Arc

Pronunciation: /ɑrk/ ?

Diagram showing a major arc, a minor arc and a semicircle.
Figure 1: Arcs on a Circle

An arc is any smooth curve joining two points.[1] This article will focus on arcs of circles. An arc of a circle is sometimes called a circular arc.

Any two points on a circle define two arcs. If the two points are on a diameter of the circle, each arc is called a semicircle. If the two points are not on a diameter of a circle, they define two arcs. The larger arc is called the major arc, and the smaller arc is called the minor arc.

Adjacent arcs are two arcs that share an endpoint.

Arc Measure

Arcs are measured based on what portion of a whole circle they occupy. A whole circle measures 360° or rad. 'rad' is an abbreviation for radians. An arc occupying 1/2 of a circle would then measure 360° / 2 = 180° or rad / 2 = π rad.

Arc Length

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Manipulative 1: Arc length. Created with GeoGebra. Double click on the manipulative to open it full screen.

Arc length is defined as the linear length of an arc. For arcs of circles, the arc length is calculated as a portion of the total circumference of the circle. if the arc measures 72°, and the circumference is 22cm, then the arc length is 72°/360° · 22cm = 4.4cm.

Cite this article as:


Arc. 2010-03-02. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/a/arc.html.

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Revision History


2010-03-02: Added sentence on adjacent arcs. (McAdams, David.)
2010-01-02: Added "References" (McAdams, David.)
2009-11-12: Added arc length. (McAdams, David.)
2008-06-11: Added paragraph on the measure of an arc (McAdams, David.)
2008-06-07: Corrected spelling (McAdams, David.)
2008-04-18: Initial version (McAdams, David.)

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