Arc Length Calculator
Calculate the length of a circular arc from radius and angle.
This tool is for informational and educational purposes only. It is not a substitute for professional financial, medical, legal, or engineering advice. See Terms of Service.
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This calculator finds the length of a circular arc using the radius and central angle.
- Enter the radius. Type the radius of the circle.
- Enter the angle. Type the central angle that defines the arc.
- Choose the unit. Select whether the angle is in degrees or radians.
- Read the result. The arc length is shown with the formula used. The calculator also converts the angle between degrees and radians for reference.
The formula is s = r * theta, where theta is in radians. When you enter degrees, the calculator converts to radians first (multiplying by pi/180), then applies the formula. A full circle (360 degrees) gives an arc length equal to the circumference: 2 * pi * r.
About Arc Length
An arc is a portion of the circumference of a circle. The arc length depends on two things: the radius and the central angle. A larger radius or a wider angle produces a longer arc. The formula s = r * theta (where theta is in radians) comes directly from the definition of a radian. One radian is the angle where the arc length equals the radius. Arc length is used in engineering for curved structures, in physics for rotational motion, in geography for distances along curved paths, and in manufacturing for bending pipes and sheet metal along circular profiles.
Frequently Asked Questions
What is the arc length formula?
The arc length formula is s = r * theta, where r is the radius and theta is the central angle in radians. If the angle is in degrees, use s = (theta/360) * 2 * pi * r, which is equivalent.
How do I convert degrees to radians?
Multiply the angle in degrees by pi/180. For example, 90 degrees = 90 * pi/180 = pi/2 radians (approximately 1.5708). This calculator handles the conversion automatically.
What is the arc length of a full circle?
The arc length of a full circle (360 degrees or 2*pi radians) equals the circumference: 2 * pi * r. For a circle with radius 10, that is approximately 62.8318 units.