What Is an Arc?

How arcs are named and measured

Arcs are closely tied to central and inscribed angles because those angles intercept arcs. In degree-based circle geometry, the measure of an arc is read from the corresponding central angle.

This page keeps the endpoints and the curved path visible so you can distinguish an arc from a chord, a sector, or a segment without collapsing different circle parts into one word.

The two endpoints do not always identify one arc by themselves because there can be a short route and a long route between them. In a careful solution, name the minor or major arc, or use three letters when the longer route must be made unmistakable.

• An arc is a portion of a circle's circumference.
• A minor arc is the shorter path between two points on the circle, while a major arc is the longer path.
• Arc measure is expressed in degrees when it refers to the intercepted turn, and arc length is expressed in linear units when it refers to distance along the curve.
• The same endpoints can define more than one arc, so naming and context matter.

Where arcs help

• Use arcs when working with central angles, inscribed angles, and intercepted-arc theorems.
• Use them when finding arc length from radius and angle measure.
• Use arc notation when reading circle diagrams that highlight only part of the circumference.

Arc mix-ups to avoid

• Do not confuse the curved arc with the straight chord connecting the same endpoints.
• Do not assume two endpoints automatically mean the minor arc if the problem is referring to the major arc.
• Do not treat an arc as a filled slice of the circle; that language belongs to a sector or another region.