{"id":66660,"date":"2026-10-13T08:30:41","date_gmt":"2026-10-13T05:30:41","guid":{"rendered":"https:\/\/wpcalc.com\/en\/?p=66660"},"modified":"2026-10-13T08:30:41","modified_gmt":"2026-10-13T05:30:41","slug":"resistors-in-series","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/engineering\/resistors-in-series\/","title":{"rendered":"Resistors in Series"},"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\">Find the Total Resistance of Series-Connected Resistors<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"66660\" data-favorite-title=\"Series Resistance\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/engineering\/resistors-in-series\/\" data-favorite-excerpt=\"Quickly add up any number of series-connected resistors. Enter the resistor values (ohms, k\u03a9 or M\u03a9) and get the total resistance, the count, and the smallest and largest value in the chain.\" 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\/resistors-in-series\/\" method=\"POST\" class=\"calculator\" id=\"calculator-66660\" data-post=\"66660\"><fieldset class=\"fieldset-input\"><legend class=\"sr-only\">Input Fields<\/legend><div class=\"field is-single\" id=\"input-1\"><label for=\"field-1\">Resistor Values (R\u2081, R\u2082, R\u2083, \u2026)<\/label><textarea id=\"field-1\" name=\"resistor_values_r_r_r_\">100; 220; 470<\/textarea><\/div><div class=\"field\" id=\"input-2\"><label for=\"field-2\">Add Another Resistor Manually<\/label><div class=\"field-group\"><input type=\"text\" name=\"add_another_resistor_manually\" id=\"field-2\" aria-describedby=\"calc-unit-2 calc-info-2\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\" value=\"0\"\/><div class=\"unit\" id=\"calc-unit-2\">\u03a9<\/div><div class=\"grid grid-cols-1\"><select id=\"field-3\" name=\"unit_for_the_list_and_manual_value\" aria-label=\"Unit for the list and manual value\"><option value=\"ohm\" selected>\u03a9<\/option><option value=\"kohm\">k\u03a9<\/option><option value=\"mohm\">M\u03a9<\/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><small id=\"calc-info-2\">Optional extra resistor added to the list above (0 = none)<\/small><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Re-Calculate\" id=\"calculate-button\" data-post=\"66660\">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> Series Resistance<\/h3><div class=\"result-box\"><div class=\"field-result\" id=\"output-1\"><span class=\"field-title\"><span>Total Series Resistance<\/span><span class=\"result-term\">R_total<\/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 class=\"field-result\" id=\"output-2\"><span class=\"field-title\"><span>Total Resistance (text)<\/span><\/span><span class=\"field-value\" id=\"result-2\"><\/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 class=\"field-result\" id=\"output-3\"><span class=\"field-title\"><span>Number of Resistors<\/span><span class=\"result-term\">n<\/span><\/span><span class=\"field-value\" id=\"result-3\"><\/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 class=\"field-result is-column\" id=\"output-4\"><span class=\"field-title\"><span>Smallest and Largest Resistor<\/span><\/span><span class=\"field-value\" id=\"result-4\"><\/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=\"66660\" 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>Series Resistance 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\">\\[ R_{total} = R_1 + R_2 + R_3 + \\dots + R_n \\]<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Where:<\/strong><\/p>\n<ul>\n<li>\\(R_{total}\\) \u2014 total resistance of the series chain (\u03a9)<\/li>\n<li>\\(R_1, R_2, \\dots, R_n\\) \u2014 the individual resistor values (\u03a9)<\/li>\n<li>\\(n\\) \u2014 the number of resistors in the chain<\/li>\n<\/ul>\n<p>Resistors in series simply add up: the same current flows through each of them one after another, so the total opposition to current is the arithmetic sum of all the individual resistances.<\/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>Series Resistance \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Example:<\/strong> three resistors of 100 \u03a9, 220 \u03a9 and 470 \u03a9 are connected in series. What is the total resistance?<\/p>\n<p>\\[ R_{total} = 100\\ \\Omega + 220\\ \\Omega + 470\\ \\Omega \\]<\/p>\n<p>\\[ R_{total} = 790\\ \\Omega \\]<\/p>\n<p><strong>Result:<\/strong> the total series resistance is 790 \u03a9 (0.79 k\u03a9), made up of 3 resistors ranging from 100 \u03a9 to 470 \u03a9.<\/p>\n<p>\n\r\n<\/section>\n<h2>How to Use the Series Resistance Calculator<\/h2>\n<ol>\n<li>In the <strong>Resistor Values (R\u2081, R\u2082, R\u2083, \u2026)<\/strong> field, list all resistors in the chain. Separate the values with spaces, semicolons or new lines \u2014 for example <code>100; 220; 470<\/code>. A decimal comma is accepted (e.g. <code>4,7<\/code>).<\/li>\n<li>If you need one more resistor that is not in the list, enter it in <strong>Add Another Resistor Manually<\/strong>. Leave it at 0 if you don't.<\/li>\n<li>Choose the <strong>Unit for the list and manual value<\/strong>: \u03a9, k\u03a9 or M\u03a9. All entered values are interpreted in this unit.<\/li>\n<li>Press <strong>Calculate<\/strong>. You get the total resistance, the number of resistors, and the smallest and largest value in the chain.<\/li>\n<\/ol>\n<h2>What Does Series Resistance Mean?<\/h2>\n<p>Resistors are connected in series when they form a single chain, with one end of each resistor joined to the next and no branching in between. Because there is only one path for the current, exactly the same current flows through every resistor. Each resistor drops part of the supply voltage, and the voltage drops add up to the total applied voltage (Kirchhoff's voltage law).<\/p>\n<p>In this arrangement the resistances simply add together. Two 100 \u03a9 resistors in series behave like a single 200 \u03a9 resistor. This makes series connection a handy way to build a resistance value you don't have in stock \u2014 for instance, a 1 k\u03a9 and a 470 \u03a9 resistor in series give you 1.47 k\u03a9, which is not a standard E-series value.<\/p>\n<p>Contrast this with <a href=\"https:\/\/wpcalc.com\/en\/engineering\/parallel-resistance\/\">parallel resistance<\/a>, where the total is always <em>smaller<\/em> than the smallest individual resistor. In series the total is always <em>larger<\/em> than the largest resistor in the chain \u2014 a quick sanity check for your result. If your calculated total is less than one of the values you entered, the resistors are probably wired in parallel, not series.<\/p>\n<p>Series chains are everywhere in electronics: voltage dividers, LED current-limiting circuits, resistive sensors, and measurement shunts. Whenever a design needs a precise voltage drop or a specific current through several components at once, series resistance is the natural tool.<\/p>\n<h2>Assumptions, Limitations and Practical Tips<\/h2>\n<ul>\n<li><strong>Same current everywhere:<\/strong> the formula assumes ideal resistors with nothing else connected between them. If a load or branch taps off current partway along the chain, the simple sum no longer describes the circuit.<\/li>\n<li><strong>Ideally matched values:<\/strong> real resistors have a tolerance (\u00b11%, \u00b15%\u2026). The worst-case total resistance of a series chain is the sum of the individual worst cases, so tolerances add along with the nominal values.<\/li>\n<li><strong>Power rating:<\/strong> the power dissipated in each resistor is \\(P = I^2 R\\). Since the current is the same through all resistors, the largest resistance dissipates the most power. Check that each resistor stays within its rating.<\/li>\n<li><strong>At least two values:<\/strong> this calculator combines two or more resistors. To combine inductors instead, use the <a href=\"https:\/\/wpcalc.com\/en\/engineering\/series-inductance\/\">series inductance<\/a> calculator; for inductors side by side, see <a href=\"https:\/\/wpcalc.com\/en\/engineering\/parallel-inductance\/\">parallel inductance<\/a>.<\/li>\n<li><strong>Watch the unit:<\/strong> all values in the list share the unit you select. If you mix a 4.7 k\u03a9 resistor with values entered in ohms, convert first (4.7 k\u03a9 = 4700 \u03a9) or enter everything in k\u03a9.<\/li>\n<\/ul>\n<h2>Quick Reference: Common Series Combinations<\/h2>\n<table>\n<thead>\n<tr>\n<th>Resistors in series<\/th>\n<th>Total resistance<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>100 \u03a9 + 100 \u03a9<\/td>\n<td>200 \u03a9<\/td>\n<\/tr>\n<tr>\n<td>100 \u03a9 + 220 \u03a9<\/td>\n<td>320 \u03a9<\/td>\n<\/tr>\n<tr>\n<td>100 \u03a9 + 220 \u03a9 + 470 \u03a9<\/td>\n<td>790 \u03a9<\/td>\n<\/tr>\n<tr>\n<td>1 k\u03a9 + 1 k\u03a9<\/td>\n<td>2 k\u03a9<\/td>\n<\/tr>\n<tr>\n<td>4.7 k\u03a9 + 10 k\u03a9<\/td>\n<td>14.7 k\u03a9<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>A related practical case is sizing the series resistor for a Zener diode voltage regulator \u2014 once you know the total series resistance needed, the <a href=\"https:\/\/wpcalc.com\/en\/engineering\/zener-diode\/\">Zener diode resistor calculator<\/a> helps you pick the right value for that circuit.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Quickly add up any number of series-connected resistors. Enter the resistor values (ohms, k\u03a9 or M\u03a9) and get the total resistance, the count, and the smallest and largest value in the chain.<\/p>\n","protected":false},"author":3168,"featured_media":0,"comment_status":"open","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[4],"tags":[94],"class_list":["post-66660","post","type-post","status-publish","format-standard","hentry","category-engineering","tag-circuits"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66660","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\/3168"}],"replies":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/comments?post=66660"}],"version-history":[{"count":2,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66660\/revisions"}],"predecessor-version":[{"id":67058,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66660\/revisions\/67058"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=66660"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=66660"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=66660"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}