{"id":17309,"date":"2021-09-27T07:58:58","date_gmt":"2021-09-27T02:28:58","guid":{"rendered":"http:\/\/www.pythonpool.com\/?p=17309"},"modified":"2026-07-13T12:37:03","modified_gmt":"2026-07-13T07:07:03","slug":"radians-to-degrees-python","status":"publish","type":"post","link":"https:\/\/www.pythonpool.com\/radians-to-degrees-python\/","title":{"rendered":"Convert Radians to Degrees in Python: math and NumPy"},"content":{"rendered":"<p><strong>Quick answer:<\/strong> Use math.degrees() for one scalar angle and numpy.degrees() for arrays. Both convert radians to degrees by multiplying by 180 divided by pi. Keep full precision while an angle participates in calculations, then round only when formatting a label or report.<\/p>\n<figure class=\"pythonpool-article-visual\"><img src=\"https:\/\/www.pythonpool.com\/wp-content\/uploads\/2026\/07\/radians-to-degrees-python.png\" alt=\"Python Pool infographic converting radians to degrees with math degrees NumPy degrees formula and round trip\" width=\"1536\" height=\"1024\" loading=\"lazy\" decoding=\"async\"><figcaption>Use math.degrees() for a scalar and numpy.degrees() for arrays; convert at the presentation boundary and round only for display.<\/figcaption><\/figure>\n<p>The easiest way to convert radians to degrees in Python is <code>math.degrees(angle)<\/code>. It converts an angle measured in radians into the matching degree value.<\/p>\n<p>The main references are Python&#8217;s <a href=\"https:\/\/docs.python.org\/3\/library\/math.html#math.degrees\">math.degrees documentation<\/a>, the <a href=\"https:\/\/docs.python.org\/3\/library\/math.html#math.radians\">math.radians documentation<\/a>, and NumPy&#8217;s <a href=\"https:\/\/numpy.org\/doc\/stable\/reference\/generated\/numpy.degrees.html\">numpy.degrees documentation<\/a>.<\/p>\n<p>Radians and degrees measure the same angle with different units. A full circle is <code>2 * pi<\/code> radians or <code>360<\/code> degrees, so <code>pi<\/code> radians equals <code>180<\/code> degrees.<\/p>\n<p>Use <code>math.degrees()<\/code> for one number. Use NumPy when you need vectorized conversion across many values.<\/p>\n<p>The most common mistake is mixing units in the same calculation. Trigonometric functions such as <code>math.sin()<\/code> and <code>math.cos()<\/code> expect radians, while user-facing reports often show degrees.<\/p>\n<p>Convert only at the boundary where the unit changes. That might be when reading input, printing output, or passing data into a library that expects a specific angle unit.<\/p>\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_85 counter-hierarchy ez-toc-counter ez-toc-transparent ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">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\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #990303;color:#990303\" 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: #990303;color:#990303\" 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><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 eztoc-toggle-hide-by-default' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/www.pythonpool.com\/radians-to-degrees-python\/#Use_mathdegrees\" >Use math.degrees<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/www.pythonpool.com\/radians-to-degrees-python\/#Convert_With_The_Formula\" >Convert With The Formula<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/www.pythonpool.com\/radians-to-degrees-python\/#Convert_A_List_Of_Angles\" >Convert A List Of Angles<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/www.pythonpool.com\/radians-to-degrees-python\/#Round_The_Output\" >Round The Output<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/www.pythonpool.com\/radians-to-degrees-python\/#Convert_Back_To_Radians\" >Convert Back To Radians<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/www.pythonpool.com\/radians-to-degrees-python\/#Use_NumPy_For_Arrays\" >Use NumPy For Arrays<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/www.pythonpool.com\/radians-to-degrees-python\/#Convert_A_Scalar_With_mathdegrees\" >Convert A Scalar With math.degrees<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/www.pythonpool.com\/radians-to-degrees-python\/#Convert_Arrays_With_NumPy\" >Convert Arrays With NumPy<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/www.pythonpool.com\/radians-to-degrees-python\/#Use_The_Formula_When_Explaining_Or_Porting\" >Use The Formula When Explaining Or Porting<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/www.pythonpool.com\/radians-to-degrees-python\/#Round_Only_At_The_Presentation_Boundary\" >Round Only At The Presentation Boundary<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/www.pythonpool.com\/radians-to-degrees-python\/#Frequently_Asked_Questions\" >Frequently Asked Questions<\/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:\/\/www.pythonpool.com\/radians-to-degrees-python\/#How_do_I_convert_radians_to_degrees_in_Python\" >How do I convert radians to degrees in Python?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/www.pythonpool.com\/radians-to-degrees-python\/#What_is_the_radians-to-degrees_formula\" >What is the radians-to-degrees formula?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/www.pythonpool.com\/radians-to-degrees-python\/#How_do_I_convert_a_list_of_radians\" >How do I convert a list of radians?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/www.pythonpool.com\/radians-to-degrees-python\/#Should_I_round_converted_angles\" >Should I round converted angles?<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Use_mathdegrees\"><\/span>Use math.degrees<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The standard library <code>math<\/code> module handles the common one-value conversion.<\/p>\n<div class=\"pythonpool-code-scroll\" style=\"max-width:100%;overflow-x:auto;-webkit-overflow-scrolling:touch;\">\n<pre><code class=\"language-python\">import math\n\nangle = math.pi\nresult = math.degrees(angle)\n\nprint(result)\n<\/code><\/pre>\n<\/div>\n<p>The output is <code>180.0<\/code>.<\/p>\n<p>This is the clearest option for scripts, formulas, and functions that work with one angle at a time.<\/p>\n<p>If the source value already comes from a trigonometric calculation, it is probably already in radians. Convert it to degrees only when a reader or downstream system needs degrees.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Convert_With_The_Formula\"><\/span>Convert With The Formula<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The formula is <code>degrees = radians * 180 \/ pi<\/code>. Python&#8217;s helper uses the same idea.<\/p>\n<div class=\"pythonpool-code-scroll\" style=\"max-width:100%;overflow-x:auto;-webkit-overflow-scrolling:touch;\">\n<pre><code class=\"language-python\">import math\n\nangle = math.pi \/ 2\nresult = angle * 180 \/ math.pi\n\nprint(result)\n<\/code><\/pre>\n<\/div>\n<p>This prints <code>90.0<\/code>. The formula is useful when explaining the math, but <code>math.degrees()<\/code> is usually better in production code.<\/p>\n<p>A named helper also avoids repeating the formula throughout a project.<\/p>\n<p>When you use the formula directly, always use <code>math.pi<\/code> instead of a shortened hand-written value. That keeps the conversion consistent with the standard library helper.<\/p>\n<p><!-- Python Pool visual layout repair 2026-07-13 --><\/p>\n<figure class=\"pythonpool-article-visual pythonpool-supporting-visual\"><img src=\"https:\/\/www.pythonpool.com\/wp-content\/uploads\/2026\/07\/radians-degrees-circle-b222.png\" alt=\"Python Pool infographic showing a unit circle, angle in radians, arc length, and one full turn\" width=\"1536\" height=\"1054\" loading=\"lazy\" decoding=\"async\"><figcaption>A radian measures an angle by the arc length it cuts from a circle of radius one.<\/figcaption><\/figure>\n<h2><span class=\"ez-toc-section\" id=\"Convert_A_List_Of_Angles\"><\/span>Convert A List Of Angles<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Use a list comprehension when you have a short list of angles.<\/p>\n<div class=\"pythonpool-code-scroll\" style=\"max-width:100%;overflow-x:auto;-webkit-overflow-scrolling:touch;\">\n<pre><code class=\"language-python\">import math\n\nangles = [0, math.pi \/ 6, math.pi \/ 4, math.pi \/ 2, math.pi]\ndegree_values = [math.degrees(item) for item in angles]\n\nprint(degree_values)\n<\/code><\/pre>\n<\/div>\n<p>This keeps the conversion readable and works without any third-party dependency.<\/p>\n<p>For large numeric arrays, NumPy is usually faster and more convenient.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Round_The_Output\"><\/span>Round The Output<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Many conversions produce floating-point results with more precision than you want to display.<\/p>\n<div class=\"pythonpool-code-scroll\" style=\"max-width:100%;overflow-x:auto;-webkit-overflow-scrolling:touch;\">\n<pre><code class=\"language-python\">import math\n\nangle = 1.234\nresult = math.degrees(angle)\nrounded = round(result, 2)\n\nprint(result)\nprint(rounded)\n<\/code><\/pre>\n<\/div>\n<p>Round only for display or reporting. Keep the unrounded value for later calculations when precision matters.<\/p>\n<p>Floating-point output may include tiny representation differences. That is normal for decimal display of binary floating-point numbers.<\/p>\n<figure class=\"pythonpool-article-visual pythonpool-supporting-visual\"><img src=\"https:\/\/www.pythonpool.com\/wp-content\/uploads\/2026\/07\/radians-degrees-convert-b222.png\" alt=\"Python Pool infographic mapping radians through math.degrees to degrees and angle output\" width=\"1536\" height=\"1054\" loading=\"lazy\" decoding=\"async\"><figcaption>math.degrees converts a radian value to its equivalent degree measure.<\/figcaption><\/figure>\n<h2><span class=\"ez-toc-section\" id=\"Convert_Back_To_Radians\"><\/span>Convert Back To Radians<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Use <code>math.radians()<\/code> to convert degrees back to radians.<\/p>\n<div class=\"pythonpool-code-scroll\" style=\"max-width:100%;overflow-x:auto;-webkit-overflow-scrolling:touch;\">\n<pre><code class=\"language-python\">import math\n\ndegree_value = 180\nangle = math.radians(degree_value)\n\nprint(angle)\nprint(math.isclose(angle, math.pi))\n<\/code><\/pre>\n<\/div>\n<p><code>math.isclose()<\/code> is a good way to compare floating-point results instead of expecting exact equality in every calculation.<\/p>\n<p>This is helpful in tests where a rounded display value and a calculated value may not match character for character.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Use_NumPy_For_Arrays\"><\/span>Use NumPy For Arrays<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>NumPy can convert an array of radians in one call.<\/p>\n<div class=\"pythonpool-code-scroll\" style=\"max-width:100%;overflow-x:auto;-webkit-overflow-scrolling:touch;\">\n<pre><code class=\"language-python\">import numpy as np\n\nangles = np.array([0, np.pi \/ 2, np.pi])\ndegree_values = np.degrees(angles)\n\nprint(degree_values)\n<\/code><\/pre>\n<\/div>\n<p>Use NumPy when your data already lives in arrays or pandas workflows. For one-off conversions, the standard <code>math<\/code> module is enough.<\/p>\n<p>The practical rule is simple: <code>math.degrees()<\/code> for one angle, a list comprehension for a small plain-Python list, and <code>numpy.degrees()<\/code> for arrays.<\/p>\n<p>When documenting formulas, include the unit in names such as <code>angle_radians<\/code> or <code>angle_degrees<\/code>. That prevents accidentally mixing the two units in later code.<\/p>\n<p>For tests, check known angle pairs: <code>0<\/code> radians is <code>0<\/code> degrees, <code>pi \/ 2<\/code> radians is <code>90<\/code> degrees, <code>pi<\/code> radians is <code>180<\/code> degrees, and <code>2 * pi<\/code> radians is <code>360<\/code> degrees.<\/p>\n<p>Use <code>math.isclose()<\/code> for calculated comparisons because floating-point results can differ by tiny amounts. This matters more when the input comes from prior calculations instead of a fixed constant.<\/p>\n<p>For display in dashboards, logs, or charts, round to the precision your audience needs. For continued math, keep the full float and round only at the final presentation step.<\/p>\n<p>Negative angles convert normally. For example, <code>-pi \/ 2<\/code> radians becomes <code>-90<\/code> degrees. If your application expects degrees in a <code>0<\/code> to <code>360<\/code> range, normalize the result after conversion.<\/p>\n<p>One common normalization pattern is <code>degrees % 360<\/code>. That keeps direction-style output positive while preserving the same circular angle. Use it only when the domain calls for wrapped angles.<\/p>\n<p>For geometry, robotics, plotting, and game code, document whether each function accepts radians or degrees. A short docstring with the expected unit is often enough to prevent mistakes.<\/p>\n<p>If data comes from a file or API, check its unit before converting it.<\/p>\n<p>Clear unit naming, one conversion point, and the standard helper function prevent most angle conversion bugs.<\/p>\n<figure class=\"pythonpool-article-visual pythonpool-supporting-visual\"><img src=\"https:\/\/www.pythonpool.com\/wp-content\/uploads\/2026\/07\/radians-degrees-numpy-b222.png\" alt=\"Python Pool infographic comparing scalar math.degrees with NumPy radians and degrees array conversion\" width=\"1536\" height=\"1054\" loading=\"lazy\" decoding=\"async\"><figcaption>NumPy provides array-aware radians and degrees helpers for vectorized angle conversion.<\/figcaption><\/figure>\n<h2><span class=\"ez-toc-section\" id=\"Convert_A_Scalar_With_mathdegrees\"><\/span>Convert A Scalar With math.degrees<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>math.degrees accepts a real number in radians and returns a floating-point degree value. Use math.radians for the inverse conversion and a tolerance when checking a round trip because floating-point representations are approximate.<\/p>\n<div class=\"pythonpool-code-scroll\" style=\"max-width:100%;overflow-x:auto;-webkit-overflow-scrolling:touch;\">\n<pre><code class=\"language-python\">import math\n\nradians = math.pi \/ 2\ndegrees = math.degrees(radians)\nprint(degrees)\nassert math.isclose(math.radians(degrees), radians)<\/code><\/pre>\n<\/div>\n<h2><span class=\"ez-toc-section\" id=\"Convert_Arrays_With_NumPy\"><\/span>Convert Arrays With NumPy<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>numpy.degrees is vectorized and preserves array shape, making it useful for angle arrays from geometry or trigonometry. Keep the input dtype and output precision in mind, especially when values are later used in comparisons or indexing.<\/p>\n<div class=\"pythonpool-code-scroll\" style=\"max-width:100%;overflow-x:auto;-webkit-overflow-scrolling:touch;\">\n<pre><code class=\"language-python\">import numpy as np\n\nradians = np.array([0, np.pi \/ 4, np.pi \/ 2])\nprint(np.degrees(radians))<\/code><\/pre>\n<\/div>\n<figure class=\"pythonpool-article-visual pythonpool-supporting-visual\"><img src=\"https:\/\/www.pythonpool.com\/wp-content\/uploads\/2026\/07\/radians-degrees-check-b222.png\" alt=\"Python Pool infographic testing pi, negative angles, precision, units, and validation\" width=\"1536\" height=\"1054\" loading=\"lazy\" decoding=\"async\"><figcaption>Check units, sign, precision, pi-based inputs, array dtypes, and whether the result is for display or computation.<\/figcaption><\/figure>\n<h2><span class=\"ez-toc-section\" id=\"Use_The_Formula_When_Explaining_Or_Porting\"><\/span>Use The Formula When Explaining Or Porting<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>The conversion is degrees = radians times 180 divided by pi. The helper functions are preferable in application code because they state intent and work with the expected numeric type, while the formula can make a port or derivation easier to verify.<\/p>\n<div class=\"pythonpool-code-scroll\" style=\"max-width:100%;overflow-x:auto;-webkit-overflow-scrolling:touch;\">\n<pre><code class=\"language-python\">import math\n\nradians = 2 * math.pi\nformula = radians * 180 \/ math.pi\nprint(math.degrees(radians), formula)<\/code><\/pre>\n<\/div>\n<h2><span class=\"ez-toc-section\" id=\"Round_Only_At_The_Presentation_Boundary\"><\/span>Round Only At The Presentation Boundary<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Rounding an angle before a later trigonometric calculation can introduce avoidable error. Keep the converted value at full precision, then use format or round for a displayed label. For arrays, choose a formatting method that does not mutate the numeric data.<\/p>\n<div class=\"pythonpool-code-scroll\" style=\"max-width:100%;overflow-x:auto;-webkit-overflow-scrolling:touch;\">\n<pre><code class=\"language-python\">import math\n\ndegrees = math.degrees(math.pi \/ 7)\nprint(degrees)\nprint(\"{:.2f} degrees\".format(degrees))<\/code><\/pre>\n<\/div>\n<p>Python&#8217;s official <a href=\"https:\/\/docs.python.org\/3\/library\/math.html#math.degrees\">math.degrees reference<\/a> defines scalar conversion, and NumPy provides <a href=\"https:\/\/numpy.org\/doc\/stable\/reference\/generated\/numpy.degrees.html\">vectorized degrees()<\/a> for arrays.<\/p>\n<p>For related angle calculations, compare <a href=\"https:\/\/www.pythonpool.com\/numpy-arctan2\/\">NumPy arctan2()<\/a>, <a href=\"https:\/\/www.pythonpool.com\/numpy-sin\/\">NumPy sin()<\/a>, and <a href=\"https:\/\/www.pythonpool.com\/numpy-angle\/\">NumPy angle()<\/a> when preserving units and quadrants across scalar and array code.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Frequently_Asked_Questions\"><\/span>Frequently Asked Questions<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3><span class=\"ez-toc-section\" id=\"How_do_I_convert_radians_to_degrees_in_Python\"><\/span>How do I convert radians to degrees in Python?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Use math.degrees(angle) for a scalar angle or numpy.degrees(values) for an array of angles.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"What_is_the_radians-to-degrees_formula\"><\/span>What is the radians-to-degrees formula?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Multiply radians by 180 divided by pi; Python&#8217;s math and NumPy helpers implement that conversion directly.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"How_do_I_convert_a_list_of_radians\"><\/span>How do I convert a list of radians?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Use a list comprehension with math.degrees or convert the list to a NumPy array and call numpy.degrees.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Should_I_round_converted_angles\"><\/span>Should I round converted angles?<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Keep full precision for calculations and round only when formatting a displayed label or report.<\/p>\n<p><script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"FAQPage\",\"mainEntity\":[{\"@type\":\"Question\",\"name\":\"How do I convert radians to degrees in Python?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Use math.degrees(angle) for a scalar angle or numpy.degrees(values) for an array of angles.\"}},{\"@type\":\"Question\",\"name\":\"What is the radians-to-degrees formula?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Multiply radians by 180 divided by pi; Python's math and NumPy helpers implement that conversion directly.\"}},{\"@type\":\"Question\",\"name\":\"How do I convert a list of 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