{"id":156408,"date":"2022-03-26T01:43:24","date_gmt":"2022-03-25T20:13:24","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/circumference-of-a-circle-definition-and-formula\/"},"modified":"2025-07-30T14:41:22","modified_gmt":"2025-07-30T09:11:22","slug":"circumference-of-a-circle-definition-and-formula","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/circumference-of-a-circle\/","title":{"rendered":"Circumference of a Circle &#8211; Definition and Formula"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/circumference-of-a-circle\/#Circumference_of_the_Circle_Meaning\" title=\"Circumference of the Circle Meaning\">Circumference of the Circle Meaning<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/circumference-of-a-circle\/#Circumference_of_the_Circle_Units\" title=\"Circumference of the Circle Units\">Circumference of the Circle Units<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/circumference-of-a-circle\/#Circumference_of_the_Circle_Definition\" title=\"Circumference of the Circle Definition\">Circumference of the Circle Definition<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/circumference-of-a-circle\/#Basic_Components_of_a_Circle\" title=\"Basic Components of a Circle\">Basic Components of a Circle<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/circumference-of-a-circle\/#Circumference_of_the_Circle_Formula\" title=\"Circumference of the Circle Formula\">Circumference of the Circle Formula<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/circumference-of-a-circle\/#Circumference_of_the_Circle_Formula_Using_Diameter\" title=\"Circumference of the Circle Formula Using Diameter\">Circumference of the Circle Formula Using Diameter<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/circumference-of-a-circle\/#How_to_find_the_Circumferences_of_a_Circle\" title=\"How to find the Circumferences of a Circle?\">How to find the Circumferences of a Circle?<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/circumference-of-a-circle\/#Method_1_The_Thread_Method\" title=\"Method 1: The Thread Method\">Method 1: The Thread Method<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/circumference-of-a-circle\/#Method_2_Calculation_Using_Radius_or_Diameter\" title=\"Method 2: Calculation Using Radius or Diameter\">Method 2: Calculation Using Radius or Diameter<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/circumference-of-a-circle\/#Circumference_of_the_semi-circle\" title=\"Circumference of the semi-circle\">Circumference of the semi-circle<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/circumference-of-a-circle\/#FAQs_on_Circumference_of_Circle\" title=\"FAQs on Circumference of Circle\">FAQs on Circumference of Circle<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/circumference-of-a-circle\/#What_is_the_circumference_of_a_circle\" title=\"What is the circumference of a circle?\">What is the circumference of a circle?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/circumference-of-a-circle\/#Find_the_circumference_of_a_circle_whose_diameter_is_given_8cm\" title=\"Find the circumference of a circle whose diameter is given 8cm.\">Find the circumference of a circle whose diameter is given 8cm.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/circumference-of-a-circle\/#Calculate_the_radius_of_a_circle_whose_circumference_is_C_25_cm\" title=\"Calculate the radius of a circle whose circumference is C= 25 cm\">Calculate the radius of a circle whose circumference is C= 25 cm<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<p><strong>Circumference of the Circle:<\/strong> The circumference of the circle is the total length of the boundary of the shape (circle). It is also known as the perimeter of the circle. The <strong><a href=\"https:\/\/infinitylearn.com\/surge\/study-materials\/cbse-notes\/maths\/circumference-of-a-circle\/\">circumference of the circle<\/a><\/strong> is the product of the diameter of the circle and the constant \u03c0, whose value is 3.14 or 22\/7.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Circumference_of_the_Circle_Meaning\"><\/span>Circumference of the Circle Meaning<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A circle is a 2D, round, and closed figure where all the boundary points are equidistant from the fixed point called the center of the circle. The total length of this Boundary is said to be the Circumference of the Circle.<\/p>\n<p>Examples of the Circumference of the Circle are the fencing around the boundary of a circular park, the border of a circular tabletop, etc. To calculate the length of these discussed examples, we need to calculate the circumference.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Circumference_of_the_Circle_Units\"><\/span>Circumference of the Circle Units<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The circumference of the circle is always a linear value and its units are the same as the units of length.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Circumference_of_the_Circle_Definition\"><\/span>Circumference of the Circle Definition<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A circle has an area and a perimeter. The <strong><a href=\"https:\/\/infinitylearn.com\/surge\/articles\/perimeter-of-circle\/\">perimeter of a circle<\/a><\/strong> is also known as the circumference of a circle. This circumference is the distance around the circle. Some of the examples of circles from our daily life are rings, bangles, coins, wheels, buttons, hula-hoop, etc.<\/p>\n<p>If the distance across the border of these examples discussed above is measured properly using the rope, then the total length of the rope covered is called the Circumference of the Circle. Radius is the main component to calculate the circumference of a circle. Therefore, we need the value of radius or the diameter of the circle to calculate the circumference of a circle.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Basic_Components_of_a_Circle\"><\/span>Basic Components of a Circle<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ol>\n<li><strong>Center of a Circle :<\/strong> There is a center point in a circle. From this point, all the distances to the point on a circle are equal.<\/li>\n<li><strong>Diameter of a Circle :<\/strong> The diameter of a Circle is a line passing through the center of a circle. Diameter of a circle is the longest chord present in a circle. The diameter is twice the radius of a circle.<\/li>\n<li><strong>Radius :<\/strong> Radius is the constant distance from the center of a circle to the point present on a circle.<\/li>\n<\/ol>\n<h2><span class=\"ez-toc-section\" id=\"Circumference_of_the_Circle_Formula\"><\/span>Circumference of the Circle Formula<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The Circumference of a Circle is calculated by using the formula: 2\u03c0r<br \/>\nwhere r is the radius of a circle and \u03c0 is a mathematical constant whose value is 3.14 or 22\/7.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Circumference_of_the_Circle_Formula_Using_Diameter\"><\/span>Circumference of the Circle Formula Using Diameter<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>The Circumference of a Circle can be calculated by using the value of the diameter of the circle. The formula to calculate the circumference is:<\/p>\n<p>C=\u03c0D<\/p>\n<p>Where C is the circumference of a circle.<\/p>\n<p>D is the diameter of a circle.<\/p>\n<p>The circumference of a circle is measured in units such as cm, m.<\/p>\n<p><strong>Solved Example: Find the circumference of a circle whose radius is 5cm.<\/strong><\/p>\n<p><strong>Solution<\/strong>: Given radius= 5cm<\/p>\n<p>Therefore, the Circumference of the circle whose radius is 5cm is calculated using the formula = 2\u03c0r<\/p>\n<p>= 2\u00d73.14\u00d75<\/p>\n<p>= 31.4cm<\/p>\n<h2><span class=\"ez-toc-section\" id=\"How_to_find_the_Circumferences_of_a_Circle\"><\/span>How to find the Circumferences of a Circle?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3><span class=\"ez-toc-section\" id=\"Method_1_The_Thread_Method\"><\/span>Method 1: The Thread Method<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>A circle is a curved surface, so the length cannot be measured using a scale or ruler. This method can be used for polygons like squares, rectangles, and triangles. The circumference of a circle can be measured using a thread placed across the circle. The path of a circle can be traced using a thread. On the thread, mark the points. Now, the length can be measured with the help of a ruler.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Method_2_Calculation_Using_Radius_or_Diameter\"><\/span>Method 2: Calculation Using Radius or Diameter<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>The most accurate way to know the circumference of a circle is to calculate it. To calculate the circumference, the radius of a circle should be known. The radius of a circle is defined as the distance from the center of the circle to any point on the circle itself. Below is the figure in which radius r and center O is shown. The diameter of the circle is twice the radius of the circle.<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-730257\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/Circumferences-of-a-Circle-Using-Radius-or-Diameter.png\" alt=\"Circumferences of a Circle - Using Radius or Diameter\" width=\"145\" height=\"141\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Circumference_of_the_semi-circle\"><\/span>Circumference of the semi-circle<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Circumference of the semi-circle is formed when a circle is divided into two equal halves. Therefore, the circumference of a semi-circle also becomes half. But, the length of the diameter of the circle is added to it.<\/p>\n<p>Therefore, the Circumference of a semi-circle = \u03c0r + 2r<\/p>\n<p><img loading=\"lazy\" class=\"alignnone size-full wp-image-730256\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/Circumference-of-the-semi-circle.png\" alt=\"Circumference of the semi-circle\" width=\"223\" height=\"163\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/Circumference-of-the-semi-circle.png 223w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/Circumference-of-the-semi-circle-150x110.png 150w\" sizes=\"(max-width: 223px) 100vw, 223px\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"FAQs_on_Circumference_of_Circle\"><\/span>FAQs on Circumference of Circle<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"What_is_the_circumference_of_a_circle\"><\/span>What is the circumference of a circle?<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tThe linear distance around a circle is the circumference of a circle. We can define the circumference of a circle in another way. If we open a circle to form a straight line, the length of that line will be the circumference of a circle. \t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"Find_the_circumference_of_a_circle_whose_diameter_is_given_8cm\"><\/span>Find the circumference of a circle whose diameter is given 8cm.<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tAs the diameter of a circle is given, we can find out the radius of a circle. Radius= diameter\/2 = 8\/2 =4 cm Now, circumference= 2\u03c0r = 2\u00d73.14\u00d74 = 25.12 cm\t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"Calculate_the_radius_of_a_circle_whose_circumference_is_C_25_cm\"><\/span>Calculate the radius of a circle whose circumference is C= 25 cm<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tCircumference = 25 cm C= 2\u03c0r 25 = 2\u00d73.14\u00d7r r= 25\/2\u00d73.14 r= 3.98 cm\t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\n<script type=\"application\/ld+json\">\n\t{\n\t\t\"@context\": \"https:\/\/schema.org\",\n\t\t\"@type\": \"FAQPage\",\n\t\t\"mainEntity\": [\n\t\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"What is the circumference of a circle?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"The linear distance around a circle is the circumference of a circle. We can define the circumference of a circle in another way. If we open a circle to form a straight line, the length of that line will be the circumference of a circle.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"Find the circumference of a circle whose diameter is given 8cm.\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"As the diameter of a circle is given, we can find out the radius of a circle. Radius= diameter\/2 = 8\/2 =4 cm Now, circumference= 2\u03c0r = 2\u00d73.14\u00d74 = 25.12 cm\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"Calculate the radius of a circle whose circumference is C= 25 cm\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"Circumference = 25 cm C= 2\u03c0r 25 = 2\u00d73.14\u00d7r r= 25\/2\u00d73.14 r= 3.98 cm\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t\t\t\t]\n\t}\n<\/script>\n\n","protected":false},"excerpt":{"rendered":"<p>Circumference of the Circle: The circumference of the circle is the total length of the boundary of the shape (circle). [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Circumference of a Circle","_yoast_wpseo_title":"Circumference of a Circle: Formula, Calculation & Examples | Infinity Learn","_yoast_wpseo_metadesc":"Learn how to calculate the circumference of a circle using the formula, explore step-by-step examples, and understand key concepts in geometry.","custom_permalink":"maths\/circumference-of-a-circle\/"},"categories":[13],"tags":[],"table_tags":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Circumference of a Circle: Formula, Calculation &amp; Examples | Infinity Learn<\/title>\n<meta name=\"description\" content=\"Learn how to calculate the circumference of a circle using the formula, explore step-by-step examples, and understand key concepts in 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