{"id":66662,"date":"2026-10-13T08:31:04","date_gmt":"2026-10-13T05:31:04","guid":{"rendered":"https:\/\/wpcalc.com\/en\/?p=66662"},"modified":"2026-10-13T11:57:22","modified_gmt":"2026-10-13T08:57:22","slug":"lc-resonant-frequency","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/engineering\/lc-resonant-frequency\/","title":{"rendered":"LC Resonant Frequency"},"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 Resonant Frequency of an LC Circuit<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"66662\" data-favorite-title=\"LC Resonance\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/engineering\/lc-resonant-frequency\/\" data-favorite-excerpt=\"Calculate the resonant frequency of an LC (tank) circuit from its inductance and capacitance using the Thomson formula. Enter L and C with their units to get frequency, period, and angular frequency.\" aria-label=\"Add to Favorites\" data-favorite-icon=\"icon icon-magnet\">\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\/lc-resonant-frequency\/\" method=\"POST\" class=\"calculator\" id=\"calculator-66662\" data-post=\"66662\"><fieldset class=\"fieldset-input is-2\"><legend class=\"sr-only\">Input Fields<\/legend><div class=\"field has-term\" id=\"input-1\"><label for=\"field-1\">Inductance (L)<\/label><div class=\"term\">L<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"text\" name=\"inductance_l\" id=\"field-1\" aria-describedby=\"calc-info-1\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"1.0E-6\" value=\"100\"\/><div class=\"grid grid-cols-1\"><select id=\"field-2\" name=\"inductance_unit\" aria-label=\"Inductance unit\"><option value=\"uH\" selected>\u00b5H<\/option><option value=\"mH\">mH<\/option><option value=\"H\">H<\/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-1\">Coil inductance in the circuit<\/small><\/div><div class=\"field has-term\" id=\"input-2\"><label for=\"field-3\">Capacitance (C)<\/label><div class=\"term\">C<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"text\" name=\"capacitance_c\" id=\"field-3\" aria-describedby=\"calc-info-3\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"1.0E-6\" value=\"100\"\/><div class=\"grid grid-cols-1\"><select id=\"field-4\" name=\"capacitance_unit\" aria-label=\"Capacitance unit\"><option value=\"pF\" selected>pF<\/option><option value=\"nF\">nF<\/option><option value=\"uF\">\u00b5F<\/option><option value=\"F\">F<\/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-3\">Capacitor capacitance in the circuit<\/small><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Re-Calculate\" id=\"calculate-button\" data-post=\"66662\">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> Resonance Results<\/h3><div class=\"result-box\"><div class=\"field-result\" id=\"output-1\"><span class=\"field-title\"><span>Resonant Frequency<\/span><span class=\"result-term\">f\u2080<\/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>Period<\/span><span class=\"result-term\">T<\/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>Angular Frequency<\/span><span class=\"result-term\">\u03c9\u2080<\/span><\/span><span class=\"field-value\" id=\"result-3\" data-unit=\"rad\/s\"><\/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=\"66662\" 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>LC Resonant Frequency 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\\[ f_0 = \\frac{1}{2\\pi\\sqrt{LC}}, \\qquad T = \\frac{1}{f_0} = 2\\pi\\sqrt{LC}, \\qquad \\omega_0 = 2\\pi f_0 = \\frac{1}{\\sqrt{LC}} \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Where:<\/strong><\/p>\n<ul>\n<li>\\(f_0\\) \u2014 resonant frequency (Hz)<\/li>\n<li>\\(L\\) \u2014 inductance of the coil (henries, H)<\/li>\n<li>\\(C\\) \u2014 capacitance of the capacitor (farads, F)<\/li>\n<li>\\(T\\) \u2014 period of one oscillation (seconds)<\/li>\n<li>\\(\\omega_0\\) \u2014 angular frequency (rad\/s)<\/li>\n<\/ul>\n<p>This is the Thomson (or tank-circuit) formula. It gives the natural frequency at which an ideal LC circuit oscillates, where the energy stored in the capacitor and the energy stored in the coil exchange back and forth with zero net reactance.<\/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>LC Resonance \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Example:<\/strong> a tank circuit uses a 100 \u00b5H coil and a 100 pF capacitor, the default values of the calculator.<\/p>\n<p>\\[ L = 100\\,\\mu\\text{H} = 1\\times10^{-4}\\ \\text{H}, \\qquad C = 100\\,\\text{pF} = 1\\times10^{-10}\\ \\text{F} \\]<\/p>\n<p>\\[ f_0 = \\frac{1}{2\\pi\\sqrt{(1\\times10^{-4})(1\\times10^{-10})}} = \\frac{1}{2\\pi\\times10^{-7}} \\approx 1.592\\times10^{6}\\ \\text{Hz} \\]<\/p>\n<p>\\[ T = \\frac{1}{f_0} \\approx 6.283\\times10^{-7}\\ \\text{s}, \\qquad \\omega_0 = 2\\pi f_0 = 10^{7}\\ \\text{rad\/s} \\]<\/p>\n<p><strong>Result:<\/strong> the circuit resonates at approximately 1.592 MHz, with a period of 628.3 ns and an angular frequency of 10,000,000 rad\/s.<\/p>\n<p>\n\r\n<\/section>\n<h2>How to Use the LC Resonance Calculator<\/h2>\n<ol>\n<li>Enter the coil inductance in the <strong>Inductance (L)<\/strong> field and select the matching unit (\u00b5H, mH, or H) from the dropdown.<\/li>\n<li>Enter the capacitor value in the <strong>Capacitance (C)<\/strong> field and choose its unit (pF, nF, \u00b5F, or F).<\/li>\n<li>Read the <strong>Resonant Frequency<\/strong> result, shown with an automatically selected SI prefix (Hz, kHz, MHz, or GHz).<\/li>\n<li>Check the <strong>Period<\/strong> and <strong>Angular Frequency<\/strong> results if you need the oscillation time or the value of \\(\\omega_0\\) in rad\/s.<\/li>\n<\/ol>\n<h2>What Is LC Resonance?<\/h2>\n<p>An LC circuit is made of an inductor (a coil) and a capacitor connected together, either in series or in parallel. When the capacitor is charged and the circuit is left to itself, current flows back and forth between the coil and the capacitor: the capacitor discharges through the coil, the coil's magnetic field builds up, then collapses and recharges the capacitor with the opposite polarity. This exchange repeats at one fixed natural frequency \u2014 the resonant frequency \u2014 determined only by the values of L and C.<\/p>\n<p>At resonance, the inductive reactance \\(X_L = 2\\pi f L\\) and the capacitive reactance \\(X_C = \\frac{1}{2\\pi f C}\\) are equal in magnitude and cancel each other. The impedance of an ideal parallel tank circuit is then purely resistive and at its maximum, while in a series circuit it is at its minimum. This is why a tuned circuit can select one frequency out of many: it responds strongly at \\(f_0\\) and barely at all elsewhere.<\/p>\n<p>This behavior is the working principle behind radio tuners, filters, oscillators, and impedance-matching networks. The classic AM radio tuner, for instance, uses a variable capacitor precisely so you can sweep \\(f_0\\) across the broadcast band and pick out one station. In an oscillator, the tank circuit sets the frequency of the generated signal; in a filter, it marks the center or corner frequency of the passband.<\/p>\n<p>Interpreting the result is straightforward: \\(f_0\\) tells you where the circuit tunes, \\(T\\) tells you how long one full oscillation cycle takes, and \\(\\omega_0\\) is the form most often used in AC circuit analysis and differential equations. Larger values of L or C both push the frequency down, and halving either one raises \\(f_0\\) by a factor of \\(\\sqrt{2}\\).<\/p>\n<h2>Assumptions, Limitations, and Practical Tips<\/h2>\n<ul>\n<li><strong>Ideal components:<\/strong> the Thomson formula ignores resistance and losses. Real coils have winding resistance and real capacitors have equivalent series resistance, which slightly shift the actual resonance and damp the oscillation.<\/li>\n<li><strong>Stray reactance:<\/strong> parasitic capacitance of the coil, lead inductance, and PCB trace effects add to the nominal L and C values. This matters most at high frequencies \u2014 for example, a 100 pF capacitor with 2 pF of stray capacitance resonates about 1% lower than calculated. To estimate the inductance contributed by a straight conductor, see the <a href=\"https:\/\/wpcalc.com\/en\/engineering\/straight-wire-inductor\/\">Straight Wire Inductance calculator<\/a>.<\/li>\n<li><strong>Self-resonance:<\/strong> every real inductor also has a self-resonant frequency set by its own parasitic capacitance. Above it, the component stops behaving as an inductor, so keep \\(f_0\\) well below the coil's rated self-resonance.<\/li>\n<li><strong>Units matter:<\/strong> the most common source of error is a unit mismatch. Always double-check whether the value is in \u00b5H or mH, pF or nF, before entering it.<\/li>\n<li><strong>Practical tuning:<\/strong> real tank circuits are rarely used in isolation. To match a resonant circuit to a source or load, a <a href=\"https:\/\/wpcalc.com\/en\/engineering\/t-matching-network\/\">T matching network<\/a> or a <a href=\"https:\/\/wpcalc.com\/en\/engineering\/pi-network-impedance-matching\/\">PI network impedance matching<\/a> design is usually built around the LC values you compute here.<\/li>\n<li><strong>Combining components:<\/strong> if several coils are used, remember that their effective inductance depends on the connection \u2014 <a href=\"https:\/\/wpcalc.com\/en\/engineering\/series-inductance\/\">series inductance<\/a> adds directly, while a <a href=\"https:\/\/wpcalc.com\/en\/engineering\/parallel-inductance\/\">parallel inductance<\/a> combination follows the reciprocal rule. Enter the total effective L into this calculator.<\/li>\n<\/ul>\n<h2>Quick Reference: Common LC Combinations<\/h2>\n<table>\n<thead>\n<tr>\n<th>Inductance<\/th>\n<th>Capacitance<\/th>\n<th>Resonant Frequency<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>1 \u00b5H<\/td>\n<td>1 pF<\/td>\n<td>159.2 MHz<\/td>\n<\/tr>\n<tr>\n<td>10 \u00b5H<\/td>\n<td>100 pF<\/td>\n<td>5.03 MHz<\/td>\n<\/tr>\n<tr>\n<td>100 \u00b5H<\/td>\n<td>100 pF<\/td>\n<td>1.59 MHz<\/td>\n<\/tr>\n<tr>\n<td>1 mH<\/td>\n<td>1 \u00b5F<\/td>\n<td>5.03 kHz<\/td>\n<\/tr>\n<tr>\n<td>10 mH<\/td>\n<td>100 \u00b5F<\/td>\n<td>159.2 Hz<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Use this table for a sanity check: radio-frequency work (kHz\u2013GHz) uses small L and C, while audio and power applications use much larger values.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Calculate the resonant frequency of an LC (tank) circuit from its inductance and capacitance using the Thomson formula. Enter L and C with their units to get frequency, period, and angular frequency.<\/p>\n","protected":false},"author":3168,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[4],"tags":[93],"class_list":["post-66662","post","type-post","status-publish","format-standard","hentry","category-engineering","tag-coils-transformers"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66662","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=66662"}],"version-history":[{"count":2,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66662\/revisions"}],"predecessor-version":[{"id":67090,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66662\/revisions\/67090"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=66662"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=66662"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=66662"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}