{"id":64413,"date":"2025-05-12T09:12:09","date_gmt":"2025-05-12T06:12:09","guid":{"rendered":"https:\/\/wpcalc.com\/en\/?p=64413"},"modified":"2026-09-30T18:02:41","modified_gmt":"2026-09-30T15:02:41","slug":"90-degree-mitered-corner-converter","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/engineering\/90-degree-mitered-corner-converter\/","title":{"rendered":"90 Degree Mitered Corner Converter"},"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\">Mitered Corner Length Estimator<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"64413\" data-favorite-title=\"90 Degree Mitered Corner\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/engineering\/90-degree-mitered-corner-converter\/\" data-favorite-excerpt=\"Calculate the effective electrical length of a 90-degree mitered corner in a PCB transmission line from the conductor width and height. Enter the trace dimensions in mm to get the extra length added by the chamfered bend.\" aria-label=\"Add to Favorites\" data-favorite-icon=\"icon icon-electrical\">\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\/engineering\/90-degree-mitered-corner-converter\/\" method=\"POST\" class=\"calculator\" id=\"calculator-64413\" data-post=\"64413\"><fieldset class=\"fieldset-input\"><legend class=\"sr-only\">Input Fields<\/legend><div class=\"field has-term\" id=\"input-1\"><label for=\"field-1\">Conductor width<\/label><div class=\"term\">w<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"conductor_width\" id=\"field-1\" aria-describedby=\"calc-unit-1 calc-info-1\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\" value=\"5\"\/><div class=\"unit\" id=\"calc-unit-1\">mm<\/div><small id=\"calc-info-1\">Width of the conductor at the corner<\/small><\/div><div class=\"field has-term\" id=\"input-2\"><label for=\"field-2\">Conductor height<\/label><div class=\"term\">h<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"conductor_height\" id=\"field-2\" aria-describedby=\"calc-unit-2 calc-info-2\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\" value=\"1.5\"\/><div class=\"unit\" id=\"calc-unit-2\">mm<\/div><small id=\"calc-info-2\">Height of the conductor at the corner<\/small><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Re-Calculate\" id=\"calculate-button\" data-post=\"64413\">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\" id=\"output-1\"><span class=\"field-title\"><span>Effective Length<\/span><\/span><span class=\"field-value\" id=\"result-1\" data-unit=\"mm\"><\/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=\"64413\" 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>90 Degree Mitered Corner 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\\[ x = w \\left( 1.04 + 1.30 \\, e^{-1.35 \\, \\frac{h}{w}} \\right) \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Where:<\/strong><\/p>\n<ul>\n<li>\\(x\\) \u2014 effective length of the mitered corner (mm)<\/li>\n<li>\\(w\\) \u2014 conductor width at the corner (mm)<\/li>\n<li>\\(h\\) \u2014 conductor height at the corner (mm)<\/li>\n<\/ul>\n<p>This empirical formula, widely used in microwave PCB design, estimates the electrical length a chamfered 90-degree bend contributes to a transmission line. The compensation depends only on the aspect ratio \\(h\/w\\): as the conductor becomes relatively taller, the exponential term shrinks and the effective length approaches \\(1.04\\,w\\).<\/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>90 Degree Mitered Corner \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Example:<\/strong> a microstrip trace makes a 90-degree mitered turn. The conductor is \\(w = 5\\) mm wide and \\(h = 1.5\\) mm high at the corner.<\/p>\n<p>\\[ x = 5 \\cdot \\left( 1.04 + 1.30 \\, e^{-1.35 \\cdot \\frac{1.5}{5}} \\right) \\]<\/p>\n<p>\\[ x = 5 \\cdot \\left( 1.04 + 1.30 \\, e^{-0.405} \\right) = 5 \\cdot (1.04 + 1.30 \\cdot 0.667) \\]<\/p>\n<p>\\[ x = 5 \\cdot 1.907 = 9.535 \\text{ mm} \\]<\/p>\n<p><strong>Result:<\/strong> the mitered corner has an effective length of approximately 9.54 mm, which should be counted as part of the line's electrical path.<\/p>\n<p>\n\r\n<\/section>\n<h2>How to Use the Calculator<\/h2>\n<ol>\n<li>Enter the <strong>Conductor width<\/strong> (\\(w\\)) in millimeters \u2014 the width of the trace as it passes through the corner.<\/li>\n<li>Enter the <strong>Conductor height<\/strong> (\\(h\\)) in millimeters \u2014 the vertical extent of the conductor at the bend.<\/li>\n<li>Read the <strong>Effective Length<\/strong> in mm. This is the electrical length contributed by the mitered 90-degree corner.<\/li>\n<\/ol>\n<h2>What Is a 90 Degree Mitered Corner?<\/h2>\n<p>In high-frequency PCB design, a transmission line rarely runs in a perfectly straight line from source to load. When a microstrip or stripline trace changes direction, the geometry of the bend itself disturbs the fields around the conductor. A sharp, unmitered 90-degree corner adds excess capacitance at the outer edge of the bend, causing impedance discontinuities, signal reflections, and degraded return loss \u2014 problems that grow more severe as frequency increases.<\/p>\n<p>The standard fix is to <em>miter<\/em> (chamfer) the corner: a triangular portion of the outer edge is cut away so the bend looks like a diagonal shortcut rather than a sharp elbow. Removing this material reduces the excess capacitance and brings the local impedance back close to the characteristic impedance of the line. A properly mitered corner behaves almost like a short, uniform section of straight line.<\/p>\n<p>That short \"equivalent section\" is exactly what this calculator computes. The mitered bend does not have zero length \u2014 electrically, it behaves as an extra segment of line of length \\(x\\), given by the empirical formula above. When you need to know the total electrical length of a routed line \u2014 for phase matching, quarter-wave transformers, resonators, filters, or distributed matching networks \u2014 you must add the effective length of every bend to the sum of the straight segments.<\/p>\n<p>The result scales with conductor width \\(w\\), so wide, low-impedance lines (which store more charge at a corner) incur more effective length than narrow ones. The \\(h\/w\\) ratio modulates this: taller conductors relative to their width reduce the added length toward the asymptotic minimum of \\(1.04\\,w\\). For more on how line geometry determines characteristic impedance, see the <a href=\"https:\/\/wpcalc.com\/en\/engineering\/microstrip-pcb-impedance\/\">Microstrip PCB Impedance<\/a> and <a href=\"https:\/\/wpcalc.com\/en\/engineering\/stripline-impedance\/\">Stripline Impedance<\/a> calculators.<\/p>\n<h2>Assumptions and Practical Tips<\/h2>\n<ul>\n<li><strong>Empirical model:<\/strong> the formula is a curve fit from measured and simulated data for typical PCB transmission lines. It gives a good engineering estimate, not an exact solution; for critical designs at very high frequencies, verify with a full-wave EM simulator or measured S-parameters.<\/li>\n<li><strong>Moderate aspect ratios:<\/strong> the fit is most reliable for ordinary trace geometries. Extreme \\(h\/w\\) values (very tall or very flat conductors) push the model outside the range it was derived for.<\/li>\n<li><strong>Consistent units:<\/strong> the formula is dimensionally homogeneous in \\(x\\), \\(w\\), and \\(h\\), so it works in any unit system \u2014 but the calculator expects millimeters, and the result comes back in millimeters.<\/li>\n<li><strong>Two bends, two corrections:<\/strong> if a route has multiple 90-degree turns, compute the effective length for each corner and add all of them to the straight-segment total.<\/li>\n<li><strong>Corners interact:<\/strong> the model assumes an isolated bend. If two corners are placed closer than a few line widths apart, their fields couple and the simple per-corner correction becomes less accurate \u2014 relevant when routing dense layouts, a situation also covered in the <a href=\"https:\/\/wpcalc.com\/en\/engineering\/pcb-microstrip-crosstalk\/\">PCB Microstrip Crosstalk<\/a> calculator.<\/li>\n<li><strong>Not a miter-cut calculator:<\/strong> this tool returns the <em>electrical length<\/em> of the corner, not the physical size of the chamfer to cut. Typical miter designs remove roughly 50\u201370% of the corner diagonal, but the exact chamfer fraction for a given line is a separate design decision.<\/li>\n<\/ul>\n<h2>Quick Reference Values<\/h2>\n<p>For a quick sanity check, the effective length is between \\(1.04\\,w\\) (very tall conductors, \\(h\/w \\gtrsim 2\\)) and about \\(2.34\\,w\\) (flat conductors, \\(h \\to 0\\)). For the common case \\(h = w\/2\\), the corner contributes roughly \\(1.62\\,w\\).<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Calculate the effective electrical length of a 90-degree mitered corner in a PCB transmission line from the conductor width and height. Enter the trace dimensions in mm to get the extra length added by the chamfered bend.<\/p>\n","protected":false},"author":70,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[4],"tags":[21],"class_list":["post-64413","post","type-post","status-publish","format-standard","hentry","category-engineering","tag-electrical"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/64413","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=64413"}],"version-history":[{"count":3,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/64413\/revisions"}],"predecessor-version":[{"id":65942,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/64413\/revisions\/65942"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=64413"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=64413"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=64413"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}