# Arc

Pronunciation: /ɑɹk/ Explain

 Figure 1: Arcs on a Circle

An arc is any smooth curve joining two points. 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

 Click on the blue points and drag them to change the figure. What is the arc length of a arc of a circle with circumference 4 that covers 90 degrees? Manipulative 1 - Arc Length Created with GeoGebra.

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 a circle. if the arc measures 72°, and the circumference is 22cm, then the arc length is 72°/360° · 22cm = 4.4cm.

### References

1. McAdams, David E.. All Math Words Dictionary, arc. 2nd Classroom edition 20150108-4799968. pg 18. Life is a Story Problem LLC. January 8, 2015. Buy the book

### More Information

• Arc length. www.khanacademy.org. Kahn Academy. 6/19/2018. https://www.khanacademy.org/math/geometry/hs-geo-circles/hs-geo-arc-length-deg/e/circles_and_arcs.

### Cite this article as:

McAdams, David E. Arc. 4/11/2019. All Math Words Encyclopedia. Life is a Story Problem LLC. https://www.allmathwords.org/en/a/arc.html.

### Revision History

4/11/2019: Changed equations and expressions to new format. (McAdams, David E.)
12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
6/14/2018: Removed broken links, changed Geogebra links to work with Geogebra 5, updated license, implemented new markup. (McAdams, David E.)
3/2/2010: Added sentence on adjacent arcs. (McAdams, David E.)
1/2/2010: Added "References". (McAdams, David E.)
11/12/2009: Added arc length. (McAdams, David E.)
6/11/2008: Added paragraph on the measure of an arc. (McAdams, David E.)
6/7/2008: Corrected spelling. (McAdams, David E.)
4/18/2008: Initial version. (McAdams, David E.)

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