{"id":100281,"date":"2026-02-15T20:31:41","date_gmt":"2026-02-15T20:31:41","guid":{"rendered":"https:\/\/vibromera.eu\/?post_type=calculator&#038;p=100281"},"modified":"2026-07-16T22:06:59","modified_gmt":"2026-07-16T22:06:59","slug":"vibration-displacement","status":"publish","type":"calculator","link":"https:\/\/vibromera.eu\/fi\/calculators\/vibration-displacement\/","title":{"rendered":"Single-Frequency Vibration Displacement Converter"},"content":{"rendered":"\n<script type=\"application\/ld+json\">\n{\"@context\":\"https:\/\/schema.org\",\"@type\":\"WebApplication\",\"name\":\"Single-Frequency Vibration Displacement Converter\",\"description\":\"Converts the RMS, peak or peak-to-peak displacement magnitude of one scalar sinusoidal vibration component to explicit displacement, velocity and acceleration magnitudes at the same frequency. Not for broadband overall values, shaft-orbit evaluation or ISO severity classification.\",\"url\":\"https:\/\/vibromera.eu\/calculators\/vibration-displacement\/\",\"applicationCategory\":\"EngineeringApplication\",\"operatingSystem\":\"Any\",\"isAccessibleForFree\":true,\"dateModified\":\"2026-07-16\",\"inLanguage\":\"en\",\"featureList\":[\"One scalar sinusoidal component only\",\"RMS, peak and peak-to-peak descriptors explicit\",\"Micrometre, millimetre, mil and inch inputs\",\"Hz and RPM conversion\",\"No ISO severity or clearance verdict\"]}\n<\/script>\n<script type=\"application\/ld+json\">\n{\"@context\":\"https:\/\/schema.org\",\"@type\":\"BreadcrumbList\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/vibromera.eu\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Calculators\",\"item\":\"https:\/\/vibromera.eu\/calculators\/\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"Single-Frequency Displacement Converter\",\"item\":\"https:\/\/vibromera.eu\/calculators\/vibration-displacement\/\"}]}\n<\/script>\n\n<style>\n#vbm-disp{--ds-ink:#19232d;--ds-muted:#596571;--ds-soft:#f5f7f8;--ds-line:#d8e0e5;--ds-accent:#b64b2a;--ds-accent2:#88351d;--ds-blue:#155a82;--ds-warn:#855800;--ds-warn-bg:#fff8df;--ds-danger:#982d2d;--ds-danger-bg:#fff0f0;--ds-radius:10px;max-width:1000px;margin:0 auto;color:var(--ds-ink);font-family:Inter,system-ui,-apple-system,\"Segoe UI\",sans-serif;line-height:1.55}\n#vbm-disp *{box-sizing:border-box}\n#vbm-disp .ds-head{text-align:center;padding:42px 20px 30px;border-bottom:1px solid var(--ds-line)}\n#vbm-disp .ds-eyebrow{margin:0 0 8px;color:var(--ds-accent);font-size:12px;font-weight:800;letter-spacing:.12em;text-transform:uppercase}\n#vbm-disp h1{margin:0 0 12px;font-size:clamp(27px,4vw,40px);line-height:1.15;letter-spacing:-.025em}\n#vbm-disp .ds-sub{max-width:830px;margin:0 auto;color:var(--ds-muted);font-size:15px}\n#vbm-disp .ds-tags{display:flex;flex-wrap:wrap;justify-content:center;gap:8px;margin-top:17px}\n#vbm-disp .ds-tag{padding:4px 10px;border:1px solid var(--ds-line);border-radius:999px;background:#fff;color:var(--ds-muted);font-size:12px;font-weight:700}\n#vbm-disp .ds-callout{margin:22px 0;padding:15px 17px;border-left:4px solid var(--ds-danger);border-radius:6px;background:var(--ds-danger-bg);color:#6f2525;font-size:14px}\n#vbm-disp .ds-card{margin-top:22px;border:1px solid var(--ds-line);border-radius:var(--ds-radius);background:#fff;box-shadow:0 5px 18px rgba(25,35,45,.06);overflow:hidden}\n#vbm-disp .ds-card-head{padding:18px 22px;border-bottom:1px solid var(--ds-line);background:var(--ds-soft)}\n#vbm-disp .ds-card-head h2{margin:0;font-size:21px}\n#vbm-disp .ds-card-head p{margin:5px 0 0;color:var(--ds-muted);font-size:13px}\n#vbm-disp .ds-body{padding:22px}\n#vbm-disp .ds-grid{display:grid;grid-template-columns:repeat(2,minmax(0,1fr));gap:16px}\n#vbm-disp .ds-field-wide{grid-column:1\/-1}\n#vbm-disp label,#vbm-disp legend{display:block;margin-bottom:6px;font-size:13px;font-weight:750;color:var(--ds-ink)}\n#vbm-disp .ds-hint{display:block;margin-top:4px;color:var(--ds-muted);font-size:11.5px;font-weight:500}\n#vbm-disp input[type=\"text\"],#vbm-disp select,#vbm-disp textarea{width:100%;padding:10px 12px;border:1.5px solid #bdc8d0;border-radius:7px;background:#fff;color:var(--ds-ink);font:inherit;font-size:14px}\n#vbm-disp textarea{min-height:92px;resize:vertical}\n#vbm-disp input:focus,#vbm-disp select:focus,#vbm-disp textarea:focus{outline:3px solid rgba(21,90,130,.14);border-color:var(--ds-blue)}\n#vbm-disp fieldset{margin:21px 0 0;padding:0;border:0}\n#vbm-disp .ds-check{display:grid;grid-template-columns:20px 1fr;gap:9px;align-items:start;margin:10px 0;color:var(--ds-muted);font-size:13px}\n#vbm-disp .ds-check input{width:17px;height:17px;margin:2px 0 0;accent-color:var(--ds-accent)}\n#vbm-disp .ds-actions{display:flex;flex-wrap:wrap;gap:10px;margin-top:20px}\n#vbm-disp button{border:0;border-radius:7px;padding:10px 16px;font:inherit;font-size:13px;font-weight:800;cursor:pointer}\n#vbm-disp .ds-primary{background:var(--ds-accent);color:#fff}\n#vbm-disp .ds-primary:hover{background:var(--ds-accent2)}\n#vbm-disp .ds-secondary{border:1px solid var(--ds-line);background:#fff;color:var(--ds-ink)}\n#vbm-disp .ds-secondary:hover{background:var(--ds-soft)}\n#vbm-disp .ds-errors{display:none;margin-top:16px;padding:13px 15px;border:1px solid #efb7b7;border-radius:7px;background:var(--ds-danger-bg);color:var(--ds-danger);font-size:13px}\n#vbm-disp .ds-errors.ds-show{display:block}\n#vbm-disp .ds-errors ul{margin:6px 0 0 20px;padding:0}\n#vbm-disp .ds-status{min-height:20px;margin-top:10px;color:var(--ds-muted);font-size:12px}\n#vbm-disp .ds-results{display:none;padding:22px;border-top:1px solid var(--ds-line);background:var(--ds-soft)}\n#vbm-disp .ds-results.ds-show{display:block}\n#vbm-disp .ds-result-grid{display:grid;grid-template-columns:repeat(3,minmax(0,1fr));gap:12px}\n#vbm-disp .ds-result{min-height:105px;padding:15px;border:1px solid var(--ds-line);border-radius:8px;background:#fff}\n#vbm-disp .ds-result-main{grid-column:1\/-1;border:2px solid var(--ds-accent);background:#fff9f6}\n#vbm-disp .ds-result-label{margin-bottom:5px;color:var(--ds-muted);font-size:10.5px;font-weight:800;letter-spacing:.07em;text-transform:uppercase}\n#vbm-disp .ds-result-value{font-variant-numeric:tabular-nums;font-size:20px;font-weight:850;line-height:1.25;overflow-wrap:anywhere}\n#vbm-disp .ds-result-main .ds-result-value{color:var(--ds-accent);font-size:29px}\n#vbm-disp .ds-result-note{margin-top:5px;color:var(--ds-muted);font-size:11.5px}\n#vbm-disp .ds-source-echo{margin-top:14px;padding:13px 15px;border:1px solid var(--ds-line);border-radius:7px;background:#fff;color:var(--ds-muted);font-size:12.5px;overflow-wrap:anywhere;white-space:pre-wrap}\n#vbm-disp .ds-safety{margin-top:14px;padding:14px 16px;border-left:4px solid var(--ds-warn);border-radius:6px;background:var(--ds-warn-bg);color:#60460f;font-size:13px}\n#vbm-disp .ds-section{margin-top:22px;border:1px solid var(--ds-line);border-radius:var(--ds-radius);background:#fff;overflow:hidden}\n#vbm-disp .ds-section h2{margin:0;padding:18px 22px;border-bottom:1px solid var(--ds-line);background:var(--ds-soft);font-size:20px}\n#vbm-disp .ds-section-in{padding:20px 22px}\n#vbm-disp .ds-section h3{margin:22px 0 8px;font-size:17px}\n#vbm-disp .ds-section h3:first-child{margin-top:0}\n#vbm-disp .ds-section p,#vbm-disp .ds-section li{color:var(--ds-muted);font-size:14px}\n#vbm-disp .ds-formula{margin:10px 0;padding:13px 15px;border:1px solid var(--ds-line);border-radius:7px;background:var(--ds-soft);font-family:\"Cascadia Mono\",Consolas,monospace;font-size:14px;overflow-x:auto}\n#vbm-disp .ds-table-wrap{overflow-x:auto}\n#vbm-disp table{width:100%;min-width:780px;border-collapse:collapse;font-size:13px}\n#vbm-disp th,#vbm-disp td{padding:10px;border:1px solid var(--ds-line);text-align:left;vertical-align:top}\n#vbm-disp th{background:var(--ds-soft);font-size:11px;text-transform:uppercase;letter-spacing:.04em}\n#vbm-disp a{color:var(--ds-blue)}\n#vbm-disp details{border-top:1px solid var(--ds-line)}\n#vbm-disp details:first-child{border-top:0}\n#vbm-disp summary{padding:14px 0;cursor:pointer;font-weight:800}\n#vbm-disp details p{margin:0 0 15px}\n#vbm-disp .ds-needs{margin-top:15px;padding:13px 15px;border:1px solid #efd794;border-radius:7px;background:var(--ds-warn-bg);color:#65490c;font-size:13px}\n#vbm-disp footer{padding:28px 16px;text-align:center;color:var(--ds-muted);font-size:12px}\n@media(max-width:760px){#vbm-disp .ds-grid,#vbm-disp .ds-result-grid{grid-template-columns:1fr}#vbm-disp .ds-result-main{grid-column:1}#vbm-disp .ds-body,#vbm-disp .ds-results,#vbm-disp .ds-section-in{padding:17px}#vbm-disp .ds-card-head,#vbm-disp .ds-section h2{padding:16px 17px}}\n@media print{#vbm-disp .ds-actions{display:none}#vbm-disp .ds-card{box-shadow:none}#vbm-disp .ds-results{display:block}}\n<\/style>\n\n<div id=\"vbm-disp\">\n  <header class=\"ds-head\">\n    <p class=\"ds-eyebrow\">Engineering reference &#8211; source controlled<\/p>\n    <h1>Single-Frequency Vibration Displacement Converter<\/h1>\n    <p class=\"ds-sub\">Convert the displacement magnitude of one scalar sinusoidal vibration component to velocity and acceleration magnitudes at that same frequency. Units and RMS, peak and peak-to-peak descriptors remain explicit.<\/p>\n    <div class=\"ds-tags\"><span class=\"ds-tag\">One scalar sine component<\/span><span class=\"ds-tag\">Exact unit conversions<\/span><span class=\"ds-tag\">No ISO severity verdict<\/span><\/div>\n  <\/header>\n\n  <div class=\"ds-callout\"><strong>Do not use a broadband overall or shaft orbit as one sine.<\/strong> A multi-frequency waveform has a different frequency weighting for velocity and acceleration. A two-axis shaft orbit is not one scalar displacement. This calculator accepts only one identified sinusoidal component along one stated measurement axis.<\/div>\n\n  <section class=\"ds-card\" aria-labelledby=\"ds-input-title\">\n    <div class=\"ds-card-head\"><h2 id=\"ds-input-title\">Single-component displacement record<\/h2><p>All fields are required. Displacement may be zero; frequency must be positive. Decimal point and decimal comma are accepted. Grouped numbers, exponents and unit suffixes are rejected.<\/p><\/div>\n    <form id=\"ds-form\" class=\"ds-body\" novalidate>\n      <div class=\"ds-grid\">\n        <div>\n          <label for=\"ds-displacement\">Displacement magnitude<\/label>\n          <input id=\"ds-displacement\" type=\"text\" inputmode=\"decimal\" autocomplete=\"off\" placeholder=\"e.g. 100\">\n          <span class=\"ds-hint\">One scalar sinusoidal component only.<\/span>\n        <\/div>\n        <div>\n          <label for=\"ds-displacement-unit\">Displacement unit<\/label>\n          <select id=\"ds-displacement-unit\" required>\n            <option value=\"\" selected>Select unit&#8230;<\/option>\n            <option value=\"um\">\u00b5m<\/option>\n            <option value=\"mm\">mm<\/option>\n            <option value=\"mil\">mil (0.001 in)<\/option>\n            <option value=\"in\">in<\/option>\n          <\/select>\n          <span class=\"ds-hint\">1 mil = 25.4 \u00b5m exactly; 1 in = 0.0254 m exactly.<\/span>\n        <\/div>\n        <div>\n          <label for=\"ds-descriptor\">Input amplitude descriptor<\/label>\n          <select id=\"ds-descriptor\" required>\n            <option value=\"\" selected>Select descriptor&#8230;<\/option>\n            <option value=\"rms\">RMS<\/option>\n            <option value=\"peak\">peak (0-to-peak)<\/option>\n            <option value=\"pp\">peak-to-peak<\/option>\n          <\/select>\n          <span class=\"ds-hint\">The sqrt(2) relations below apply to a sine wave only.<\/span>\n        <\/div>\n        <div>\n          <label for=\"ds-frequency\">Component frequency<\/label>\n          <input id=\"ds-frequency\" type=\"text\" inputmode=\"decimal\" autocomplete=\"off\" placeholder=\"e.g. 25\">\n          <span class=\"ds-hint\">Frequency of the same displacement component.<\/span>\n        <\/div>\n        <div>\n          <label for=\"ds-frequency-unit\">Frequency unit<\/label>\n          <select id=\"ds-frequency-unit\" required>\n            <option value=\"\" selected>Select unit&#8230;<\/option>\n            <option value=\"hz\">Hz<\/option>\n            <option value=\"rpm\">r\/min (RPM)<\/option>\n          <\/select>\n          <span class=\"ds-hint\">RPM\/60 is valid only for the rotational order being converted.<\/span>\n        <\/div>\n        <div class=\"ds-field-wide\">\n          <label for=\"ds-record\">Measurement\/component record<\/label>\n          <textarea id=\"ds-record\" placeholder=\"Asset and point; axis; absolute housing or relative shaft displacement; sensor\/probe; descriptor; component\/order; frequency; bandwidth\/window\/filter; operating state and source reference\"><\/textarea>\n          <span class=\"ds-hint\">Absolute casing motion, relative shaft motion and a two-axis orbit are not interchangeable quantities.<\/span>\n        <\/div>\n      <\/div>\n\n      <fieldset>\n        <legend>Required confirmations<\/legend>\n        <label class=\"ds-check\"><input id=\"ds-confirm-sine\" type=\"checkbox\"><span>The input is one scalar sinusoidal displacement component at the entered frequency, not broadband overall displacement, runout, transient motion, a sum of components or a two-axis shaft orbit.<\/span><\/label>\n        <label class=\"ds-check\"><input id=\"ds-confirm-descriptor\" type=\"checkbox\"><span>I verified the displacement unit and amplitude descriptor. RMS, peak and peak-to-peak are not interchangeable; the displayed factors assume a sine wave.<\/span><\/label>\n        <label class=\"ds-check\"><input id=\"ds-confirm-scope\" type=\"checkbox\"><span>I understand that this arithmetic is not an ISO 20816 evaluation, clearance\/stress check, orbit assessment, alarm limit, machine diagnosis or proof of mechanical acceptability.<\/span><\/label>\n      <\/fieldset>\n\n      <div class=\"ds-actions\">\n        <button class=\"ds-primary\" type=\"submit\">Convert one displacement component<\/button>\n        <button class=\"ds-secondary\" id=\"ds-example\" type=\"button\">Load worked sine example<\/button>\n        <button class=\"ds-secondary\" id=\"ds-clear\" type=\"button\">Clear<\/button>\n      <\/div>\n      <div id=\"ds-errors\" class=\"ds-errors\" role=\"alert\" aria-live=\"assertive\"><\/div>\n      <div id=\"ds-status\" class=\"ds-status\" aria-live=\"polite\">No result until the form is submitted.<\/div>\n    <\/form>\n\n    <div id=\"ds-results\" class=\"ds-results\" aria-live=\"polite\">\n      <div class=\"ds-result-grid\">\n        <div class=\"ds-result ds-result-main\"><div class=\"ds-result-label\">Velocity magnitude, RMS<\/div><div id=\"ds-out-vrms\" class=\"ds-result-value\">&#8211;<\/div><div class=\"ds-result-note\">For the same scalar sinusoidal component.<\/div><\/div>\n        <div class=\"ds-result\"><div class=\"ds-result-label\">Displacement, RMS<\/div><div id=\"ds-out-xrms\" class=\"ds-result-value\">&#8211;<\/div><div class=\"ds-result-note\">Normalized descriptor.<\/div><\/div>\n        <div class=\"ds-result\"><div class=\"ds-result-label\">Displacement, peak<\/div><div id=\"ds-out-xpeak\" class=\"ds-result-value\">&#8211;<\/div><div class=\"ds-result-note\">sqrt(2) x RMS; sine only.<\/div><\/div>\n        <div class=\"ds-result\"><div class=\"ds-result-label\">Displacement, peak-to-peak<\/div><div id=\"ds-out-xpp\" class=\"ds-result-value\">&#8211;<\/div><div class=\"ds-result-note\">2 x peak; sine only.<\/div><\/div>\n        <div class=\"ds-result\"><div class=\"ds-result-label\">Velocity, peak<\/div><div id=\"ds-out-vpeak\" class=\"ds-result-value\">&#8211;<\/div><div class=\"ds-result-note\">sqrt(2) x velocity RMS.<\/div><\/div>\n        <div class=\"ds-result\"><div class=\"ds-result-label\">Acceleration, RMS<\/div><div id=\"ds-out-arms\" class=\"ds-result-value\">&#8211;<\/div><div class=\"ds-result-note\">omega\u00b2 x displacement RMS.<\/div><\/div>\n        <div class=\"ds-result\"><div class=\"ds-result-label\">Acceleration, peak<\/div><div id=\"ds-out-apeak\" class=\"ds-result-value\">&#8211;<\/div><div class=\"ds-result-note\">sqrt(2) x acceleration RMS.<\/div><\/div>\n        <div class=\"ds-result\"><div class=\"ds-result-label\">Acceleration, RMS in g_n<\/div><div id=\"ds-out-grms\" class=\"ds-result-value\">&#8211;<\/div><div class=\"ds-result-note\">aRMS \/ 9.80665 m\/s\u00b2.<\/div><\/div>\n        <div class=\"ds-result\"><div class=\"ds-result-label\">Acceleration, peak in g_n<\/div><div id=\"ds-out-gpeak\" class=\"ds-result-value\">&#8211;<\/div><div class=\"ds-result-note\">aPeak \/ 9.80665 m\/s\u00b2.<\/div><\/div>\n        <div class=\"ds-result\"><div class=\"ds-result-label\">Component frequency<\/div><div id=\"ds-out-frequency\" class=\"ds-result-value\">&#8211;<\/div><div class=\"ds-result-note\">Hz and r\/min shown together.<\/div><\/div>\n      <\/div>\n      <div id=\"ds-out-record\" class=\"ds-source-echo\"><\/div>\n      <div class=\"ds-safety\"><strong>Not a clearance, stress or condition assessment.<\/strong> The result inherits sensor\/probe calibration, runout compensation, mounting, filters, integration\/differentiation, window, bandwidth, leakage, phase and operating-state limitations. Relative shaft displacement, absolute shaft\/casing motion and orbit measurements require their own applicable procedures.<\/div>\n    <\/div>\n  <\/section>\n\n  <section class=\"ds-section\">\n    <h2>Equations, descriptors and units<\/h2>\n    <div class=\"ds-section-in\">\n      <h3>Normalize the displacement descriptor<\/h3>\n      <div class=\"ds-formula\">input RMS: xRMS = x<br>input peak: xRMS = x \/ sqrt(2)<br>input peak-to-peak: xRMS = x \/ (2 sqrt(2))<\/div>\n      <p>These descriptor factors apply to one sine wave. The page first converts the selected displacement unit to metres, then normalizes it to RMS.<\/p>\n      <h3>Single sinusoidal component<\/h3>\n      <div class=\"ds-formula\">omega = 2 pi f<br>vRMS = omega xRMS<br>aRMS = omega\u00b2 xRMS<br>peak = sqrt(2) RMS<br>peak-to-peak = 2 peak<\/div>\n      <p>Velocity leads displacement by 90 degrees and acceleration is 180 degrees from displacement for the stated sine convention. This page reports magnitudes only; it does not reconstruct a time waveform or preserve phase.<\/p>\n      <h3>Exact unit factors and conventional standard acceleration<\/h3>\n      <div class=\"ds-formula\">1 \u00b5m = 10^-6 m<br>1 mm = 10^-3 m<br>1 mil = 0.001 in = 25.4 \u00b5m<br>1 in = 0.0254 m<br>a[g_n] = a[m\/s\u00b2] \/ 9.80665<\/div>\n      <p>The metre and inch conversion is exact. BIPM records the conventional standard acceleration as 980.665 cm\/s\u00b2, equal to 9.80665 m\/s\u00b2. A value in g_n is a reference ratio and not a severity category.<\/p>\n    <\/div>\n  <\/section>\n\n  <section class=\"ds-section\">\n    <h2>Why the former general recommendations were removed<\/h2>\n    <div class=\"ds-section-in\">\n      <ul>\n        <li>A broadband overall displacement cannot be converted with one representative frequency. Each complex frequency component has its own omega weighting.<\/li>\n        <li>\u201cDisplacement below 10 Hz, velocity from 10 to 1000 Hz, acceleration above 1000 Hz\u201d is not a universal ISO rule. Quantity and band depend on the machine, measurement purpose, sensor\/probe response, point, direction and applicable procedure.<\/li>\n        <li>Peak = sqrt(2) x RMS and peak-to-peak = 2 x peak are sine-wave relationships, not general rules for shocks, runout, non-sinusoidal motion or an orbit.<\/li>\n        <li>RPM is a rotational rate. It equals the component frequency only for the 1x rotational order; harmonics, blade\/vane pass, gear mesh and bearing components have other frequencies.<\/li>\n        <li>A displacement magnitude alone cannot establish shaft-to-bearing clearance, stress, rub risk, orbit shape, phase, machine condition or acceptance.<\/li>\n      <\/ul>\n    <\/div>\n  <\/section>\n\n  <section class=\"ds-section\">\n    <h2>Standard and source record<\/h2>\n    <div class=\"ds-section-in\">\n      <div class=\"ds-table-wrap\">\n        <table>\n          <thead><tr><th>Source<\/th><th>Status checked 16 Jul 2026<\/th><th>What it supports here<\/th><th>What it does not support<\/th><\/tr><\/thead>\n          <tbody>\n            <tr><td><a href=\"https:\/\/www.iso.org\/standard\/63180.html\" rel=\"noopener\" target=\"_blank\">ISO 20816-1:2016<\/a>, Edition 1<\/td><td>Published; stage 90.92, to be revised; ISO\/FDIS 20816-1 is under development.<\/td><td>General machine-vibration measurement\/evaluation framework and the need to define quantities, measurement types and scope.<\/td><td>It is not the source of these elementary sine equations and does not make this an ISO severity or shaft-clearance calculator.<\/td><\/tr>\n            <tr><td><a href=\"https:\/\/www.iso.org\/standard\/68734.html\" rel=\"noopener\" target=\"_blank\">ISO 2041:2018<\/a>, Edition 4<\/td><td>Published and confirmed in 2024; stage 90.93.<\/td><td>Current mechanical-vibration, shock and condition-monitoring vocabulary record.<\/td><td>A vocabulary standard is not a machine alarm or clearance table.<\/td><\/tr>\n            <tr><td><a href=\"https:\/\/www.bksv.com\/media\/doc\/br0094.pdf\" rel=\"noopener\" target=\"_blank\">Br\u00fcel &amp; Kj\u00e6r, Measuring Vibration, br0094<\/a>, pp. 5-7<\/td><td>Official manufacturer full-text primer; relevant printed pages visually checked.<\/td><td>Sine RMS\/peak\/peak-to-peak descriptors, scalar sinusoidal displacement\/velocity\/acceleration relationships, phase relationships and frequency weighting.<\/td><td>Historical practical discussion is not imported as a current universal ISO band or limit.<\/td><\/tr>\n            <tr><td><a href=\"https:\/\/www.bipm.org\/en\/si-brochure-9\" rel=\"noopener\" target=\"_blank\">BIPM SI Brochure, 9th edition, version 4.01<\/a>, June 2026, Appendix 1 p. 154<\/td><td>Current official SI brochure version at the audit date.<\/td><td>Conventional standard acceleration g_n = 980.665 cm\/s\u00b2 = 9.80665 m\/s\u00b2.<\/td><td>g_n conversion does not establish vibration severity.<\/td><\/tr>\n          <\/tbody>\n        <\/table>\n      <\/div>\n      <div class=\"ds-needs\"><strong>NEEDS_LICENSED_SOURCE:<\/strong> the full normative texts of ISO 20816-1:2016 and ISO 2041:2018 are not licensed in this audit record. No clause number, alarm boundary, clearance, measurement band or \u201cISO conversion formula\u201d is invented. The retained equations are classified as single-frequency simple-harmonic-motion mathematics supported by the cited full manufacturer primer.<\/div>\n    <\/div>\n  <\/section>\n\n  <section class=\"ds-section\">\n    <h2>Worked sine example<\/h2>\n    <div class=\"ds-section-in\">\n      <p>For one scalar 25 Hz sinusoidal component with displacement 100 \u00b5m peak-to-peak: xPeak = 50 \u00b5m, xRMS = 35.35533906 \u00b5m, vRMS = 5.553603673 mm\/s, vPeak = 7.853981634 mm\/s, aRMS = 0.872358025 m\/s\u00b2 and aPeak = 1.233700550 m\/s\u00b2. The button loads these values but leaves every scope confirmation unchecked. This is an arithmetic example, not an acceptance limit.<\/p>\n    <\/div>\n  <\/section>\n\n  <section class=\"ds-section\">\n    <h2>Frequently asked questions<\/h2>\n    <div class=\"ds-section-in\">\n      <details><summary>Can I use overall displacement and running speed?<\/summary><p>Only when the value is demonstrably one scalar sinusoidal component at that frequency. A broadband overall or waveform containing harmonics requires component-wise or validated time-domain processing.<\/p><\/details>\n      <details><summary>Is peak-to-peak always twice peak?<\/summary><p>For one centered sine wave, yes. It is not a general relation for arbitrary waveforms, runout, transients or a two-dimensional orbit.<\/p><\/details>\n      <details><summary>Does the result comply with ISO 20816?<\/summary><p>No compliance verdict is produced. An evaluation needs the applicable part, machine scope, absolute or relative quantity, descriptor, frequency band, measurement point\/direction, support and operating state.<\/p><\/details>\n      <details><summary>Can the result be compared directly with shaft clearance?<\/summary><p>No. Probe geometry, runout, scale factor, reference position, orbit, phase, thermal position and the applicable machinery procedure must be considered. This page calculates one scalar component magnitude only.<\/p><\/details>\n      <details><summary>Why is g_n written with a subscript?<\/summary><p>It identifies the conventional standard acceleration 9.80665 m\/s\u00b2 used as a reference ratio, not location-dependent free-fall acceleration and not a severity class.<\/p><\/details>\n    <\/div>\n  <\/section>\n\n  <footer>Scientific audit revision: 16 July 2026. English source page; translations are reviewed only after the source is verified.<\/footer>\n<\/div>\n\n<script>\n(function(){\n  'use strict';\n  var root=document.getElementById('vbm-disp');if(!root)return;\n  var G_N=9.80665,UM_TO_M=0.000001,MM_TO_M=0.001,MIL_TO_M=0.0000254,IN_TO_M=0.0254;\n  function byId(id){return document.getElementById(id)}\n  var form=byId('ds-form'),results=byId('ds-results'),errors=byId('ds-errors'),status=byId('ds-status');\n  function parseDecimal(raw,allowZero){var s=String(raw).trim();if(!s||s.length>40||!\/^(?:\\d+(?:[.,]\\d*)?|[.,]\\d+)$\/.test(s))throw new Error('format');var n=Number(s.replace(',','.'));if(!Number.isFinite(n)||n<0||(!allowZero&&n===0)||n>1000000000000)throw new Error('range');return n}\n  function fmt(n,d){if(!Number.isFinite(n))return'-';if(n===0)return'0';var a=Math.abs(n);if(a>=100000000||a<0.000001)return n.toExponential(6);return n.toFixed(d).replace(\/(\\.\\d*?[1-9])0+$\/,'$1').replace(\/\\.0+$\/,'')}\n  function displacementToM(value,unit){if(unit==='um')return value*UM_TO_M;if(unit==='mm')return value*MM_TO_M;if(unit==='mil')return value*MIL_TO_M;if(unit==='in')return value*IN_TO_M;return NaN}\n  function frequencyToHz(value,unit){if(unit==='hz')return value;if(unit==='rpm')return value\/60;return NaN}\n  function toRms(value,descriptor){if(descriptor==='rms')return value;if(descriptor==='peak')return value\/Math.SQRT2;if(descriptor==='pp')return value\/(2*Math.SQRT2);return NaN}\n  function hideResults(){results.classList.remove('ds-show');errors.classList.remove('ds-show');errors.textContent='';status.textContent='Inputs changed; submit again to create a new controlled result.'}\n  function showErrors(items){errors.textContent='';var strong=document.createElement('strong');strong.textContent='Correct the following:';errors.appendChild(strong);var list=document.createElement('ul');items.forEach(function(item){var li=document.createElement('li');li.textContent=item;list.appendChild(li)});errors.appendChild(list);errors.classList.add('ds-show');status.textContent='No result was produced.'}\n  function collect(){\n    var messages=[],displacement=NaN,frequency=NaN;try{displacement=parseDecimal(byId('ds-displacement').value,true)}catch(e){messages.push('Displacement must be one non-negative ungrouped decimal number.')}try{frequency=parseDecimal(byId('ds-frequency').value,false)}catch(e){messages.push('Frequency must be one positive ungrouped decimal number.')}\n    var unit=byId('ds-displacement-unit').value,descriptor=byId('ds-descriptor').value,funit=byId('ds-frequency-unit').value;if(!['um','mm','mil','in'].includes(unit))messages.push('Select the displacement unit.');if(!['rms','peak','pp'].includes(descriptor))messages.push('Select the input amplitude descriptor.');if(!['hz','rpm'].includes(funit))messages.push('Select Hz or r\/min for frequency.');\n    var record=byId('ds-record').value.trim();if(record.length<20||record.length>3000)messages.push('Enter an identifiable measurement\/component record (20 to 3,000 characters).');if(!byId('ds-confirm-sine').checked)messages.push('Confirm the one-scalar-sinusoidal-component scope.');if(!byId('ds-confirm-descriptor').checked)messages.push('Confirm the unit and amplitude descriptor.');if(!byId('ds-confirm-scope').checked)messages.push('Confirm the non-evaluation and non-clearance scope.');if(messages.length)return{messages:messages};\n    var xM=displacementToM(displacement,unit),fHz=frequencyToHz(frequency,funit),xRms=toRms(xM,descriptor);if(![xM,fHz,xRms].every(Number.isFinite)||xM<0||xRms<0||fHz<=0){messages.push('The normalized displacement and frequency must be finite.');return{messages:messages}}return{messages:messages,xRms:xRms,fHz:fHz,record:record};\n  }\n  function convert(x){var omega=2*Math.PI*x.fHz,xPeak=Math.SQRT2*x.xRms,xPP=2*xPeak,vRms=omega*x.xRms,vPeak=Math.SQRT2*vRms,aRms=omega*omega*x.xRms,aPeak=Math.SQRT2*aRms,gRms=aRms\/G_N,gPeak=aPeak\/G_N,rpm=60*x.fHz;var values=[omega,xPeak,xPP,vRms,vPeak,aRms,aPeak,gRms,gPeak,rpm];if(!values.every(Number.isFinite))throw new Error('nonfinite');return{omega:omega,xPeak:xPeak,xPP:xPP,vRms:vRms,vPeak:vPeak,aRms:aRms,aPeak:aPeak,gRms:gRms,gPeak:gPeak,rpm:rpm}}\n  form.addEventListener('submit',function(event){event.preventDefault();results.classList.remove('ds-show');errors.classList.remove('ds-show');errors.textContent='';var x=collect();if(x.messages.length){showErrors(x.messages);return}var r;try{r=convert(x)}catch(e){showErrors(['The normalized calculation exceeded the supported finite range.']);return}\n    byId('ds-out-vrms').textContent=fmt(r.vRms*1000,9)+' mm\/s RMS';byId('ds-out-xrms').textContent=fmt(x.xRms*1000000,9)+' \u00b5m RMS';byId('ds-out-xpeak').textContent=fmt(r.xPeak*1000000,9)+' \u00b5m peak';byId('ds-out-xpp').textContent=fmt(r.xPP*1000000,9)+' \u00b5m p-p';byId('ds-out-vpeak').textContent=fmt(r.vPeak*1000,9)+' mm\/s peak';byId('ds-out-arms').textContent=fmt(r.aRms,9)+' m\/s\u00b2 RMS';byId('ds-out-apeak').textContent=fmt(r.aPeak,9)+' m\/s\u00b2 peak';byId('ds-out-grms').textContent=fmt(r.gRms,10)+' g_n RMS';byId('ds-out-gpeak').textContent=fmt(r.gPeak,10)+' g_n peak';byId('ds-out-frequency').textContent=fmt(x.fHz,9)+' Hz; '+fmt(r.rpm,6)+' r\/min';byId('ds-out-record').textContent='Measurement\/component record: '+x.record;results.classList.add('ds-show');status.textContent='Single-component conversion created from the current visible inputs. No adequacy or acceptance verdict was produced.';\n  });\n  form.addEventListener('input',hideResults);form.addEventListener('change',hideResults);\n  byId('ds-example').addEventListener('click',function(){form.reset();byId('ds-displacement').value='100';byId('ds-displacement-unit').value='um';byId('ds-descriptor').value='pp';byId('ds-frequency').value='25';byId('ds-frequency-unit').value='hz';byId('ds-record').value='Worked equation example: one scalar 25 Hz sine component, displacement 100 \u00b5m peak-to-peak; no machine acceptance or clearance context';hideResults();status.textContent='Worked sine values loaded. Confirmations remain unchecked; verify the record, descriptor and scope before submitting.'});\n  byId('ds-clear').addEventListener('click',function(){form.reset();results.classList.remove('ds-show');errors.classList.remove('ds-show');errors.textContent='';status.textContent='Cleared. No result until the form is submitted.'});\n})();\n<\/script>\n\n","protected":false},"excerpt":{"rendered":"<p>Convert one scalar sinusoidal displacement component between explicit RMS, peak and peak-to-peak displacement, velocity and acceleration at one frequency; not for broadband overall, shaft-orbit, clearance or ISO severity evaluation.<\/p>","protected":false},"featured_media":0,"template":"","meta":{"ai_generated_summary":"","footnotes":""},"categories":[],"tags":[],"class_list":["post-100281","calculator","type-calculator","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/vibromera.eu\/fi\/wp-json\/wp\/v2\/calculator\/100281","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/vibromera.eu\/fi\/wp-json\/wp\/v2\/calculator"}],"about":[{"href":"https:\/\/vibromera.eu\/fi\/wp-json\/wp\/v2\/types\/calculator"}],"version-history":[{"count":3,"href":"https:\/\/vibromera.eu\/fi\/wp-json\/wp\/v2\/calculator\/100281\/revisions"}],"predecessor-version":[{"id":102629,"href":"https:\/\/vibromera.eu\/fi\/wp-json\/wp\/v2\/calculator\/100281\/revisions\/102629"}],"wp:attachment":[{"href":"https:\/\/vibromera.eu\/fi\/wp-json\/wp\/v2\/media?parent=100281"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/vibromera.eu\/fi\/wp-json\/wp\/v2\/categories?post=100281"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/vibromera.eu\/fi\/wp-json\/wp\/v2\/tags?post=100281"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}