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 2π rad. 'rad' is an abbreviation for radians. An arc occupying 1/2 of a circle would then measure 360° / 2 = 180° or 2π 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.

Image Credits

• All images and manipulatives are by David McAdams unless otherwise stated. All images by David McAdams are Copyright © Life is a Story Problem LLC and are licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

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.)