Understanding Arc Length
Arc length is the distance measured along the curved edge of a circle between two points. It is different from chord length, which measures the straight-line distance between those same points. Arc length is useful when working with curved materials or layouts, such as pipe and tubing bends, sheet metal, curved woodworking projects, landscaping, machining, and CNC work.
How Arc Length Is Calculated
Arc length depends on the radius of the circle and the central angle of the arc. When the angle is measured in radians, the formula is:
Arc Length = Radius × Angle in Radians
If the angle is given in degrees, it is first converted to radians by multiplying the angle by π and dividing by 180. A larger radius or a larger central angle produces a longer arc.
Arc Length Example
Suppose a circle has a radius of 12 units and a central angle of 90°. A 90° angle represents one-quarter of a full circle. The circumference of a circle with a radius of 12 is approximately 75.398 units, so one-quarter of that circumference is approximately 18.850 units. That is the length of the 90° arc.
Arc Length vs. Chord Length
Arc length follows the curve of the circle, while chord length is a straight line connecting the two endpoints of the arc. The two measurements are not interchangeable. For fabrication, bending, cutting, or layout work, make sure you know whether your project requires the curved arc length or the straight chord distance.