{"id":64470,"date":"2025-05-12T09:42:27","date_gmt":"2025-05-12T06:42:27","guid":{"rendered":"https:\/\/wpcalc.com\/en\/?p=64470"},"modified":"2026-09-30T18:32:30","modified_gmt":"2026-09-30T15:32:30","slug":"r1-r2","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/engineering\/r1-r2\/","title":{"rendered":"R1 R2 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\">Resistance Split Calculator from Ze and Zs<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"64470\" data-favorite-title=\"R1 R2\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/engineering\/r1-r2\/\" data-favorite-excerpt=\"Calculate R1 + R2 (line and earth conductor resistance) from the total earth fault loop impedance and the source impedance. Enter both values in ohms to verify circuit earth continuity.\" 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\/r1-r2\/\" method=\"POST\" class=\"calculator\" id=\"calculator-64470\" data-post=\"64470\"><fieldset class=\"fieldset-input\"><legend class=\"sr-only\">Input Fields<\/legend><div class=\"field has-term\" id=\"input-1\"><label for=\"field-1\">Total circuit impedance<\/label><div class=\"term\">Z\u2091<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"total_circuit_impedance\" id=\"field-1\" aria-describedby=\"calc-unit-1 calc-info-1\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\" value=\"0.76\"\/><div class=\"unit\" id=\"calc-unit-1\">\u03a9<\/div><small id=\"calc-info-1\">Total earth fault loop impedance<\/small><\/div><div class=\"field has-term\" id=\"input-2\"><label for=\"field-2\">Source impedance<\/label><div class=\"term\">Z\u209b<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"source_impedance\" id=\"field-2\" aria-describedby=\"calc-unit-2 calc-info-2\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\" value=\"0.28\"\/><div class=\"unit\" id=\"calc-unit-2\">\u03a9<\/div><small id=\"calc-info-2\">Impedance of the supply transformer\/source<\/small><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Re-Calculate\" id=\"calculate-button\" data-post=\"64470\">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>R1 + R2<\/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=\"64470\" 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\">1<\/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\">1<\/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>R1 + R2 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\\[ R_1 + R_2 = Z_e - Z_s \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Where:<\/strong><\/p>\n<ul>\n<li>\\(R_1\\) \u2014 resistance of the line (phase) conductor of the circuit (\u03a9)<\/li>\n<li>\\(R_2\\) \u2014 resistance of the circuit protective conductor, CPC (\u03a9)<\/li>\n<li>\\(Z_e\\) \u2014 total earth fault loop impedance measured at the furthest point of the circuit (\u03a9)<\/li>\n<li>\\(Z_s\\) \u2014 source impedance, i.e. the part of the loop contributed by the supply transformer and incoming cables (\u03a9)<\/li>\n<\/ul>\n<p>The formula rearranges the earth fault loop relationship \\(Z_e = Z_s + (R_1 + R_2)\\): the impedance measured at the end of the circuit, minus the impedance contributed by the supply, leaves the combined resistance of the circuit's own line and protective conductors.<\/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>R1 + R2 \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Example:<\/strong> a final circuit is tested at the point furthest from the consumer unit. The measured total earth fault loop impedance is 0.76 \u03a9, and the impedance of the source side of the installation is 0.28 \u03a9.<\/p>\n<p>\\[ R_1 + R_2 = 0.76 - 0.28 = 0.48~\\Omega \\]<\/p>\n<p><strong>Result:<\/strong> \\(R_1 + R_2 = 0.48~\\Omega\\). These are the calculator's default values, so you can reproduce the result directly.<\/p>\n<p>\n\r\n<\/section>\n<h2>How to use the calculator<\/h2>\n<ol>\n<li>Enter the <strong>Total circuit impedance<\/strong> \\(Z_e\\) \u2014 the earth fault loop impedance measured at the furthest point of the circuit, in ohms.<\/li>\n<li>Enter the <strong>Source impedance<\/strong> \\(Z_s\\) \u2014 the impedance of the supply transformer and incoming service, in ohms. Typical declared values are 0.35 \u03a9 for TN-C-S and 0.8 \u03a9 for TN-S supplies in the UK.<\/li>\n<li>The calculator returns <strong>R1 + R2<\/strong>, the combined resistance of the line and protective conductors. The source impedance must not exceed the total impedance, or the calculator shows an error.<\/li>\n<\/ol>\n<h2>What are R1 and R2?<\/h2>\n<p>\\(R_1\\) is the resistance of the line (live) conductor of a circuit, measured from the consumer unit to the furthest outlet or accessory. \\(R_2\\) is the resistance of the circuit protective conductor (CPC, the earth wire) over the same route. Together they form the part of the earth fault loop that lies inside the installation, and their sum is one of the key numbers recorded when testing a new circuit or certifying an installation under BS 7671 (the UK Wiring Regulations).<\/p>\n<p>When a line-to-earth fault occurs, fault current flows through the line conductor, back through the CPC, and around the supply source. The total impedance of this path \u2014 the earth fault loop impedance \u2014 determines how large the fault current will be, and therefore how quickly the protective device (fuse, MCB or RCBO) can operate. If the loop impedance is too high, the fault current is too small to trip the breaker within the required disconnection time, leaving exposed metalwork live and dangerous.<\/p>\n<p>Splitting the measured loop impedance into the source part and the installation part lets you check the wiring itself. An \\(R_1 + R_2\\) value that is much higher than expected for the cable size and length points to loose connections, damaged conductors, undersized cable, or joints with high resistance \u2014 problems that a whole-loop measurement alone might not isolate. The result is also used to verify conductor sizing against the adiabatic equation and to confirm that the calculated \\(Z_s\\) at the design stage will keep the protective device within its maximum permitted impedance.<\/p>\n<h2>Assumptions, limitations and practical tips<\/h2>\n<ul>\n<li><strong>Notation warning:<\/strong> conventions vary. In BS 7671 the total measured loop impedance is usually written \\(Z_s\\) and the external (supply) part \\(Z_e\\). In this calculator, \"Total circuit impedance\" is the full measured value at the end of the circuit and \"Source impedance\" is the upstream part \u2014 always check which convention your test instrument or form uses before entering values.<\/li>\n<li><strong>Temperature:<\/strong> tabulated conductor resistances apply at 20 \u00b0C, but during a fault the conductors heat up and their resistance rises. Design and verification tables in BS 7671 apply correction factors for this; a measured \\(R_1 + R_2\\) that looks marginally acceptable cold may not be acceptable in fault conditions.<\/li>\n<li><strong>The result is a sum:<\/strong> this calculator gives \\(R_1 + R_2\\), not the individual values. If you need \\(R_1\\) and \\(R_2\\) separately, measure them individually with a low-resistance ohmmeter (the standard \\(R_1 + R_2\\) test method) or split the sum in the measured ratio.<\/li>\n<li><strong>System type:<\/strong> the earth fault loop concept applies to TN systems (TN-S, TN-C-S). In a TT system most of the loop impedance is in the earth electrode and the supply's earth return, so \\(R_1 + R_2\\) is a small part of a much larger loop that normally requires an RCD for fault protection.<\/li>\n<li><strong>Cable size:<\/strong> to check whether the result is reasonable, compare it against the resistance per metre of the installed cable \u2014 our <a href=\"https:\/\/wpcalc.com\/en\/engineering\/wire-gauge\/\">Wire Gauge calculator<\/a> helps with conductor sizes, and the <a href=\"https:\/\/wpcalc.com\/en\/engineering\/parallel-resistance\/\">Parallel Resistance calculator<\/a> is useful when conductors run in parallel.<\/li>\n<li><strong>Source impedance:<\/strong> if you don't have a measured value, use the supply operator's declared figure; for a privately owned transformer you can estimate it from the nameplate data with the <a href=\"https:\/\/wpcalc.com\/en\/engineering\/single-phase-transformer\/\">Single Phase Transformer calculator<\/a>.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Calculate R1 + R2 (line and earth conductor resistance) from the total earth fault loop impedance and the source impedance. Enter both values in ohms to verify circuit earth continuity.<\/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-64470","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\/64470","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=64470"}],"version-history":[{"count":3,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/64470\/revisions"}],"predecessor-version":[{"id":66006,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/64470\/revisions\/66006"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=64470"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=64470"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=64470"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}