{"id":64496,"date":"2025-05-12T09:50:59","date_gmt":"2025-05-12T06:50:59","guid":{"rendered":"https:\/\/wpcalc.com\/en\/?p=64496"},"modified":"2026-09-30T18:29:57","modified_gmt":"2026-09-30T15:29:57","slug":"parallel-wire-impedance","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/engineering\/parallel-wire-impedance\/","title":{"rendered":"Parallel Wire Impedance Calculator"},"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\">Impedance Estimator for Parallel Wire Transmission Lines<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"64496\" data-favorite-title=\"Parallel Wire Impedance\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/engineering\/parallel-wire-impedance\/\" data-favorite-excerpt=\"Calculate the characteristic impedance of a parallel wire (two-wire) transmission line from the wire diameter and center-to-center spacing. Useful for designing twin-lead, ladder line, and balanced RF feeder systems.\" aria-label=\"Add to Favorites\" data-favorite-icon=\"icon icon-engineering\">\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\/parallel-wire-impedance\/\" method=\"POST\" class=\"calculator\" id=\"calculator-64496\" data-post=\"64496\"><fieldset class=\"fieldset-input\"><legend class=\"sr-only\">Input Fields<\/legend><div class=\"field has-term\" id=\"input-1\"><label for=\"field-1\">Wire diameter<\/label><div class=\"term\">d<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"wire_diameter\" id=\"field-1\" aria-describedby=\"calc-unit-1 calc-info-1\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0.01\" value=\"2\"\/><div class=\"unit\" id=\"calc-unit-1\">mm<\/div><small id=\"calc-info-1\">Diameter of each conductor<\/small><\/div><div class=\"field has-term\" id=\"input-2\"><label for=\"field-2\">Distance between wires<\/label><div class=\"term\">D<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"distance_between_wires\" id=\"field-2\" aria-describedby=\"calc-unit-2 calc-info-2\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0.01\" value=\"20\"\/><div class=\"unit\" id=\"calc-unit-2\">mm<\/div><small id=\"calc-info-2\">Center-to-center distance between the wires<\/small><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Re-Calculate\" id=\"calculate-button\" data-post=\"64496\">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>Characteristic Impedance<\/span><\/span><span class=\"field-value\" id=\"result-1\" data-unit=\"\u03a9\"><\/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=\"64496\" 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\">5<\/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\">3<\/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>Parallel Wire Impedance 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\\[ Z_0 = 276\\,\\log_{10}\\!\\left(\\frac{2D}{d}\\right)\\ \\Omega \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Where:<\/strong><\/p>\n<ul>\n<li>\\(Z_0\\) \u2014 characteristic impedance of the line (\u03a9)<\/li>\n<li>\\(D\\) \u2014 center-to-center distance between the two wires (mm)<\/li>\n<li>\\(d\\) \u2014 diameter of each wire (mm)<\/li>\n<\/ul>\n<p>This formula gives the impedance of a balanced two-wire line in air, assuming thin, parallel, cylindrical conductors. Equivalently, \\(Z_0 = 120\\ln(2D\/d)\\) \u03a9, since \\(276\\log_{10}(x) = 120\\ln(x)\\).<\/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>Parallel Wire Impedance \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Example:<\/strong> a ladder line built from two wires of 2 mm diameter, spaced 20 mm apart (center to center), running through air.<\/p>\n<p>\\[ \\frac{2D}{d} = \\frac{2 \\times 20}{2} = 20 \\]<\/p>\n<p>\\[ Z_0 = 276\\,\\log_{10}(20) = 276 \\times 1.30103 \\approx 359.08\\ \\Omega \\]<\/p>\n<p><strong>Result:<\/strong> the characteristic impedance is approximately <strong>359.08 \u03a9<\/strong>.<\/p>\n<p>\n\r\n<\/section>\n<h2>How to Use the Calculator<\/h2>\n<ol>\n<li>Enter the <strong>Wire diameter<\/strong> in millimeters \u2014 the diameter of each of the two identical conductors.<\/li>\n<li>Enter the <strong>Distance between wires<\/strong> in millimeters \u2014 measured from the center of one wire to the center of the other.<\/li>\n<li>Read the <strong>Characteristic Impedance<\/strong> in ohms (\u03a9) in the result field.<\/li>\n<\/ol>\n<p>The calculator requires \\(D &gt; d\/2\\); otherwise the wires would overlap, and an error message is shown. Any consistent units work, because only the ratio \\(D\/d\\) matters \u2014 the millimeter labels are just a convenience.<\/p>\n<h2>What Is Parallel Wire Impedance?<\/h2>\n<p>A parallel wire line (also called a two-wire line, twin-lead, or ladder line) is a balanced transmission line made of two parallel conductors held at a fixed spacing. It is one of the oldest and simplest transmission line geometries, still widely used in amateur radio, shortwave receiving antennas, and balanced feeders where low loss matters.<\/p>\n<p>The characteristic impedance \\(Z_0\\) describes how voltage and current relate to each other as a wave travels along the line. When the line is terminated in a load equal to \\(Z_0\\), all the transmitted power is absorbed by the load and no reflection occurs. If the load impedance differs from \\(Z_0\\), part of the signal reflects back toward the source, creating standing waves, higher losses, and potential damage to transmitters. Matching the line, the antenna, and the equipment to the same impedance is therefore essential for maximum power transfer.<\/p>\n<p>Notice what the formula tells you physically: the impedance depends only on the geometry \u2014 the ratio of spacing to wire diameter. Widening the spacing increases the impedance; using thicker wires decreases it. A typical 300 \u03a9 twin-lead, for example, achieves its impedance purely through a particular choice of \\(D\/d\\) (plus a modest reduction from its plastic dielectric). Because the conductors must be small compared to the wavelength, the formula is accurate when the spacing is well under about 1\/10 of the wavelength of the signal being carried.<\/p>\n<h2>Assumptions, Limitations and Practical Tips<\/h2>\n<ul>\n<li><strong>Air dielectric:<\/strong> the calculator assumes \\(\\varepsilon_r = 1\\). For a line embedded in a homogeneous dielectric (e.g. ribbon cable or insulated twin-lead), divide the result by \\(\\sqrt{\\varepsilon_r}\\). Real twin-lead has only partial dielectric filling, so the true impedance lies between the air value and the fully filled value.<\/li>\n<li><strong>Thin-wire approximation:<\/strong> the formula is derived for \\(D \\gg d\\). It remains reasonably accurate down to \\(D \\approx 2d\\), but the error grows when the wires nearly touch.<\/li>\n<li><strong>Negligible skin-effect corrections:<\/strong> conductor loss and internal inductance are ignored; \\(Z_0\\) is treated as purely resistive (real), which is an excellent approximation at radio frequencies.<\/li>\n<li><strong>Uniform geometry:<\/strong> the line must be straight and maintain constant spacing. Bends, twists, spacers, or nearby objects disturb the impedance and can unbalance the line.<\/li>\n<li><strong>Balanced operation:<\/strong> a two-wire line should be fed symmetrically. Connecting it directly to unbalanced coaxial cable requires a balun.<\/li>\n<\/ul>\n<p>If you are working with other transmission line geometries, try the <a href=\"https:\/\/wpcalc.com\/en\/engineering\/microstrip-pcb-impedance\/\">Microstrip PCB Impedance<\/a> or <a href=\"https:\/\/wpcalc.com\/en\/engineering\/stripline-impedance\/\">Stripline Impedance<\/a> calculators, or the <a href=\"https:\/\/wpcalc.com\/en\/engineering\/stripline-pcb-differential-impedance\/\">Stripline PCB Differential Impedance<\/a> calculator for paired traces on a circuit board. To match the line to a specific load, see the <a href=\"https:\/\/wpcalc.com\/en\/engineering\/pi-network-impedance-matching\/\">PI Network Impedance Matching<\/a> calculator. For related wire properties, the <a href=\"https:\/\/wpcalc.com\/en\/engineering\/straight-wire-inductor\/\">Straight Wire Inductance<\/a> and <a href=\"https:\/\/wpcalc.com\/en\/engineering\/wire-gauge\/\">Wire Gauge<\/a> calculators may also be useful.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Calculate the characteristic impedance of a parallel wire (two-wire) transmission line from the wire diameter and center-to-center spacing. Useful for designing twin-lead, ladder line, and balanced RF feeder systems.<\/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":[92],"class_list":["post-64496","post","type-post","status-publish","format-standard","hentry","category-engineering","tag-rf-microwave"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/64496","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=64496"}],"version-history":[{"count":4,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/64496\/revisions"}],"predecessor-version":[{"id":65999,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/64496\/revisions\/65999"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=64496"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=64496"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=64496"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}