Circular arc

A circular arc is the arc of a circle between a pair of distinct points. If the two points are not directly opposite each other, one of these arcs, the minor arc, subtends an angle at the center of the circle that is less than π radians (180 degrees); and the other arc, the major arc, subtends an angle greater than π radians. The arc of a circle is defined as the part or segment of the circumference of a circle. A straight line that connects the two ends of the arc is known as a chord of a circle. If the length of an arc is exactly half of the circle, it is known as a semicircular arc.

The length (more precisely, arc length) of an arc of a circle with radius r and subtending an angle θ (measured in radians) with the circle center — i.e., the central angle — is

This is because

Substituting in the circumference

and, with α being the same angle measured in degrees, since θ = ⁠α/180⁠π, the arc length equals

A practical way to determine the length of an arc in a circle is to plot two lines from the arc's endpoints to the center of the circle, measure the angle where the two lines meet the center, then solve for L by cross-multiplying the statement:

For example, if the measure of the angle is 60 degrees and the circumference is 24 inches, then

This is so because the circumference of a circle and the degrees of a circle, of which there are always 360, are directly proportional.