{"id":100155,"date":"2026-02-15T20:21:24","date_gmt":"2026-02-15T20:21:24","guid":{"rendered":"https:\/\/vibromera.eu\/?post_type=calculator&#038;p=100155"},"modified":"2026-07-12T20:40:54","modified_gmt":"2026-07-12T20:40:54","slug":"motor-capacitor-calculator","status":"publish","type":"calculator","link":"https:\/\/vibromera.eu\/hi\/calculators\/motor-capacitor-calculator\/","title":{"rendered":"Ideal Sinusoidal AC Capacitor Worksheet"},"content":{"rendered":"\n<script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"WebApplication\",\"name\":\"Ideal Sinusoidal AC Capacitor Worksheet\",\"description\":\"Calculate ideal capacitance from the same-frequency RMS voltage and current measured at capacitor terminals,with explicit motor-selection and IEC safety boundaries.\",\"url\":\"https:\/\/vibromera.eu\/calculators\/motor-capacitor-calculator\/\",\"applicationCategory\":\"Engineering 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h1{font-size:clamp(28px,4vw,44px);line-height:1.08;margin:8px 0 12px}.ac-lead{font-size:17px;line-height:1.65;color:var(--sec);max-width:960px}.ac-badges{display:flex;flex-wrap:wrap;gap:8px;margin-top:18px}.ac-badge{padding:6px 10px;border-radius:99px;background:#fff;border:1px solid var(--b);font-size:12px;font-weight:700}.ac-main{padding:30px 38px}.ac-panel{border:1px solid var(--b);border-radius:14px;padding:24px}.ac-panel h2{font-size:22px;margin:0 0 8px}.ac-note{font-size:14px;line-height:1.55;color:var(--sec)}.ac-grid{display:grid;grid-template-columns:1fr 1fr;gap:18px;margin-top:20px}.ac-field{display:flex;flex-direction:column;gap:7px}.ac-wide{grid-column:1\/-1}.ac-label{font-size:13px;font-weight:800}.ac-input,.ac-select,.ac-textarea{width:100%;border:1px solid var(--b);border-radius:9px;background:#fff;color:var(--ink);font:inherit;padding:11px 12px}.ac-input:focus,.ac-select:focus,.ac-textarea:focus{outline:3px solid #abd1d5;outline-offset:1px;border-color:var(--ac)}.ac-textarea{min-height:92px;resize:vertical}.ac-help{font-size:12px;line-height:1.45;color:var(--mut)}.ac-error{min-height:22px;margin:14px 0 0;color:var(--red);font-size:13px;font-weight:800}.ac-results{margin-top:22px;border:1px solid var(--b);border-radius:12px;overflow:hidden}.ac-rhead{background:var(--acl);padding:18px 20px}.ac-rtitle{font-size:20px;font-weight:900;color:var(--ac)}.ac-rsub{font-size:13px;color:var(--sec);margin-top:4px}.ac-rgrid{display:grid;grid-template-columns:repeat(3,1fr);gap:1px;background:var(--bl)}.ac-card{background:#fff;padding:18px}.ac-card h3{font-size:12px;text-transform:uppercase;letter-spacing:.06em;color:var(--mut);margin:0 0 8px}.ac-val{font-size:20px;font-weight:900;overflow-wrap:anywhere}.ac-unit{font-size:12px;color:var(--mut);margin-top:4px}.ac-alert{border-left:4px solid var(--amb);background:var(--yel);padding:14px 16px;margin-top:18px;font-size:14px;line-height:1.55}.ac-danger{border-left-color:var(--red);background:#fff0ee}.ac-section{border-top:1px solid var(--bl);padding:28px 38px}.ac-section h2{font-size:24px;margin:0 0 10px}.ac-section h3{font-size:18px;margin:22px 0 8px}.ac-section p,.ac-section li{font-size:14px;line-height:1.65;color:var(--sec)}.ac-table-wrap{overflow-x:auto;border:1px solid var(--b);border-radius:10px}.ac-table{width:100%;border-collapse:collapse;min-width:780px}.ac-table th,.ac-table td{padding:12px 13px;text-align:left;vertical-align:top;border-bottom:1px solid var(--bl);font-size:13px;line-height:1.45}.ac-table th{background:var(--alt);font-weight:900}.ac-table tr:last-child td{border-bottom:0}.ac-code{font-family:ui-monospace,SFMono-Regular,Consolas,monospace}.ac-footer{padding:20px 38px;background:var(--alt);font-size:12px;color:var(--mut)}.ac-footer a,.ac-section a{color:var(--ac)}@media(max-width:700px){.ac-hero,.ac-main,.ac-section{padding-left:20px;padding-right:20px}.ac-grid,.ac-rgrid{grid-template-columns:1fr}.ac-wide{grid-column:auto}.ac-panel{padding:18px}.ac-table{min-width:700px}}<\/style>\n<div class=\"ac-wrap\"><header class=\"ac-hero\"><div class=\"ac-kicker\">Ideal capacitor relation \u00b7 same terminal quantities \u00b7 sinusoidal RMS<\/div><h1>Ideal Sinusoidal AC Capacitor Worksheet<\/h1><p class=\"ac-lead\">Infer capacitance from voltage and current measured or specified for the capacitor itself at one sinusoidal frequency. This worksheet does not size a motor start or run capacitor from motor power,line current or supply voltage.<\/p><div class=\"ac-badges\"><span class=\"ac-badge\">Starts blank<\/span><span class=\"ac-badge\">Same-frequency RMS only<\/span><span class=\"ac-badge\">No motor-size multiplier<\/span><span class=\"ac-badge\">No voltage-rating recommendation<\/span><\/div><\/header>\n<main class=\"ac-main\"><section class=\"ac-panel\"><h2>Document one capacitor operating point<\/h2><p class=\"ac-note\">Use the fundamental-frequency RMS voltage directly across the capacitor and the corresponding RMS current through that capacitor. They must describe the same operating state and frequency component.<\/p><form id=\"ac-form\" novalidate><div class=\"ac-grid\"><div class=\"ac-field ac-wide\"><label class=\"ac-label\" for=\"ac-basis\">Quantity basis<\/label><select class=\"ac-select\" id=\"ac-basis\"><option value=\"\">Select\u2026<\/option><option value=\"same-rms\">Same-frequency sinusoidal RMS voltage and current at capacitor terminals<\/option><\/select><\/div><div class=\"ac-field\"><label class=\"ac-label\" for=\"ac-f\">Frequency f (Hz)<\/label><input class=\"ac-input\" id=\"ac-f\" inputmode=\"decimal\" autocomplete=\"off\"><span class=\"ac-help\">Frequency of the voltage\/current component\u2014not an assumed motor speed.<\/span><\/div><div class=\"ac-field\"><label class=\"ac-label\" for=\"ac-v\">Capacitor terminal voltage V<sub>C<\/sub> (V RMS)<\/label><input class=\"ac-input\" id=\"ac-v\" inputmode=\"decimal\" autocomplete=\"off\"><span class=\"ac-help\">Voltage across the capacitor,which can differ from supply voltage.<\/span><\/div><div class=\"ac-field\"><label class=\"ac-label\" for=\"ac-i\">Capacitor current I<sub>C<\/sub> (A RMS)<\/label><input class=\"ac-input\" id=\"ac-i\" inputmode=\"decimal\" autocomplete=\"off\"><span class=\"ac-help\">Current through the capacitor\u2014not motor line current.<\/span><\/div><div class=\"ac-field ac-wide\"><label class=\"ac-label\" for=\"ac-source\">Measurement,circuit and source record<\/label><textarea class=\"ac-textarea\" id=\"ac-source\" maxlength=\"1800\" placeholder=\"Motor\/circuit identity and state;capacitor terminals;frequency;RMS\/fundamental measurement method and instrument;waveform\/harmonic assessment;OEM or component document revision\"><\/textarea><\/div><\/div><p class=\"ac-error\" id=\"ac-error\" role=\"alert\"><\/p><\/form>\n<section class=\"ac-results\" id=\"ac-results\" hidden data-json=\"\"><div class=\"ac-rhead\"><div class=\"ac-rtitle\">Ideal single-frequency result<\/div><div class=\"ac-rsub\" id=\"ac-summary\">\u2014<\/div><\/div><div class=\"ac-rgrid\"><article class=\"ac-card\"><h3>Inferred capacitance C<\/h3><div class=\"ac-val\" id=\"ac-r-uf\">\u2014<\/div><div class=\"ac-unit\" id=\"ac-r-farad\">\u2014<\/div><\/article><article class=\"ac-card\"><h3>Capacitive reactance |X<sub>C<\/sub>|<\/h3><div class=\"ac-val\" id=\"ac-r-x\">\u2014<\/div><div class=\"ac-unit\">V RMS \u00f7 A RMS at the stated frequency<\/div><\/article><article class=\"ac-card\"><h3>Angular frequency \u03c9<\/h3><div class=\"ac-val\" id=\"ac-r-omega\">\u2014<\/div><div class=\"ac-unit\">\u03c9=2\u03c0f<\/div><\/article><article class=\"ac-card\"><h3>Ideal reactive-power magnitude<\/h3><div class=\"ac-val\" id=\"ac-r-q\">\u2014<\/div><div class=\"ac-unit\">|Q<sub>C<\/sub>|=V<sub>C<\/sub>I<sub>C<\/sub> under the stated ideal conditions<\/div><\/article><article class=\"ac-card\"><h3>Input voltage component<\/h3><div class=\"ac-val\" id=\"ac-r-v\">\u2014<\/div><div class=\"ac-unit\">capacitor-terminal RMS<\/div><\/article><article class=\"ac-card\"><h3>Input current component<\/h3><div class=\"ac-val\" id=\"ac-r-i\">\u2014<\/div><div class=\"ac-unit\">capacitor-branch RMS<\/div><\/article><\/div><\/section>\n<div class=\"ac-alert\"><strong>Model boundary:<\/strong> <span class=\"ac-code\">I<sub>C<\/sub>=2\u03c0fCV<sub>C<\/sub><\/span> is the magnitude relation for an ideal linear capacitor in sinusoidal steady state. Do not combine total RMS current with a fundamental-only voltage,or motor line current with supply voltage. Harmonics,ESR,dielectric loss,temperature,voltage dependence and waveform distortion require component-wise impedance or validated instrumentation.<\/div><div class=\"ac-alert ac-danger\"><strong>Electrical hazard:<\/strong> motor circuits can expose hazardous voltage,and a capacitor can retain charge after disconnection. Selection,installation,testing and discharge must be performed by a qualified person using the motor,capacitor and equipment manufacturer&#8217;s approved procedure and applicable electrical-safety rules. This page does not provide an energized-work or discharge procedure.<\/div><\/section><\/main>\n<section class=\"ac-section\"><h2>Equations implemented<\/h2><div class=\"ac-table-wrap\"><table class=\"ac-table\"><thead><tr><th>Quantity<\/th><th>Equation<\/th><th>Scope<\/th><\/tr><\/thead><tbody><tr><td>angular frequency<\/td><td class=\"ac-code\">\u03c9=2\u03c0f<\/td><td>f in hertz;\u03c9 in rad\/s.<\/td><\/tr><tr><td>ideal capacitive reactance magnitude<\/td><td class=\"ac-code\">|X<sub>C<\/sub>|=1\/(\u03c9C)=V<sub>C<\/sub>\/I<sub>C<\/sub><\/td><td>Same-frequency sinusoidal RMS terminal quantities.<\/td><\/tr><tr><td>inferred capacitance<\/td><td class=\"ac-code\">C=I<sub>C<\/sub>\/(2\u03c0fV<sub>C<\/sub>)<\/td><td>C in farads;multiply by10\u2076 for \u00b5F.<\/td><\/tr><tr><td>ideal reactive-power magnitude<\/td><td class=\"ac-code\">|Q<sub>C<\/sub>|=V<sub>C<\/sub>I<sub>C<\/sub>=\u03c9CV<sub>C<\/sub>\u00b2<\/td><td>Magnitude in var for the ideal single-frequency component;no loss estimate.<\/td><\/tr><\/tbody><\/table><\/div><p>The code uses the entered terminal quantities directly. It does not infer capacitor current from motor output power,efficiency or power factor and contains no hidden selection multiplier.<\/p><\/section>\n<section class=\"ac-section\"><h2>Authoritative scope<\/h2><p>The IEC Electropedia defines an <a href=\"https:\/\/www.electropedia.org\/iev\/iev.nsf\/display?ievref=131-12-12&amp;openform=\" target=\"_blank\" rel=\"noopener\">ideal capacitor<\/a> as a linear capacitive two-terminal element and <a href=\"https:\/\/www.electropedia.org\/iev\/iev.nsf\/display?ievref=131-12-13&amp;openform=\" target=\"_blank\" rel=\"noopener\">capacitance<\/a> as charge divided by terminal voltage. IEC&#8217;s reactance entry gives the capacitive term <span class=\"ac-code\">\u22121\/(\u03c9C)<\/span>,and its sinusoidal-condition and phasor entries establish the same-frequency RMS basis used here.<\/p><p><a href=\"https:\/\/webstore.iec.ch\/en\/publication\/1154\" target=\"_blank\" rel=\"noopener\">IEC60252-1:2010+A1:2013,Edition2.1<\/a> is listed valid with a2026 stability date. Its public scope covers specified motor capacitors connected to asynchronous-motor windings,up to100Hz and rated voltages through660V,and addresses performance,testing,rating,safety,installation and operation. It explicitly notes that operation above rated voltage reduces life expectancy.<\/p><p><a href=\"https:\/\/webstore.iec.ch\/en\/publication\/1157\" target=\"_blank\" rel=\"noopener\">IEC60252-2:2010+A1:2013,Edition2.1<\/a> separately covers motor start capacitors for asynchronous motors at mains frequency,including metallized paper\/plastic-film constructions and electrolytic capacitors within its scope. Both Part1 and Part2 Edition3 projects are under development with forecast publication in2028;the current consolidated editions remain valid at the2026-07-12 access date.<\/p><p>The public IEC cards do not provide a universal motor-capacitance selection equation,voltage multiplier,start\/run ratio,duty cycle or discharge procedure. Exact selection,rating,marking,installation and safety clauses remain <strong>NEEDS_LICENSED_SOURCE<\/strong> and must be applied with the motor and capacitor manufacturers&#8217; controlled data.<\/p><\/section>\n<section class=\"ac-section\"><h2>What was corrected<\/h2><p>The former calculator estimated motor line current from output power,efficiency and power factor,assumed capacitor-branch current was60% of that value,treated supply voltage as capacitor voltage,multiplied the result by3.5 for a start capacitor and proposed a voltage rating at1.5 times supply rounded to50V. None of those hidden multipliers was sourced or generally valid.<\/p><p>It also published unsourced30\u201350\u00b5F\/HP and100\u2013150\u00b5F\/HP rules,universal start\/run ranges and the statement that start capacitors are always electrolytic,although IEC60252-2 also covers film\/paper constructions. Defaults,presets,prefix parsing and local history could silently preserve an unsuitable result. All of those paths are removed.<\/p><\/section>\n<section class=\"ac-section\"><h2>Motor-capacitor decision boundary<\/h2><ul><li>Use the exact replacement capacitance,tolerance,rated voltage,duty class,temperature category,protective class and switching arrangement specified by the motor\/equipment manufacturer.<\/li><li>Capacitor terminal voltage can exceed or otherwise differ from supply voltage because it is set by the winding\/capacitor circuit. Do not derive a rating from supply voltage alone.<\/li><li>A start capacitor is selected together with starting winding impedance,required torque,switching threshold and permitted duty. A fixed multiple of a run capacitor is not a design method.<\/li><li>A measured value from this worksheet can support diagnosis only after instrument bandwidth,waveform,harmonics,temperature and capacitor tolerance are documented;it is not an authorization to energize or replace a component.<\/li><\/ul><\/section>\n<footer class=\"ac-footer\">\u00a92024\u20132026 <a href=\"https:\/\/vibromera.eu\/\">Vibromera<\/a> \u00b7 Scientific review July2026<\/footer><\/div>\n<script>(function(){'use strict';function $(id){return document.getElementById(id)}function num(s){s=String(s).trim();if(!s||s.includes('.')&&s.includes(',')||!\/^[+-]?(?:\\d+(?:[.,]\\d*)?|[.,]\\d+)(?:[eE][+-]?\\d+)?$\/.test(s))return NaN;var n=Number(s.replace(',','.'));return Number.isFinite(n)&&Math.abs(n)<=1e100?n:NaN}function fmt(n){if(n===0)return'0';var a=Math.abs(n);return a>=1e12||a<1e-8?n.toExponential(9):Number(n.toPrecision(12)).toLocaleString('en-US',{maximumFractionDigits:20})}function 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recommendation.';$('ac-results').dataset.json=JSON.stringify({frequency_hz:f,capacitor_voltage_rms_v:v,capacitor_current_rms_a:i,angular_frequency_rad_s:omega,capacitance_f:c,capacitance_uf:uf,capacitive_reactance_ohm:x,reactive_power_magnitude_var:q,basis:basis});$('ac-results').hidden=false}$('ac-form').addEventListener('input',calc);$('ac-form').addEventListener('change',calc);calc()})();<\/script>\n","protected":false},"excerpt":{"rendered":"<p>\u0938\u093f\u0902\u0917\u0932 \u092b\u0947\u091c \u092e\u094b\u091f\u0930 \u0915\u0948\u092a\u0947\u0938\u093f\u091f\u0930 \u0915\u093e \u092e\u0941\u092b\u094d\u0924 \u0911\u0928\u0932\u093e\u0907\u0928 \u0915\u0948\u0932\u0915\u0941\u0932\u0947\u091f\u0930\u0964 \u0938\u094d\u091f\u093e\u0930\u094d\u091f \u0914\u0930 \u0930\u0928 \u0915\u0948\u092a\u0947\u0938\u093f\u091f\u0930 \u0915\u0947 \u092e\u093e\u0928\u094b\u0902 \u0915\u0940 \u0917\u0923\u0928\u093e \u0915\u0930\u0947\u0902\u0964 C = I\/(2\u03c0fV)\u0964 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