{"id":100294,"date":"2026-02-15T20:32:18","date_gmt":"2026-02-15T20:32:18","guid":{"rendered":"https:\/\/vibromera.eu\/?post_type=calculator&#038;p=100294"},"modified":"2026-07-17T05:56:04","modified_gmt":"2026-07-17T05:56:04","slug":"vibration-phase-angle","status":"publish","type":"calculator","link":"https:\/\/vibromera.eu\/vi\/calculators\/vibration-phase-angle\/","title":{"rendered":"C\u00f4ng c\u1ee5 t\u00ednh to\u00e1n g\u00f3c pha dao \u0111\u1ed9ng | C\u00f4ng c\u1ee5 vector mi\u1ec5n ph\u00ed"},"content":{"rendered":"\n<script type=\"application\/ld+json\">\n{\"@context\":\"https:\/\/schema.org\",\"@type\":\"WebApplication\",\"name\":\"Vibration Phase Angle Calculator\",\"description\":\"Calculate relative phase, vector sum and difference of two vibration signals.\",\"url\":\"https:\/\/vibromera.eu\/calculators\/vibration-phase-angle\/\",\"applicationCategory\":\"Engineering Calculator\",\"operatingSystem\":\"Any (Web Browser)\",\"offers\":{\"@type\":\"Offer\",\"price\":\"0\",\"priceCurrency\":\"EUR\"},\"creator\":{\"@type\":\"Organization\",\"name\":\"Vibromera\",\"url\":\"https:\/\/vibromera.eu\/\"},\"datePublished\":\"2024-01-01\",\"dateModified\":\"2025-02-14\",\"inLanguage\":\"en\",\"isAccessibleForFree\":true}\n<\/script>\n\n<script type=\"application\/ld+json\">\n{\"@context\":\"https:\/\/schema.org\",\"@type\":\"FAQPage\",\"mainEntity\":[\n{\"@type\":\"Question\",\"name\":\"What is vibration phase angle?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Phase angle describes the timing relationship between a vibration signal and a reference. It is measured in degrees (0\u2013360\u00b0) and indicates where in the rotation cycle the peak vibration occurs. Phase is critical for balancing and diagnosing machine faults.\"}},\n{\"@type\":\"Question\",\"name\":\"How do I measure phase angle?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Phase is measured using a tachometer (keyphasor) as a reference, combined with a vibration sensor. The phase angle is the angular difference between the tachometer pulse and the peak of the 1\u00d7 vibration signal.\"}},\n{\"@type\":\"Question\",\"name\":\"What is the vector sum of two vibration signals?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"The vector sum combines two vibration signals (each with amplitude and phase) into a single resultant vector. It uses the formula: add the x-components and y-components separately, then calculate the resultant amplitude and phase.\"}},\n{\"@type\":\"Question\",\"name\":\"Why is relative phase important in balancing?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"In single-plane balancing, the phase shift between the original vibration and the trial-weight run indicates the angular correction needed. A 180\u00b0 phase shift means the correction weight should be placed opposite to the trial weight.\"}},\n{\"@type\":\"Question\",\"name\":\"What does 0\u00b0 vs 180\u00b0 phase mean?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"0\u00b0 phase between two measurement points means the points move in the same direction simultaneously (in-phase, common with unbalance). 180\u00b0 means they move in opposite directions (out-of-phase, typical of misalignment or a rotor operating above its critical speed).\"}}\n]}\n<\/script>\n\n<script type=\"application\/ld+json\">\n{\"@context\":\"https:\/\/schema.org\",\"@type\":\"BreadcrumbList\",\"itemListElement\":[\n{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/vibromera.eu\/\"},\n{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Calculators\",\"item\":\"https:\/\/vibromera.eu\/calculators\/\"},\n{\"@type\":\"ListItem\",\"position\":3,\"name\":\"Vibration Phase Angle 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16px;font-size:13px;color:var(--vc-ink-muted)}.vc-footer a{color:var(--vc-accent);text-decoration:none}.vc-footer a:hover{text-decoration:underline}.vc-footer-links{margin-top:8px;font-size:12px}.vc-footer-links a{margin:0 8px}\n@media print{.vc-section-body{max-height:none!important}.vc-faq-a{max-height:none!important}.vc-results{max-height:none!important;padding:24px!important}.vc-copy-btn,.vc-section-chevron,.vc-faq-chevron,.vc-presets,.vc-promo{display:none!important}}\n<\/style>\n\n<div class=\"vc-calculator\" id=\"vc-phase-angle\">\n<header class=\"vc-header\">\n    <p class=\"vc-header-eyebrow\">Free Engineering Tool \u2014 #018<\/p>\n    <h1 class=\"vc-header-title\">Vibration Phase Angle Calculator<\/h1>\n    <p class=\"vc-header-subtitle\">Calculate relative phase, vector sum, and vector difference of two vibration signals. Enter amplitude and phase for each signal.<\/p>\n    <div class=\"vc-badges\"><span class=\"vc-badge\">Vector Sum<\/span><span class=\"vc-badge\">Vector Difference<\/span><span class=\"vc-badge\">Relative Phase<\/span><\/div>\n<\/header>\n\n<div class=\"vc-card\">\n    <form class=\"vc-form\" id=\"vc-form\" autocomplete=\"off\">\n        <div class=\"vc-form-grid\">\n            <div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-a1\">Signal 1 \u2014 Amplitude<\/label><input class=\"vc-input\" type=\"number\" id=\"vc-a1\" inputmode=\"decimal\" step=\"any\" min=\"0\" placeholder=\"e.g. 5.2\" value=\"5.2\"><\/div>\n            <div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-p1\">Signal 1 \u2014 Phase <span class=\"vc-label-hint\">(\u00b0)<\/span><\/label><input class=\"vc-input\" type=\"number\" id=\"vc-p1\" inputmode=\"decimal\" step=\"any\" placeholder=\"e.g. 45\" value=\"45\"><\/div>\n            <div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-a2\">Signal 2 \u2014 Amplitude<\/label><input class=\"vc-input\" type=\"number\" id=\"vc-a2\" inputmode=\"decimal\" step=\"any\" min=\"0\" placeholder=\"e.g. 3.8\" value=\"3.8\"><\/div>\n            <div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-p2\">Signal 2 \u2014 Phase <span class=\"vc-label-hint\">(\u00b0)<\/span><\/label><input class=\"vc-input\" type=\"number\" id=\"vc-p2\" inputmode=\"decimal\" step=\"any\" placeholder=\"e.g. 200\" value=\"200\"><\/div>\n        <\/div>\n        <div class=\"vc-presets\">\n            <div class=\"vc-presets-label\">Quick presets<\/div>\n            <button type=\"button\" class=\"vc-preset-btn\" data-a1=\"5.2\" data-p1=\"45\" data-a2=\"3.8\" data-p2=\"200\">Balancing run: 5.2\u222045\u00b0 \/ 3.8\u2220200\u00b0<\/button>\n            <button type=\"button\" class=\"vc-preset-btn\" data-a1=\"4.0\" data-p1=\"0\" data-a2=\"4.0\" data-p2=\"180\">Equal opposing: 4\u22200\u00b0 \/ 4\u2220180\u00b0<\/button>\n            <button type=\"button\" class=\"vc-preset-btn\" data-a1=\"3.0\" data-p1=\"90\" data-a2=\"3.0\" data-p2=\"90\">In-phase: 3\u222090\u00b0 \/ 3\u222090\u00b0<\/button>\n        <\/div>\n    <\/form>\n\n    <div class=\"vc-results\" id=\"vc-results\">\n        <div class=\"vc-results-head\">\n            <h2 class=\"vc-results-title\">Results<\/h2>\n            <button type=\"button\" class=\"vc-copy-btn\" id=\"vc-copy-btn\"><svg width=\"14\" height=\"14\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><rect x=\"9\" y=\"9\" width=\"13\" height=\"13\" rx=\"2\"\/><path d=\"M5 15H4a2 2 0 01-2-2V4a2 2 0 012-2h9a2 2 0 012 2v1\"\/><\/svg> Copy<\/button>\n        <\/div>\n        <div class=\"vc-result-grid\">\n            <div class=\"vc-rcard vc-rcard-primary\">\n                <div class=\"vc-rcard-label\">Relative Phase Angle<\/div>\n                <div class=\"vc-rcard-value\" id=\"vc-r-rel\">\u2014<\/div>\n            <\/div>\n            <div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Vector Sum (Amplitude)<\/div><div class=\"vc-rcard-value\" id=\"vc-r-sum-a\">\u2014<\/div><\/div>\n            <div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Vector Sum (Phase)<\/div><div class=\"vc-rcard-value\" id=\"vc-r-sum-p\">\u2014<\/div><\/div>\n            <div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Vector Difference (Amplitude)<\/div><div class=\"vc-rcard-value\" id=\"vc-r-diff-a\">\u2014<\/div><\/div>\n            <div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Vector Difference (Phase)<\/div><div class=\"vc-rcard-value\" id=\"vc-r-diff-p\">\u2014<\/div><\/div>\n        <\/div>\n    <\/div>\n<\/div>\n\n<div class=\"vc-section vc-open\" id=\"vc-sec-theory\">\n    <button type=\"button\" class=\"vc-section-toggle\" aria-expanded=\"true\"><span class=\"vc-section-toggle-text\"><span class=\"vc-section-icon\">\ud83d\udcd8<\/span><span class=\"vc-section-title\">Theory &amp; Formulas<\/span><\/span><svg class=\"vc-section-chevron\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><path d=\"M6 9l6 6 6-6\"\/><\/svg><\/button>\n    <div class=\"vc-section-body\">\n        <div class=\"vc-section-inner vc-theory\">\n            <h3>Vector Representation<\/h3>\n            <p>Each vibration signal is a vector V = A\u2220\u03c6, with Cartesian components:<\/p>\n            <div class=\"vc-formula-box\" id=\"vc-katex-1\"><\/div>\n            <h3>Vector Sum &amp; Difference<\/h3>\n            <div class=\"vc-formula-box\" id=\"vc-katex-2\"><\/div>\n            <div class=\"vc-formula-box\" id=\"vc-katex-3\"><\/div>\n            <h3>Relative Phase<\/h3>\n            <p>The relative phase angle between two signals:<\/p>\n            <div class=\"vc-formula-box\" id=\"vc-katex-4\"><\/div>\n\n            <h3>Practical Example<\/h3>\n            <div class=\"vc-example-box\">\n                <div class=\"vc-example-title\">Example \u2014 Balancing Run Comparison<\/div>\n                <p><strong>Signal 1:<\/strong> 5.2 \u222045\u00b0 \u2192 x\u2081 = 3.677, y\u2081 = 3.677<\/p>\n                <p><strong>Signal 2:<\/strong> 3.8 \u2220200\u00b0 \u2192 x\u2082 = \u22123.571, y\u2082 = \u22121.300<\/p>\n                <p><strong>Vector difference:<\/strong> \u0394x = 7.248, \u0394y = 4.977 \u2192 <strong>|\u0394V| = 8.79 \u222034.4\u00b0<\/strong><\/p>\n                <p><strong>Relative phase:<\/strong> |200\u00b0 \u2212 45\u00b0| = <strong>155\u00b0<\/strong><\/p>\n            <\/div>\n            <div class=\"vc-info-box\"><p><strong>\u2139\ufe0f Tip:<\/strong> In single-plane balancing, the vector difference between the original run and the trial-weight run represents the effect of the trial weight alone.<\/p><\/div>\n        <\/div>\n    <\/div>\n<\/div>\n\n<div class=\"vc-section\" id=\"vc-sec-related\">\n    <button type=\"button\" class=\"vc-section-toggle\" aria-expanded=\"false\"><span class=\"vc-section-toggle-text\"><span class=\"vc-section-icon\">\ud83d\udd17<\/span><span class=\"vc-section-title\">Related Calculators<\/span><\/span><svg class=\"vc-section-chevron\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><path d=\"M6 9l6 6 6-6\"\/><\/svg><\/button>\n    <div class=\"vc-section-body\"><div class=\"vc-section-inner\"><div class=\"vc-related\">\n        <a class=\"vc-related-link\" href=\"\/calculators\/residual-unbalance-iso1940\/\">Residual Unbalance (ISO 21940)<\/a>\n        <a class=\"vc-related-link\" href=\"\/calculators\/trial-weight-calculator\/\">Trial Weight Calculator<\/a>\n        <a class=\"vc-related-link\" href=\"\/calculators\/vibration-transmissibility\/\">Vibration Transmissibility<\/a>\n        <a class=\"vc-related-link\" href=\"\/calculators\/vibration-overall-level\/\">Overall Vibration Level<\/a>\n    <\/div><\/div><\/div>\n<\/div>\n\n<div class=\"vc-section\" id=\"vc-sec-faq\">\n    <button type=\"button\" class=\"vc-section-toggle\" aria-expanded=\"false\"><span class=\"vc-section-toggle-text\"><span class=\"vc-section-icon\">\u2753<\/span><span class=\"vc-section-title\">Frequently Asked Questions<\/span><\/span><svg class=\"vc-section-chevron\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><path d=\"M6 9l6 6 6-6\"\/><\/svg><\/button>\n    <div class=\"vc-section-body\"><div class=\"vc-section-inner\"><div class=\"vc-faq-list\" id=\"vc-faq-list\"><\/div><\/div><\/div>\n<\/div>\n\n<div class=\"vc-promo\"><div class=\"vc-promo-text\"><strong>Vibromera \u2014 Portable Balancing &amp; Vibration Analysis<\/strong><br>Measure phase angles and perform field balancing with professional portable instruments. Used in 50+ countries.<\/div><a class=\"vc-promo-link\" href=\"https:\/\/vibromera.eu\/\" target=\"_blank\" rel=\"noopener\">Learn More<\/a><\/div>\n\n<footer class=\"vc-footer\">\n    <p>\u00a9 2024\u20132025 <a href=\"https:\/\/vibromera.eu\/\">Vibromera<\/a> \u2014 Engineering Calculators<\/p>\n    <p style=\"font-size:12px;margin-top:4px;\">Vibration phase angle and vector calculations. Last updated: February 2025<\/p>\n    <div class=\"vc-footer-links\"><a href=\"\/calculators\/engineering-calculators\/\">All Calculators<\/a><a href=\"https:\/\/vibromera.eu\/contacts\/\">Contact<\/a><\/div>\n<\/footer>\n<\/div>\n\n<script src=\"https:\/\/cdn.jsdelivr.net\/npm\/katex@0.16.11\/dist\/katex.min.js\"><\/script>\n<script>\n(function(){\n    'use strict';\n    var SLUG='vibration-phase-angle';\n    function $(id){return document.getElementById(id)}\n    function fmt(n,d){if(isNaN(n)||!isFinite(n))return '\u2014';return n.toFixed(d===undefined?2:d).replace(\/(\\.\\d*?)0+$\/,'$1').replace(\/\\.$\/,'')}\n    function deg2rad(d){return d*Math.PI\/180}\n    function rad2deg(r){return r*180\/Math.PI}\n    function normDeg(d){d=d%360;return d<0?d+360:d}\n\n    function calculate(){\n        var a1=parseFloat($('vc-a1').value), p1=parseFloat($('vc-p1').value);\n        var a2=parseFloat($('vc-a2').value), p2=parseFloat($('vc-p2').value);\n        if(isNaN(a1)||a1<0||isNaN(p1)||isNaN(a2)||a2<0||isNaN(p2)){$('vc-results').classList.remove('vc-visible');return}\n\n        var x1=a1*Math.cos(deg2rad(p1)), y1=a1*Math.sin(deg2rad(p1));\n        var x2=a2*Math.cos(deg2rad(p2)), y2=a2*Math.sin(deg2rad(p2));\n\n        \/\/ Relative phase\n        var relPhase=normDeg(p2-p1);if(relPhase>180)relPhase=360-relPhase;\n        if(relPhase>180) relPhase=360-relPhase;\n\n        \/\/ Vector sum\n        var sx=x1+x2, sy=y1+y2;\n        var sAmp=Math.sqrt(sx*sx+sy*sy);\n        var sPhase=normDeg(rad2deg(Math.atan2(sy,sx)));\n\n        \/\/ Vector difference (V1 - V2)\n        var dx=x1-x2, dy=y1-y2;\n        var dAmp=Math.sqrt(dx*dx+dy*dy);\n        var dPhase=normDeg(rad2deg(Math.atan2(dy,dx)));\n\n        $('vc-r-rel').innerHTML=fmt(relPhase,1)+' <span class=\"vc-rcard-unit\">\u00b0<\/span>';\n        $('vc-r-sum-a').innerHTML=fmt(sAmp,3);\n        $('vc-r-sum-p').innerHTML=fmt(sPhase,1)+' <span class=\"vc-rcard-unit\">\u00b0<\/span>';\n        $('vc-r-diff-a').innerHTML=fmt(dAmp,3);\n        $('vc-r-diff-p').innerHTML=fmt(dPhase,1)+' <span class=\"vc-rcard-unit\">\u00b0<\/span>';\n        $('vc-results').classList.add('vc-visible');\n\n        saveHistory({a1:a1,p1:p1,a2:a2,p2:p2,_summary:a1+'\u2220'+p1+'\u00b0 & '+a2+'\u2220'+p2+'\u00b0 \u2192 \u0394\u03c6='+fmt(relPhase,1)+'\u00b0'});\n    }\n\n    document.querySelectorAll('.vc-preset-btn').forEach(function(btn){btn.addEventListener('click',function(e){e.preventDefault();$('vc-a1').value=this.getAttribute('data-a1');$('vc-p1').value=this.getAttribute('data-p1');$('vc-a2').value=this.getAttribute('data-a2');$('vc-p2').value=this.getAttribute('data-p2');calculate()})});\n    $('vc-form').addEventListener('input',calculate);\n    $('vc-form').addEventListener('change',calculate);\n\n    $('vc-copy-btn').addEventListener('click',function(){\n        var text='Phase Angle Calculation\\n\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\\nSignal 1: '+$('vc-a1').value+' \u2220'+$('vc-p1').value+'\u00b0\\nSignal 2: '+$('vc-a2').value+' \u2220'+$('vc-p2').value+'\u00b0\\nRelative Phase: '+$('vc-r-rel').textContent+'\\nVector Sum: '+$('vc-r-sum-a').textContent+' \u2220'+$('vc-r-sum-p').textContent+'\\nVector Diff: '+$('vc-r-diff-a').textContent+' \u2220'+$('vc-r-diff-p').textContent+'\\n\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\\nvibromera.eu\/calculators\/vibration-phase-angle\/';\n        if(navigator.clipboard){navigator.clipboard.writeText(text).then(function(){var b=$('vc-copy-btn');b.classList.add('vc-copied');b.innerHTML='<svg width=\"14\" height=\"14\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><polyline points=\"20 6 9 17 4 12\"\/><\/svg> Copied!';setTimeout(function(){b.classList.remove('vc-copied');b.innerHTML='<svg width=\"14\" height=\"14\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><rect x=\"9\" y=\"9\" width=\"13\" height=\"13\" rx=\"2\"\/><path d=\"M5 15H4a2 2 0 01-2-2V4a2 2 0 012-2h9a2 2 0 012 2v1\"\/><\/svg> Copy'},2000)})}\n    });\n\n    document.querySelectorAll('.vc-section-toggle').forEach(function(btn){btn.addEventListener('click',function(){var s=this.closest('.vc-section');s.classList.toggle('vc-open');this.setAttribute('aria-expanded',s.classList.contains('vc-open'))})});\n\n    var faqData=[\n        {q:'What is vibration phase angle?',a:'<p>Phase angle describes the timing relationship between a vibration signal and a reference (e.g., tachometer pulse). 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