{"appState":{"pageLoadApiCallsStatus":true},"articleState":{"article":{"headers":{"creationTime":"2016-03-26T20:32:07+00:00","modifiedTime":"2017-04-13T23:43:10+00:00","timestamp":"2022-09-14T18:18:16+00:00"},"data":{"breadcrumbs":[{"name":"Academics & The Arts","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33662"},"slug":"academics-the-arts","categoryId":33662},{"name":"Math","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33720"},"slug":"math","categoryId":33720},{"name":"Geometry","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33725"},"slug":"geometry","categoryId":33725}],"title":"How to Determine the Length of an Arc","strippedTitle":"how to determine the length of an arc","slug":"how-to-determine-the-length-of-an-arc-2","canonicalUrl":"","seo":{"metaDescription":"An arc’s length means the same commonsense thing length always means — you know, like the length of a piece of string (with an arc , of course, it’d be a curved","noIndex":0,"noFollow":0},"content":"An arc’s length means the same commonsense thing length always means — you know, like the length of a piece of string (with an<a href=\"https://www.dummies.com/education/math/geometry/identify-arcs-central-angles/\"> arc</a>, of course, it’d be a curved piece of string). Make sure you don’t mix up arc length with the <i>measure</i> of an arc which is the degree size of its central angle.\r\n\r\nA circle is 360° all the way around; therefore, if you divide an arc’s degree measure by 360°, you find the fraction of the circle’s <a href=\"https://www.dummies.com/education/math/trigonometry/radius-diameter-circumference-and-area-of-circles/\">circumference</a> that the arc makes up. Then, if you multiply the length all the way around the circle (the circle’s circumference) by that fraction, you get the length along the arc. So finally, here’s the formula you’ve been waiting for.\r\n\r\n<img src=\"https://www.dummies.com/wp-content/uploads/262063.image0.jpg\" alt=\"image0.jpg\" width=\"400\" height=\"375\" />\r\n\r\n<b>Arc length:</b>\r\n\r\n<img src=\"https://www.dummies.com/wp-content/uploads/262064.image1.png\" alt=\"image1.png\" width=\"497\" height=\"176\" />\r\n\r\nIts degree measure is 45° and the radius of the circle is 12, so here’s the math for its length:\r\n\r\n<img src=\"https://www.dummies.com/wp-content/uploads/262065.image2.png\" alt=\"image2.png\" width=\"487\" height=\"216\" />\r\n\r\nPretty simple, eh?","description":"An arc’s length means the same commonsense thing length always means — you know, like the length of a piece of string (with an<a href=\"https://www.dummies.com/education/math/geometry/identify-arcs-central-angles/\"> arc</a>, of course, it’d be a curved piece of string). Make sure you don’t mix up arc length with the <i>measure</i> of an arc which is the degree size of its central angle.\r\n\r\nA circle is 360° all the way around; therefore, if you divide an arc’s degree measure by 360°, you find the fraction of the circle’s <a href=\"https://www.dummies.com/education/math/trigonometry/radius-diameter-circumference-and-area-of-circles/\">circumference</a> that the arc makes up. Then, if you multiply the length all the way around the circle (the circle’s circumference) by that fraction, you get the length along the arc. So finally, here’s the formula you’ve been waiting for.\r\n\r\n<img src=\"https://www.dummies.com/wp-content/uploads/262063.image0.jpg\" alt=\"image0.jpg\" width=\"400\" height=\"375\" />\r\n\r\n<b>Arc length:</b>\r\n\r\n<img src=\"https://www.dummies.com/wp-content/uploads/262064.image1.png\" alt=\"image1.png\" width=\"497\" height=\"176\" />\r\n\r\nIts degree measure is 45° and the radius of the circle is 12, so here’s the math for its length:\r\n\r\n<img src=\"https://www.dummies.com/wp-content/uploads/262065.image2.png\" alt=\"image2.png\" width=\"487\" height=\"216\" />\r\n\r\nPretty simple, eh?","blurb":"","authors":[{"authorId":8957,"name":"Mark Ryan","slug":"mark-ryan","description":" <p><b>Mark Ryan</b> has taught pre-algebra through calculus for more than 25 years. In 1997, he founded The Math Center in Winnetka, Illinois, where he teaches junior high and high school mathematics courses as well as standardized test prep classes. He also does extensive one-on-one tutoring. He is a member of the Authors Guild and the National Council of Teachers of Mathematics. 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How to Determine the Length of an Arc

By: Mark Ryan and

Updated: 04-13-2017

Geometry For Dummies

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An arc’s length means the same commonsense thing length always means — you know, like the length of a piece of string (with an arc, of course, it’d be a curved piece of string). Make sure you don’t mix up arc length with the measure of an arc which is the degree size of its central angle.

A circle is 360° all the way around; therefore, if you divide an arc’s degree measure by 360°, you find the fraction of the circle’s circumference that the arc makes up. Then, if you multiply the length all the way around the circle (the circle’s circumference) by that fraction, you get the length along the arc. So finally, here’s the formula you’ve been waiting for.