{"id":32726,"date":"2023-08-06T16:59:00","date_gmt":"2023-08-06T16:59:00","guid":{"rendered":"https:\/\/www.splashlearn.com\/math-vocabulary\/?page_id=32726"},"modified":"2023-08-08T05:12:16","modified_gmt":"2023-08-08T05:12:16","slug":"degrees-to-radians-conversion-steps-formula-examples-facts","status":"publish","type":"post","link":"https:\/\/www.splashlearn.com\/math-vocabulary\/degrees-to-radians","title":{"rendered":"Degrees to Radians: Conversion, Steps, Formula, Examples, Facts"},"content":{"rendered":"<div class=\"aioseo-breadcrumbs\"><span class=\"aioseo-breadcrumb\">\n\tMath-Vocabulary\n<\/span><\/div>\n\n<div class=\"ub_table-of-contents\" data-showtext=\"show\" data-hidetext=\"hide\" data-scrolltype=\"auto\" id=\"ub_table-of-contents-185a6426-c17f-4f15-93e5-7040d02c4497\" data-initiallyhideonmobile=\"false\"\n                    data-initiallyshow=\"true\"><div class=\"ub_table-of-contents-extra-container\"><div class=\"ub_table-of-contents-container ub_table-of-contents-1-column \"><ul><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/degrees-to-radians#0-what-is-the-degrees-to-radians-conversion>What Is the Degrees to Radians Conversion?<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/degrees-to-radians#1-degrees-to-radians-formula>Degrees to Radians Formula<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/degrees-to-radians#3-how-to-convert-degree-measure-to-radian-measure>How to Convert Degree Measure to Radian Measure<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/degrees-to-radians#9-solved-examples-on-degrees-to-radians>Solved Examples on Degrees to Radians<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/degrees-to-radians#10-practice-problems-on-degrees-to-radians>Practice Problems on Degrees to Radians<\/a><\/li><li><a href=https:\/\/www.splashlearn.com\/math-vocabulary\/degrees-to-radians#11-frequently-asked-questions-about-degrees-to-radians>Frequently Asked Questions about Degrees to Radians<\/a><\/li><\/ul><\/div><\/div><\/div>\n\n\n<h2 class=\"wp-block-heading\" id=\"0-what-is-the-degrees-to-radians-conversion\">What Is the Degrees to Radians Conversion?<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Any <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/angle\">angle<\/a> in degrees can be converted into radians using the degrees to radians conversion. The relationship between degrees and radians is given as $2\\pi = 360^{\\circ}$ or $\\pi = 180^{\\circ}$. One complete counterclockwise revolution is represented by $2\u03c0$ (in radians) or $360^{\\circ}$ (in degrees).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Degree and radian are the units for measuring an angle. An angle is a <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometric-shapes\">geometric figure<\/a> formed when two rays meet at a common point, called <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/vertex\">vertex<\/a>. When the angle is measured counterclockwise, it is called a positive angle. Angle measured in a clockwise direction is called a negative angle.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"360\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/angle-and-angle-measure.png\" alt=\"Angle and angle measure\" class=\"wp-image-32739\" title=\"Angle and angle measure\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/angle-and-angle-measure.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/angle-and-angle-measure-300x174.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>What Are Degrees?<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>A degree <\/strong><strong>(<\/strong><strong>\u00b0<\/strong><strong>)<\/strong><strong> is a unit for measuring the magnitude of an angle. It is the SI unit to measure angles.&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The measure of an angle in <a href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/geometry\/degree-angle-measure\">degrees<\/a> is determined by the amount of rotation from the initial side to the terminal side. One complete counterclockwise rotation is $360^{\\circ}$. If it is divided into 360 equal parts, each part equals one degree. Thus, 1 degree equals $\\frac{1}{360}$ of a complete revolution in magnitude.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$180\u00b0 = \\pi$ radians<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$360=&nbsp; 2\\pi$ radians<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"628\" height=\"390\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/relationship-between-degrees-and-radians.png\" alt=\"Relationship between degrees and radians\" class=\"wp-image-32741\" title=\"Relationship between degrees and radians\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/relationship-between-degrees-and-radians.png 628w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/relationship-between-degrees-and-radians-300x186.png 300w\" sizes=\"auto, (max-width: 628px) 100vw, 628px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>What Are Radians?<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Radian is an SI unit used to measure angles. Radian is sometimes denoted by a \u201cc\u201d in the exponent, <\/strong>or by writing rad in the front of the measurement. For example, 2 radian is written as $2^{c}$ or 2 rad. Note that this symbol is often omitted in mathematical expressions.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">One radian is the angle where the arc length equals the radius. The formula for angle in radians is<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$\\theta = \\frac{Arc\\;length}{Radius}$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">For example, consider a unit circle (circle with radius 1 unit). An angle subtended at the center by an arc with a length of 1 unit has the measure of 1 radian.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"767\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/understanding-1-radian.png\" alt=\"Understanding 1 radian\" class=\"wp-image-32742\" title=\"Understanding 1 radian\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/understanding-1-radian.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/understanding-1-radian-243x300.png 243w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Note that all circles are similar. Thus, the measure of an angle in radians is the same regardless of the size of the circle. So, for any circle, if radius = arc length, the angle is 1 radian. One radian is approximately equal to 57.296 degrees.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"388\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/one-radian-in-terms-of-degrees.png\" alt=\"1 radian in terms of degrees\" class=\"wp-image-32743\" title=\"1 radian in terms of degrees\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/one-radian-in-terms-of-degrees.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/one-radian-in-terms-of-degrees-300x188.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">When we are dividing a circle in radians, about 3.14 radians will fit in each half of the circle. So, 6.28 radians will fit in a full circle. The exact amount of radians that fit in half a circle is \u03c0, which is about 3.14 radians. So, a full circle fits 2\u03c0 radians (which is about 6.28 radians).<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"630\" height=\"395\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/dividing-a-circle-in-radians.png\" alt=\"Dividing a circle in radians\" class=\"wp-image-32744\" title=\"Dividing a circle in radians\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/dividing-a-circle-in-radians.png 630w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/dividing-a-circle-in-radians-300x188.png 300w\" sizes=\"auto, (max-width: 630px) 100vw, 630px\" \/><\/figure>\n\n\n\n<div id=\"recommended-games-container-id\" class=\"recommended-games-container\"><h4 class=\"recommended-games-container-headline\">Recommended Games<\/h4><div class=\"recommended-games-container-slides\"><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/draw-angles-in-multiples-of-10-degrees\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geo_meas_draw_angle_1_pt.png\" alt=\"Draw Angles in Multiples of 10 Degrees Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Draw Angles in Multiples of 10 Degrees Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/draw-angles-nearest-5-and-1-degrees\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geo_meas_draw_angle_2_pt.png\" alt=\"Draw Angles Nearest 5 and 1 Degrees Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Draw Angles Nearest 5 and 1 Degrees Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><div class=\"game-card-container-outer\">\r\n\t<a href=\"https:\/\/www.splashlearn.com\/s\/math-games\/measure-the-angles-in-multiples-of-10-degrees\" data-vars-ga-category=\"splashlearn_vocab\" data-vars-ga-action=\"games_recommendations\" data-vars-ga-label=\"post_widget\">\r\n\t\t<div class=\"game-card-container-inner-block\">\r\n\t\t\t<img decoding=\"async\" class=\"game-card-container-inner-img\" src=\"https:\/\/cdn.splashmath.com\/curriculum_uploads\/images\/playables\/geo_meas_measure_angle_1_pt.png\" alt=\"Measure the Angles in Multiples of 10 Degrees Game\">\r\n\t\t<\/div>\r\n\t\r\n\t\t<div class=\"game-card-container-inner\">\r\n\t\t\t<div class=\"game-card-container-inner-name\">Measure the Angles in Multiples of 10 Degrees Game<\/div>\r\n\t\t\t<span class=\"game-card-container-inner-cta\">Play<\/span>\r\n\t\t<\/div>\r\n\t<\/a>\r\n<\/div><\/div><p class=\"recommended-games-container-desc\"><a href=\"https:\/\/www.splashlearn.com\/games\">More Games<\/a><\/p><button class=\"scroll-right-arrow\"><\/button><\/div><script type=\"text\/javascript\">\n        document.addEventListener(\"DOMContentLoaded\", function() {\n            const container = document.querySelector(\"#recommended-games-container-id\");\n            const slidesContainer = container.querySelector(\".recommended-games-container-slides\");\n            const cards = slidesContainer.querySelectorAll(\".game-card-container-outer\");\n            const scrollRightArrow = container.querySelector(\".scroll-right-arrow\");\n\n            function adjustContainerStyles() {\n                const numCards = cards.length;\n\n                if (numCards === 1) {\n                    container.style.maxWidth = \"30%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 2) {\n                    container.style.maxWidth = \"50%\";\n                    container.style.textAlign = \"center\";\n                } else if (numCards === 3) {\n                    container.style.maxWidth = \"75%\";\n                    container.style.textAlign = \"center\";\n                } else {\n                    container.style.maxWidth = \"\";\n                    container.style.textAlign = \"\";\n                }\n            }\n\n            function checkScrollPosition() {\n                const maxScrollLeft = slidesContainer.scrollWidth - slidesContainer.clientWidth;\n                if ((slidesContainer.scrollLeft + 10) >= maxScrollLeft) {\n                    scrollRightArrow.style.display = \"none\"; \/\/ Hide the arrow if fully scrolled\n                } else {\n                    scrollRightArrow.style.display = \"block\"; \/\/ Show the arrow if not fully scrolled\n                }\n            }\n\n            scrollRightArrow.addEventListener(\"click\", function() {\n                const scrollAmount = 300; \/\/ Adjust based on the container's width and your needs\n                slidesContainer.scrollLeft += scrollAmount;\n                setTimeout(checkScrollPosition, 100); \/\/ Delay to allow scroll update\n            });\n\n            adjustContainerStyles();\n            checkScrollPosition();\n            slidesContainer.addEventListener(\"scroll\", checkScrollPosition);\n        });\n    <\/script><h2 class=\"wp-block-heading\" id=\"1-degrees-to-radians-formula\">Degrees to Radians Formula<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">To convert angle in degrees to radians in terms of , we have to multiply the angle in degrees by $\\frac{\\pi}{180^{\\circ}}$.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Angle in Radians<\/strong> $=$ <strong>Angle in Degrees<\/strong> $\\times \\frac{\\pi}{180^{\\circ}}$<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"2-derivation-of-degrees-to-radians-formula\">Derivation of Degrees to Radians Formula<\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li>One complete counterclockwise revolution in degrees $= 360^{\\circ}$<\/li>\n\n\n\n<li>One complete counterclockwise revolution in radians $= 2\\pi$<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">The relationship between degree measure and radian measure can be given as<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$360^{\\circ} = 2\\pi$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Hence, $180^{\\circ} = \\pi$ radians.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">$1^{\\circ} = \\frac{\\pi}{180^{\\circ}}$ Radians<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Thus, to convert degrees to radians, the formula is<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Angle in Radians $=$ Angle in Degrees $\\times \\frac{\\pi}{180^{\\circ}}$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">To find the value of $1^{\\circ}$, use the approximate value to be 3.14.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"3-how-to-convert-degree-measure-to-radian-measure\">How to Convert Degree Measure to Radian Measure<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">We know that, 180\u00b0= radians. So, how to change degrees to radians? In order to convert any angle from the degree measure to radians, the value in degrees must simply be multiplied by $\\frac{\\pi}{180^{\\circ}}$.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Angle in Radian $=$ Angle in Degrees $\\times \\frac{\\pi}{180^{\\circ}}$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Let&#8217;s take a look at a few examples. Convert the given angle measures from degrees to radians in terms of pi.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>$45^{\\circ} = 45^{\\circ} \\times \\frac{\\pi}{180^{\\circ}} = &nbsp;\\frac{\\pi}{4}$ radians<\/li>\n\n\n\n<li>$90^{\\circ} = 90^{\\circ} \\times \\frac{\\pi}{180^{\\circ}} = &nbsp;\\frac{\\pi}{2}$ radians<\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"4-degrees-to-radians-chart\">Degrees to Radians Chart<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">The degrees to radians chart helps us understand the conversions better.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"620\" height=\"565\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/degrees-to-radians-chart.png\" alt=\"Degrees to radians chart\" class=\"wp-image-32745\" title=\"Degrees to radians chart\" srcset=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/degrees-to-radians-chart.png 620w, https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/degrees-to-radians-chart-300x273.png 300w\" sizes=\"auto, (max-width: 620px) 100vw, 620px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">In the chart given above, values of angles are given in degrees as well as the radians that helps to do the calculations faster and easier.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"5-degrees-to-radians-conversion-table\">Degrees to Radians Conversion Table<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Let&#8217;s look at the table with some standard angles in degrees and the corresponding angles in radians.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"wj-table-class\"><thead><tr><th class=\"has-text-align-left\" data-align=\"left\"><strong>Degrees<\/strong><\/th><th class=\"has-text-align-left\" data-align=\"left\"><strong>Radians<\/strong><\/th><\/tr><\/thead><tbody><tr><td class=\"has-text-align-left\" data-align=\"left\">$30^{\\circ}$<\/td><td class=\"has-text-align-left\" data-align=\"left\">$\\frac{\\pi}{6}$<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">$45^{\\circ}$<\/td><td class=\"has-text-align-left\" data-align=\"left\">$\\frac{\\pi}{4}$<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">$60^{\\circ}$<\/td><td class=\"has-text-align-left\" data-align=\"left\">$\\frac{\\pi}{3}$<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">$90^{\\circ}$<\/td><td class=\"has-text-align-left\" data-align=\"left\">$\\frac{\\pi}{2}$<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">$180^{\\circ}$<\/td><td class=\"has-text-align-left\" data-align=\"left\">$\\pi$<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">$270^{\\circ}$<\/td><td class=\"has-text-align-left\" data-align=\"left\">$$\\frac{\\pi3}{2}$<\/td><\/tr><tr><td class=\"has-text-align-left\" data-align=\"left\">$360^{\\circ}$<\/td><td class=\"has-text-align-left\" data-align=\"left\">$2\\pi$<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"6-negative-degree-to-radians\">Negative Degree to Radians<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">An angle measured in a clockwise direction is called a negative angle. The method for converting negative degrees to radians is the same as for positive degrees. We simply have to multiply the value of the angle in degrees by $\\frac{\\pi}{180^{\\circ}}$.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Example:<\/strong> If you need to convert $(\\;-\\;180^{\\circ})$ degrees to radian:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Angle in radians $= (\\frac{\\pi}{180^{\\circ}}) \\times (\\text{Angle in degrees})$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Angle in radian $= (\\frac{\\pi}{180^{\\circ}}) \\times (\\;-\\;180^{\\circ})$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Angle in radians $= \\;-\\;\\pi$<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"7-facts-about-degrees-to-radians\">Facts about Degrees to Radians<\/h2>\n\n\n\n<div style=\"color:#0369a1;background-color:#e0f2fe\" class=\"wp-block-roelmagdaleno-callout-block has-text-color has-background is-layout-flex wp-container-roelmagdaleno-callout-block-is-layout-4fc3f8e1 wp-block-roelmagdaleno-callout-block-is-layout-flex\"><div>\n<ul class=\"wp-block-list\">\n<li>One degree is relatively small compared to one radian.<\/li>\n\n\n\n<li>The factors of the number 360 are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 45, 60, 90, 120, 180, 360. This helps in dividing the circle into equal parts and also to easily understand and compare different angles.<\/li>\n\n\n\n<li>Degrees and radians are related by the equations $360^{\\circ} = 2\\pi$ radians<\/li>\n\n\n\n<li>We can convert angle in degrees to angle in radians and vice versa using the following formulas:<br>Angle in Degrees $=$ Angle in Radians $\\times&nbsp;\\frac{180^{\\circ}}{\\pi}$<br>Angle in Radians $=$ Angle in Degrees $\\times&nbsp;\\frac{\\pi}{180^{\\circ}}$<\/li>\n\n\n\n<li>The method for converting negative degrees to radians is the same as for positive<a href=\"https:\/\/collegedunia.com\/exams\/gram-positive-bacteria-characteristics-types-and-gram-stain-test-biology-articleid-1715\"> <\/a>degrees. We simply have to multiply the value of the angle in degrees by&nbsp;$\\frac{\\pi}{180}$.<\/li>\n<\/ul>\n<\/div><\/div>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"8-conclusion\">Conclusion<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">In this article, we learned about the units, degrees and radians and their interconversions. Let&#8217;s solve some examples for better understanding.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"9-solved-examples-on-degrees-to-radians\">Solved Examples on Degrees to Radians<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>1. Convert each degree measure into radians.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>a) <\/strong>$120^{\\circ}$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>b) <\/strong>$150^{\\circ}$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Angle in Radians $=$ Angle in Degrees $ \\times \\frac{\\pi}{180^{\\circ}}$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">a) $120^{\\circ}$<strong> <\/strong>angle in radians $= &nbsp;120^{\\circ} \\times\\frac{\\pi}{180^{\\circ}} = \\frac{2\\pi}{3}$&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">b) $150^{\\circ}$<strong> <\/strong>angle in radians $= 150^{\\circ} \\times\\frac{\\pi}{180^{\\circ}} = \\frac{5\\pi}{6}$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>2. Convert <\/strong>$\\frac{2\\pi}{6}$<strong> radians to degrees.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Angle in degrees $=$ Angle in Radians $ \\times \\frac{180^{\\circ}{\\pi}$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Angle in degrees $= &nbsp;\\frac{2\\pi}{6} \\times \\frac{180^{\\circ}{\\pi}&nbsp; = 60^{\\circ}$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>3. Convert <\/strong>$-\\;100^{\\circ}$<strong> to radians.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Solution:&nbsp;<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Angle in radians $= (\\frac{\\pi}{180^{\\circ}}) \\times$ (angle in degrees)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Angle in radians $= \\frac{\\pi}{180^{\\circ}} \\times (-\\;100^{\\circ})$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Angle in radians $= \\;-\\;\\frac{5\\pi}{9}$ radians.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>4. Convert <\/strong>$540^{\\circ}$<strong> to radians.<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Solution:<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Angle in Radians $=$ Angle in Degrees $\\times \\frac{\\pi}{180^{\\circ}}$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Angle in radians $= 540^{\\circ} \\times \\frac{\\pi}{180^{\\circ}} = 3\\pi$ rad<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Thus,&nbsp; $540^{\\circ} =&nbsp; 9.425$ radians<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"10-practice-problems-on-degrees-to-radians\">Practice Problems on Degrees to Radians<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><div class=\"spq_wrapper\"><h2 style=\"display:none;\">Degrees to Radians: Conversion, Steps, Formula, Examples, Facts<\/h2><p style=\"display:none;\">Attend this quiz & Test your knowledge.<\/p><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">1<\/span><h3 class=\"sqp_question_text\">How many radians does a complete circle have?<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">360<\/div><div class=\"spq_answer_block\" data-value=\"1\">$2\\pi$ radians<\/div><div class=\"spq_answer_block\" data-value=\"2\">$\\pi$ radians<\/div><div class=\"spq_answer_block\" data-value=\"3\">2 radians<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $2\\pi$ radians<br\/>One complete counterclockwise revolution in degrees $= 360^{\\circ}$<br>\r\nOne complete counterclockwise revolution in radians $= 2\\pi$<br>\r\nThus, $360^{\\circ} = 2\\pi$ radians.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"0\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">2<\/span><h3 class=\"sqp_question_text\">Select the incorrect match.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">$60^{\\circ} = \\frac{\\pi}{4}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">$30^{\\circ} = \\frac{\\pi}{6}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">$90^{\\circ} = \\frac{\\pi}{2}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">$360^{\\circ} = 2\\pi$<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: $60^{\\circ} = \\frac{\\pi}{4}$<br\/>We convert degrees to radians by multiplying by $\\frac{\\pi}{180^{\\circ}}$.<br>\r\nThus, $60^{\\circ} \\times \\frac{\\pi}{180^{\\circ}} = \\frac{\\pi}{3}$ radians<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"3\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">3<\/span><h3 class=\"sqp_question_text\">1 degree = ___________ radians<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">017453<\/div><div class=\"spq_answer_block\" data-value=\"1\">0.107453<\/div><div class=\"spq_answer_block\" data-value=\"2\">0.17453<\/div><div class=\"spq_answer_block\" data-value=\"3\">0.017453<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: 0.017453<br\/>To convert degrees to radians, the derived formula is<br>\r\n$1^{\\circ} \\times \\frac{\\pi}{180} = 0.017453$ radians.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"1\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">4<\/span><h3 class=\"sqp_question_text\">_______ is an SI unit used to measure angles.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">Degrees<\/div><div class=\"spq_answer_block\" data-value=\"1\">Radians<\/div><div class=\"spq_answer_block\" data-value=\"2\">Both a and b<\/div><div class=\"spq_answer_block\" data-value=\"3\">None of the above<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: Radians<br\/>The SI unit of angle measure is the radian. The degree is not an SI unit, but it is mentioned in the SI brochure as an accepted unit.<\/span><\/div><\/div><\/div><div class=\"spq_question_wrapper\" data-answer=\"2\"><span class=\"spq_question_header\"><span class=\"sqp_question_number\">5<\/span><h3 class=\"sqp_question_text\">Degrees are converted into radians by formula,  Angle in radians = _______.<\/h3><\/span><div class=\"spq_answer_block\" data-value=\"0\">Angle in degrees $\\times \\frac{2\\pi}{180^{\\circ}}$<\/div><div class=\"spq_answer_block\" data-value=\"1\">Angle in radians $\\times \\frac{\\pi}{180^{\\circ}}$<\/div><div class=\"spq_answer_block\" data-value=\"2\">Angle in degrees $\\times \\frac{\\pi}{180^{\\circ}}$<\/div><div class=\"spq_answer_block\" data-value=\"3\">None of the above.<\/div><div class=\"sqp_question_hint\"><div class=\"sqp_question_hint__header\"><span class=\"spq_correct\">Correct<\/span><span class=\"spq_incorrect\">Incorrect<\/span><\/div><div class=\"sqp_question_hint__content\"><span>Correct answer is: Angle in degrees $\\times \\frac{\\pi}{180^{\\circ}}$<br\/>In order to convert any angle from the degree measure to radians, the value must simply  be multiplied by $\\frac{\\pi}{180^{\\circ}}$.\r\nAngle in Radians $=$ Angle in Degrees $\\times \\frac{\\pi}{180^{\\circ}}$<\/span><\/div><\/div><\/div><\/div>  <script type=\"application\/ld+json\">{\n        \"@context\": \"https:\/\/schema.org\/\", \n        \"@type\": \"Quiz\", \n        \"typicalAgeRange\": \"3-11\",\n        \"educationalLevel\":  \"beginner\",\n        \"assesses\" : \"Attend this quiz & Test your knowledge.\",\n        \"educationalAlignment\": [\n              {\n                \"@type\": \"AlignmentObject\",\n                \"alignmentType\": \"educationalSubject\",\n                \"targetName\": \"Math\"\n              }] ,\n        \"name\": \"Degrees to Radians: Conversion, Steps, Formula, Examples, Facts\",        \n        \"about\": {\n                \"@type\": \"Thing\",\n                \"name\": \"Degrees to Radians\"\n        },  \n        \"hasPart\": [{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"How many radians does a complete circle have?\",\n                    \"text\": \"How many radians does a complete circle have?\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"One complete counterclockwise revolution in degrees $$= 360^{\\\\circ}$$<br>\r\nOne complete counterclockwise revolution in radians $$= 2\\\\pi$$<br>\r\nThus, $$360^{\\\\circ} = 2\\\\pi$$ radians.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"360\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"One complete counterclockwise revolution in degrees $$= 360^{\\\\circ}$$<br>\r\nOne complete counterclockwise revolution in radians $$= 2\\\\pi$$<br>\r\nThus, $$360^{\\\\circ} = 2\\\\pi$$ radians.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$\\\\pi$$ radians\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"One complete counterclockwise revolution in degrees $$= 360^{\\\\circ}$$<br>\r\nOne complete counterclockwise revolution in radians $$= 2\\\\pi$$<br>\r\nThus, $$360^{\\\\circ} = 2\\\\pi$$ radians.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"2 radians\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"One complete counterclockwise revolution in degrees $$= 360^{\\\\circ}$$<br>\r\nOne complete counterclockwise revolution in radians $$= 2\\\\pi$$<br>\r\nThus, $$360^{\\\\circ} = 2\\\\pi$$ radians.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$2\\\\pi$$ radians\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"One complete counterclockwise revolution in degrees $$= 360^{\\\\circ}$$<br>\r\nOne complete counterclockwise revolution in radians $$= 2\\\\pi$$<br>\r\nThus, $$360^{\\\\circ} = 2\\\\pi$$ radians.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"One complete counterclockwise revolution in degrees $$= 360^{\\\\circ}$$<br>\r\nOne complete counterclockwise revolution in radians $$= 2\\\\pi$$<br>\r\nThus, $$360^{\\\\circ} = 2\\\\pi$$ radians.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Select the incorrect match.\",\n                    \"text\": \"Select the incorrect match.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"We convert degrees to radians by multiplying by $$\\\\frac{\\\\pi}{180^{\\\\circ}}$$.<br>\r\nThus, $$60^{\\\\circ} \\\\times \\\\frac{\\\\pi}{180^{\\\\circ}} = \\\\frac{\\\\pi}{3}$$ radians\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$30^{\\\\circ} = \\\\frac{\\\\pi}{6}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"We convert degrees to radians by multiplying by $$\\\\frac{\\\\pi}{180^{\\\\circ}}$$.<br>\r\nThus, $$60^{\\\\circ} \\\\times \\\\frac{\\\\pi}{180^{\\\\circ}} = \\\\frac{\\\\pi}{3}$$ radians\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$90^{\\\\circ} = \\\\frac{\\\\pi}{2}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"We convert degrees to radians by multiplying by $$\\\\frac{\\\\pi}{180^{\\\\circ}}$$.<br>\r\nThus, $$60^{\\\\circ} \\\\times \\\\frac{\\\\pi}{180^{\\\\circ}} = \\\\frac{\\\\pi}{3}$$ radians\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"$$360^{\\\\circ} = 2\\\\pi$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"We convert degrees to radians by multiplying by $$\\\\frac{\\\\pi}{180^{\\\\circ}}$$.<br>\r\nThus, $$60^{\\\\circ} \\\\times \\\\frac{\\\\pi}{180^{\\\\circ}} = \\\\frac{\\\\pi}{3}$$ radians\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 0,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"$$60^{\\\\circ} = \\\\frac{\\\\pi}{4}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"We convert degrees to radians by multiplying by $$\\\\frac{\\\\pi}{180^{\\\\circ}}$$.<br>\r\nThus, $$60^{\\\\circ} \\\\times \\\\frac{\\\\pi}{180^{\\\\circ}} = \\\\frac{\\\\pi}{3}$$ radians\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"We convert degrees to radians by multiplying by $$\\\\frac{\\\\pi}{180^{\\\\circ}}$$.<br>\r\nThus, $$60^{\\\\circ} \\\\times \\\\frac{\\\\pi}{180^{\\\\circ}} = \\\\frac{\\\\pi}{3}$$ radians\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"1 degree = ___________ radians\",\n                    \"text\": \"1 degree = ___________ radians\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"To convert degrees to radians, the derived formula is<br>\r\n$$1^{\\\\circ} \\\\times \\\\frac{\\\\pi}{180} = 0.017453$$ radians.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"017453\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"To convert degrees to radians, the derived formula is<br>\r\n$$1^{\\\\circ} \\\\times \\\\frac{\\\\pi}{180} = 0.017453$$ radians.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"0.107453\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"To convert degrees to radians, the derived formula is<br>\r\n$$1^{\\\\circ} \\\\times \\\\frac{\\\\pi}{180} = 0.017453$$ radians.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"0.17453\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"To convert degrees to radians, the derived formula is<br>\r\n$$1^{\\\\circ} \\\\times \\\\frac{\\\\pi}{180} = 0.017453$$ radians.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 3,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"0.017453\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"To convert degrees to radians, the derived formula is<br>\r\n$$1^{\\\\circ} \\\\times \\\\frac{\\\\pi}{180} = 0.017453$$ radians.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"To convert degrees to radians, the derived formula is<br>\r\n$$1^{\\\\circ} \\\\times \\\\frac{\\\\pi}{180} = 0.017453$$ radians.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"_______ is an SI unit used to measure angles.\",\n                    \"text\": \"_______ is an SI unit used to measure angles.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"The SI unit of angle measure is the radian. The degree is not an SI unit, but it is mentioned in the SI brochure as an accepted unit.\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Degrees\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The SI unit of angle measure is the radian. The degree is not an SI unit, but it is mentioned in the SI brochure as an accepted unit.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 2,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Both a and b\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The SI unit of angle measure is the radian. The degree is not an SI unit, but it is mentioned in the SI brochure as an accepted unit.\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"None of the above\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"The SI unit of angle measure is the radian. The degree is not an SI unit, but it is mentioned in the SI brochure as an accepted unit.\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 1,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"Radians\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"The SI unit of angle measure is the radian. The degree is not an SI unit, but it is mentioned in the SI brochure as an accepted unit.\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"The SI unit of angle measure is the radian. The degree is not an SI unit, but it is mentioned in the SI brochure as an accepted unit.\"\n                      }\n                    } \n\n                    },{\n                    \"@type\": \"Question\",   \n                    \"eduQuestionType\": \"Multiple choice\",\n                    \"learningResourceType\": \"Practice problem\",\n                    \"name\": \"Degrees are converted into radians by formula,  Angle in radians = _______.\",\n                    \"text\": \"Degrees are converted into radians by formula,  Angle in radians = _______.\",\n                    \"comment\": {\n                      \"@type\": \"Comment\",\n                      \"text\": \"In order to convert any angle from the degree measure to radians, the value must simply  be multiplied by $$\\\\frac{\\\\pi}{180^{\\\\circ}}$$.\r\nAngle in Radians $$=$$ Angle in Degrees $$\\\\times \\\\frac{\\\\pi}{180^{\\\\circ}}$$\"\n                    },\n                    \"encodingFormat\": \"text\/html\",\n                    \"suggestedAnswer\": [ {\n                                \"@type\": \"Answer\",\n                                \"position\": 0,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Angle in degrees $$\\\\times \\\\frac{2\\\\pi}{180^{\\\\circ}}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"In order to convert any angle from the degree measure to radians, the value must simply  be multiplied by $$\\\\frac{\\\\pi}{180^{\\\\circ}}$$.\r\nAngle in Radians $$=$$ Angle in Degrees $$\\\\times \\\\frac{\\\\pi}{180^{\\\\circ}}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 1,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"Angle in radians $$\\\\times \\\\frac{\\\\pi}{180^{\\\\circ}}$$\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"In order to convert any angle from the degree measure to radians, the value must simply  be multiplied by $$\\\\frac{\\\\pi}{180^{\\\\circ}}$$.\r\nAngle in Radians $$=$$ Angle in Degrees $$\\\\times \\\\frac{\\\\pi}{180^{\\\\circ}}$$\"\n                                    }\n                                }, {\n                                \"@type\": \"Answer\",\n                                \"position\": 3,\n                                \"encodingFormat\": \"text\/html\",\n                                \"text\": \"None of the above.\",\n                                \"comment\": {\n                                    \"@type\": \"Comment\",\n                                    \"text\": \"In order to convert any angle from the degree measure to radians, the value must simply  be multiplied by $$\\\\frac{\\\\pi}{180^{\\\\circ}}$$.\r\nAngle in Radians $$=$$ Angle in Degrees $$\\\\times \\\\frac{\\\\pi}{180^{\\\\circ}}$$\"\n                                    }\n                                }],\n                    \"acceptedAnswer\": {\n                      \"@type\": \"Answer\",\n                      \"position\": 2,\n                      \"encodingFormat\": \"text\/html\",\n                      \"text\": \"Angle in degrees $$\\\\times \\\\frac{\\\\pi}{180^{\\\\circ}}$$\",\n                      \"comment\": {\n                          \"@type\": \"Comment\",\n                          \"text\": \"In order to convert any angle from the degree measure to radians, the value must simply  be multiplied by $$\\\\frac{\\\\pi}{180^{\\\\circ}}$$.\r\nAngle in Radians $$=$$ Angle in Degrees $$\\\\times \\\\frac{\\\\pi}{180^{\\\\circ}}$$\"\n                        },\n                      \"answerExplanation\": {\n                        \"@type\": \"Comment\",\n                        \"text\": \"In order to convert any angle from the degree measure to radians, the value must simply  be multiplied by $$\\\\frac{\\\\pi}{180^{\\\\circ}}$$.\r\nAngle in Radians $$=$$ Angle in Degrees $$\\\\times \\\\frac{\\\\pi}{180^{\\\\circ}}$$\"\n                      }\n                    } \n\n                    }]}<\/script><\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"11-frequently-asked-questions-about-degrees-to-radians\">Frequently Asked Questions about Degrees to Radians<\/h2>\n\n\n<div class=\"wp-block-ub-content-toggle\" id=\"ub-content-toggle-4fd02faf-bd7c-4533-9f0c-a2130a5c271a\" data-mobilecollapse=\"true\" data-desktopcollapse=\"true\">\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-0-4fd02faf-bd7c-4533-9f0c-a2130a5c271a\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-4fd02faf-bd7c-4533-9f0c-a2130a5c271a\"><strong>What is the measure of 0 radians in degrees?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-0-4fd02faf-bd7c-4533-9f0c-a2130a5c271a\">\n\n<p class=\"wp-block-paragraph\">To convert 0 radians to degrees, we multiply it by $\\frac{180^{\\circ}}{\\pi}$.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">So, 0 radians $= 0 \\times \\frac{180^{\\circ}}{\\pi} = 0$<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Thus, the measure of 0 radian in degrees is zero.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-1-4fd02faf-bd7c-4533-9f0c-a2130a5c271a\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-4fd02faf-bd7c-4533-9f0c-a2130a5c271a\"><strong>What is the difference between degrees and radians?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-1-4fd02faf-bd7c-4533-9f0c-a2130a5c271a\">\n\n<p class=\"wp-block-paragraph\">Degree measurement is based on the extent of rotation from the initial arm to the terminal arm of an angle. As an observer, degrees indicate how much you tilted your head from the starting point to the end point of the angle.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In contrast, radians measure an angle based on the distance traveled along the circumference of a circle. When the distance traveled is equal to the radius of the circle, it is referred to as 1 radian.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">It&#8217;s important to note that both degrees and radians are used to quantify angles, but they represent angles in different ways.<\/p>\n\n<\/div><\/div>\n\n<div class=\"wp-block-ub-content-toggle-accordion\">\n                <div class=\"wp-block-ub-content-toggle-accordion-title-wrap\" aria-expanded=\"false\" aria-controls=\"ub-content-toggle-panel-2-4fd02faf-bd7c-4533-9f0c-a2130a5c271a\" tabindex=\"0\">\n                    <p class=\"wp-block-ub-content-toggle-accordion-title ub-content-toggle-title-4fd02faf-bd7c-4533-9f0c-a2130a5c271a\"><strong>What is 1 radian?<\/strong><\/p><div class=\"wp-block-ub-content-toggle-accordion-toggle-wrap right\"><span class=\"wp-block-ub-content-toggle-accordion-state-indicator wp-block-ub-chevron-down\"><\/span>\n                    <\/div><\/div><div role=\"region\" class=\"wp-block-ub-content-toggle-accordion-content-wrap ub-hide\" id=\"ub-content-toggle-panel-2-4fd02faf-bd7c-4533-9f0c-a2130a5c271a\">\n\n<p class=\"wp-block-paragraph\">One radian is the measure of the central angle spanned by the arc whose arc-length equals radius.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"228\" height=\"252\" src=\"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-content\/uploads\/2023\/08\/one-radian.png\" alt=\"1 radian\" class=\"wp-image-32747\" title=\"1 radian\"\/><\/figure>\n\n<\/div><\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>What Is the Degrees to Radians Conversion? Any angle in degrees can be converted into radians using the degrees to radians conversion. The relationship between degrees and radians is given as $2\\pi = 360^{\\circ}$ or $\\pi = 180^{\\circ}$. One complete counterclockwise revolution is represented by $2\u03c0$ (in radians) or $360^{\\circ}$ (in degrees). Degree and radian &#8230; <a title=\"Degrees to Radians: Conversion, Steps, Formula, Examples, Facts\" class=\"read-more\" href=\"https:\/\/www.splashlearn.com\/math-vocabulary\/degrees-to-radians\" aria-label=\"More on Degrees to Radians: Conversion, Steps, Formula, Examples, Facts\">Read more<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"ub_ctt_via":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-32726","post","type-post","status-publish","format-standard","hentry","category-all"],"featured_image_src":null,"author_info":{"display_name":"Mithun Jhawar","author_link":"https:\/\/www.splashlearn.com\/math-vocabulary\/author\/mithun-jhawarsplashlearn-com\/"},"acf":[],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/32726","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/comments?post=32726"}],"version-history":[{"count":18,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/32726\/revisions"}],"predecessor-version":[{"id":32753,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/posts\/32726\/revisions\/32753"}],"wp:attachment":[{"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/media?parent=32726"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/categories?post=32726"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.splashlearn.com\/math-vocabulary\/wp-json\/wp\/v2\/tags?post=32726"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}