounded by two radii and the arc.
Should I enter degrees or radians?
Either. Select the unit that matches your angle, and the tool converts to radians internally for the calculation.
What fraction of the circle is my arc?
Divide the arc length by the full circumference, both of which the tool shows, to find what fraction of the circle the arc covers.
Privacy & Security
Everything runs in your browser; nothing is uploaded.
How to Use
Enter the radius and the central angle in degrees or radians.
Disclaimer: This tool is provided "as is" without warranty of any kind. Results are for educational and utility purposes.
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