{"id":55796,"date":"2014-12-17T10:05:40","date_gmt":"2014-12-17T08:05:40","guid":{"rendered":"http:\/\/wpcalc.com\/?p=55796"},"modified":"2026-10-23T17:01:01","modified_gmt":"2026-10-23T14:01:01","slug":"circumference","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/converters\/circumference\/","title":{"rendered":"Degrees to Radians Converter \u2013 Angle Units"},"content":{"rendered":"<section class=\"not-prose calculator-box\" aria-labelledby=\"calculator-title\"><div class=\"flex items-baseline sm:items-center justify-between gap-2 sm:gap-3\"><div class=\"flex flex-col sm:flex-row sm:items-center gap-2\"><span class=\"icon icon-calculator text-primary-700! text-base! dark:text-primary-300!\" aria-hidden=\"true\"><\/span><h2 id=\"calculator-title\" class=\"text-lg font-display font-bold\">Convert Circle Units to Angle Measures<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"55796\" data-favorite-title=\"Circle to Angle Units\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/converters\/circumference\/\" data-favorite-excerpt=\"Convert an angle between degrees, radians, gradians, sextants, arcminutes, and arcseconds. Enter an angle value, then select the source and target units.\" aria-label=\"Add to Favorites\" data-favorite-icon=\"icon icon-units\">\n    <span class=\"icon icon-shape-star-empty\" aria-hidden=\"true\"><\/span>\n  <\/button>\n  <div class=\"calcdash-favorite__tip\" aria-hidden=\"true\">\n   <span class=\"favorite-tooltip\" id=\"favorite-tooltip\"><\/span>\n  <\/div>\n  <span class=\"sr-only\" role=\"status\" id=\"favorite-status\"><\/span>\n<\/div><\/div><form action=\"https:\/\/wpcalc.com\/en\/converters\/circumference\/\" method=\"POST\" class=\"calculator\" id=\"calculator-55796\" data-post=\"55796\"><fieldset class=\"fieldset-input\"><legend class=\"sr-only\">Input Fields<\/legend><div class=\"field is-single\" id=\"input-1\"><label for=\"field-1\">Angle value<\/label><input type=\"number\" name=\"angle_value\" id=\"field-1\" aria-describedby=\"calc-info-1\" step=\"any\" value=\"180\"\/><small id=\"calc-info-1\">Enter the value of the angle you want to convert<\/small><\/div><div class=\"field\" id=\"input-2\"><label for=\"field-2\">From unit<\/label><div class=\"grid grid-cols-1\"><select id=\"field-2\" name=\"from_unit\"><option value=\"degree\">Degree (\u00b0)<\/option><option value=\"radian\">Radian (rad)<\/option><option value=\"gradian\">Gradian (gon)<\/option><option value=\"sextant\">Sextant (1\/6 circle)<\/option><option value=\"minute\">Minute (\u2032)<\/option><option value=\"second\">Second (\u2033)<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><div class=\"field\" id=\"input-3\"><label for=\"field-3\">To unit<\/label><div class=\"grid grid-cols-1\"><select id=\"field-3\" name=\"to_unit\"><option value=\"degree\">Degree (\u00b0)<\/option><option value=\"radian\">Radian (rad)<\/option><option value=\"gradian\">Gradian (gon)<\/option><option value=\"sextant\">Sextant (1\/6 circle)<\/option><option value=\"minute\">Minute (\u2032)<\/option><option value=\"second\">Second (\u2033)<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Re-Calculate\" id=\"calculate-button\" data-post=\"55796\">Calculate<\/button><button type=\"reset\">Reset<\/button><\/div><div class=\"field is-checkbox hidden!\" id=\"field-auto-calc\"><input type=\"checkbox\" id=\"auto-calc\"><label for=\"auto-calc\">Calculate automatically<\/label><small>If enabled, the result will update automatically when you change any value.<\/small><\/div><div class=\"fieldset-result is-hidden\" aria-labelledby=\"result-title\" aria-live=\"polite\" role=\"region\"> <h3 class=\"result-title bg-gradient-to-r from-primary-50 to-gray-50 dark:from-primary-900 dark:to-gray-800\" id=\"result-title\"><span class=\"icon icon-s-pulse\" aria-hidden=\"true\"><\/span> Your Results<\/h3><div class=\"result-box\"><div class=\"field-result is-column\" id=\"output-1\"><span class=\"field-title\"><span>Converted value<\/span><\/span><span class=\"field-value\" id=\"result-1\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copy Result\" aria-label=\"Copy Result\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><\/div><div class=\"result-actions\"><button type=\"button\" class=\"copy-link\"><svg viewBox=\"0 0 20 20\" fill=\"currentColor\" aria-hidden=\"true\"><path d=\"M12.232 4.232a2.5 2.5 0 0 1 3.536 3.536l-1.225 1.224a.75.75 0 0 0 1.061 1.06l1.224-1.224a4 4 0 0 0-5.656-5.656l-3 3a4 4 0 0 0 .225 5.865.75.75 0 0 0 .977-1.138 2.5 2.5 0 0 1-.142-3.667l3-3Z\"\/><path d=\"M11.603 7.963a.75.75 0 0 0-.977 1.138 2.5 2.5 0 0 1 .142 3.667l-3 3a2.5 2.5 0 0 1-3.536-3.536l1.225-1.224a.75.75 0 0 0-1.061-1.06l-1.224 1.224a4 4 0 1 0 5.656 5.656l3-3a4 4 0 0 0-.225-5.865Z\"\/><\/svg><span class=\"copy-link__text\">Copy link to this calculation<\/span><\/button><span class=\"sr-only\" role=\"status\" id=\"copy-link-status\"><\/span><\/div><\/div><a href=\"#respond\" class=\"hidden transition-opacity duration-300 opacity-0 w-50 text-sm justify-center items-center gap-2 px-4 py-2 rounded bg-gray-200 text-gray-700 hover:bg-gray-300\" id=\"leave-comment\"><span class=\"icon icon-comments\" aria-hidden=\"true\"><\/span>Leave a Comment<\/a><\/form><\/section><section id=\"calc-reactions\" class=\"not-prose hidden my-12 bg-gradient-to-r from-primary-50 to-gray-50 border border-indigo-100 rounded-xl px-6 py-4 shadow-sm\" data-post=\"55796\" aria-live=\"polite\" aria-labelledby=\"calc-reactions-title\"><p id=\"calc-reactions-title\" class=\"text-sm text-gray-500 text-center mb-2\">How did this result make you feel?<\/p><div role=\"group\" aria-labelledby=\"calc-reactions-title\" class=\"grid grid-cols-3 sm:flex sm:flex-row sm:justify-around gap-4 sm:items-center sm:flex-wrap\"><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"like\"><span class=\"reaction-count\" data-reaction-count=\"like\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude00 <\/span><span class=\"reaction-description font-medium\">Like <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"helpful\"><span class=\"reaction-count\" data-reaction-count=\"helpful\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\udca1 <\/span><span class=\"reaction-description font-medium\">Helpful <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"confused\"><span class=\"reaction-count\" data-reaction-count=\"confused\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude15 <\/span><span class=\"reaction-description font-medium\">Confused <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"disappointed\"><span class=\"reaction-count\" data-reaction-count=\"disappointed\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude1e <\/span><span class=\"reaction-description font-medium\">Disappointed <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"inaccurate\"><span class=\"reaction-count\" data-reaction-count=\"inaccurate\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\u274c <\/span><span class=\"reaction-description font-medium\">Inaccurate <\/span><\/button><\/div><div id=\"reaction-message\" class=\"hidden mt-8 rounded-md border border-primary-100 bg-white\/50 backdrop-blur-sm px-4 py-2 text-sm text-center shadow-sm\"><\/div><\/section><div class=\"calcdash-ad not-prose calcdash-ad--calc_result calcdash-ad--in-article\"><ins class=\"adsbygoogle\" style=\"display:block\" data-ad-client=\"ca-pub-1721569815777345\" data-ad-slot=\"6317458308\" data-ad-layout=\"in-article\" data-ad-format=\"fluid\"><\/ins><script>(adsbygoogle = window.adsbygoogle || []).push({});<\/script><\/div>\n<style id=\"wpcoderpro-inline-1\">.formula-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section class=\"formula-box\" aria-labelledby=\"formula-title\">\r\n\t<div id=\"formula-title\" class=\"not-prose font-display mb-4\"><span class=\"icon icon-formula\" aria-hidden=\"true\"><\/span><h2>Circle to Angle Units Formula<\/h2><\/div>\r\n\t<figure class=\"not-prose formula\">\r\n\t\t<figcaption class=\"formula-title\">Formula<\/figcaption>\r\n\t\t<div class=\"text-base text-gray-800\" id=\"formula\">\n\\[d=x f_{\\mathrm{from}},\\qquad y=\\frac{d}{f_{\\mathrm{to}}}\\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Where:<\/strong><\/p>\n<ul>\n<li>\\(x\\) \u2014 the angle value entered<\/li>\n<li>\\(f_{\\mathrm{from}}\\) \u2014 degrees per source unit<\/li>\n<li>\\(d\\) \u2014 the angle expressed in degrees<\/li>\n<li>\\(f_{\\mathrm{to}}\\) \u2014 degrees per target unit<\/li>\n<li>\\(y\\) \u2014 the converted angle in the target unit<\/li>\n<\/ul>\n<p>The calculator first expresses the angle in degrees, then converts it to the selected target unit. The degrees-per-unit factors are 1 for a degree, \\(180\/\\pi\\) for a radian, 0.9 for a gradian, 60 for a sextant, \\(1\/60\\) for an arcminute, and \\(1\/3600\\) for an arcsecond.<\/p>\n<p>\r\n<\/section>\n<style id=\"wpcoderpro-inline-459\">.calculation-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section id=\"calculation\" class=\"calculation-box\" aria-labelledby=\"calculation-title\">\r\n\t<div id=\"calculation-title\" class=\"not-prose font-display\"><span class=\"icon icon-unordered-list\" aria-hidden=\"true\"><\/span><h2>Circle to Angle Units \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Example:<\/strong> use the default settings to convert an angle of 180 degrees to radians.<\/p>\n<p>\\[d=180\\times1=180^\\circ,\\qquad y=\\frac{180}{180\/\\pi}=\\pi\\approx3.141593\\text{ rad}\\]<\/p>\n<p><strong>Result:<\/strong> 180\u00b0 equals approximately 3.141593 rad.<\/p>\n<p>\n\r\n<\/section>\n<h2>How to use the calculator<\/h2>\n<ol>\n<li>Enter the number you want to convert in <strong>Angle value<\/strong>. Decimals and negative values are accepted.<\/li>\n<li>Choose its current unit in <strong>From unit<\/strong>: Degree (\u00b0), Radian (rad), Gradian (gon), Sextant (1\/6 circle), Minute (\u2032), or Second (\u2033).<\/li>\n<li>Choose the unit you want in <strong>To unit<\/strong>. The <strong>Converted value<\/strong> shows the result in that unit, rounded to six decimal places.<\/li>\n<\/ol>\n<p>For example, to convert 2.5 radians to degrees, enter 2.5, select Radian (rad) as <strong>From unit<\/strong>, and select Degree (\u00b0) as <strong>To unit<\/strong>. You can reverse a conversion by swapping the two unit selections.<\/p>\n<h2>Understanding circle and angle units<\/h2>\n<p>An angle describes an amount of rotation. A complete circle is 360 degrees, \\(2\\pi\\) radians, or 400 gradians. These units describe the same rotation using different scales: a right angle is 90\u00b0, \\(\\pi\/2\\) rad, or 100 gon. Converting units changes the number shown, not the angle itself.<\/p>\n<p>Radians are common in trigonometry, calculus, and rotational formulas because they relate an angle directly to a circle\u2019s radius and arc length. Degrees are often easier to read in everyday geometry. Gradians divide a right angle into 100 parts and may appear in surveying. A sextant, as defined in this calculator, is one-sixth of a full circle: 60\u00b0, or \\(\\pi\/3\\) rad. It is an angular unit here, not a measurement from a navigational instrument.<\/p>\n<p>Minute (\u2032) and Second (\u2033) mean <em>arcminute<\/em> and <em>arcsecond<\/em>. There are 60 arcminutes in one degree and 60 arcseconds in one arcminute. They measure small angles, not elapsed time. The result is always expressed in the single unit selected under <strong>To unit<\/strong>; the calculator does not split an angle into degrees, minutes, and seconds.<\/p>\n<h2>Assumptions and practical tips<\/h2>\n<p>The converter treats each entry as an angular measurement, including entries larger than one full circle or smaller than zero. For instance, 450\u00b0 converts to \\(5\\pi\/2\\) radians rather than being reduced to 90\u00b0. A negative result indicates rotation in the opposite direction under the usual angle convention; it does not change the size of the conversion factor.<\/p>\n<p>Results are rounded to six decimal places for display. If you convert a displayed decimal result back to its original unit, that rounding may produce a small difference. Calculations involving \\(\\pi\\), such as degrees to radians, are generally not exact when written as finite decimals. For manual work, keep an exact form such as \\(\\pi\/2\\) rad when possible, and round only at the end.<\/p>\n<p>Angle alone does not tell you how far a point travels or how quickly something rotates: those questions also require a radius or a time interval. For related rotational quantities, see the <a href=\"https:\/\/wpcalc.com\/en\/converters\/frequency\/\">frequency converter<\/a> for cycles per unit of time and the <a href=\"https:\/\/wpcalc.com\/en\/converters\/torque\/\">torque converter<\/a> for turning effects of force.<\/p>\n<h2>Full-circle reference<\/h2>\n<table>\n<thead>\n<tr>\n<th>Unit<\/th>\n<th>One complete circle<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>Degrees<\/td>\n<td>360\u00b0<\/td>\n<\/tr>\n<tr>\n<td>Radians<\/td>\n<td>\\(2\\pi\\) rad (about 6.283185 rad)<\/td>\n<\/tr>\n<tr>\n<td>Gradians<\/td>\n<td>400 gon<\/td>\n<\/tr>\n<tr>\n<td>Sextants<\/td>\n<td>6 sextants<\/td>\n<\/tr>\n<tr>\n<td>Arcminutes<\/td>\n<td>21,600\u2032<\/td>\n<\/tr>\n<tr>\n<td>Arcseconds<\/td>\n<td>1,296,000\u2033<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>This table provides a quick check on conversions. Half of any listed value represents a half-turn; one-quarter represents a right angle. To convert a fraction of a circle into a unit, multiply that fraction by the unit\u2019s full-circle value.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Convert an angle between degrees, radians, gradians, sextants, arcminutes, and arcseconds. Enter an angle value, then select the source and target units.<\/p>\n","protected":false},"author":70,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[3],"tags":[13],"class_list":["post-55796","post","type-post","status-publish","format-standard","hentry","category-converters","tag-basic-units"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/55796","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/users\/70"}],"replies":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/comments?post=55796"}],"version-history":[{"count":3,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/55796\/revisions"}],"predecessor-version":[{"id":67500,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/55796\/revisions\/67500"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=55796"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=55796"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=55796"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}