{"id":100293,"date":"2026-02-15T20:32:15","date_gmt":"2026-02-15T20:32:15","guid":{"rendered":"https:\/\/vibromera.eu\/?post_type=calculator&#038;p=100293"},"modified":"2026-07-17T05:14:57","modified_gmt":"2026-07-17T05:14:57","slug":"vibration-overall-level","status":"publish","type":"calculator","link":"https:\/\/vibromera.eu\/uk\/calculators\/vibration-overall-level\/","title":{"rendered":"Spectral RMS Integration Worksheet | PSD, ASD &#038; RMS Bands"},"content":{"rendered":"\n<script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"WebApplication\",\"name\":\"Spectral RMS Integration Worksheet\",\"description\":\"Combine documented non-overlapping RMS band contributions or integrate documented PSD\/ASD values over explicit effective bandwidths. The result is not automatically a machine overall level, ISO acceptance decision or diagnosis.\",\"url\":\"https:\/\/vibromera.eu\/calculators\/vibration-overall-level\/\",\"applicationCategory\":\"EngineeringApplication\",\"operatingSystem\":\"Any\",\"isAccessibleForFree\":true,\"creator\":{\"@type\":\"Organization\",\"name\":\"Vibromera\",\"url\":\"https:\/\/vibromera.eu\/\"},\"dateModified\":\"2026-07-17\",\"inLanguage\":\"en\"}<\/script>\n<script type=\"application\/ld+json\">{\"@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\":\"Spectral RMS Integration Worksheet\",\"item\":\"https:\/\/vibromera.eu\/calculators\/vibration-overall-level\/\"}]}<\/script>\n<style>\n#vbm-si{--si-ink:#17313a;--si-muted:#52656c;--si-blue:#0b6477;--si-blue2:#084b5a;--si-line:#b9cbd0;--si-bg:#f5f8f8;--si-white:#fff;--si-warn:#8a4b08;--si-warnbg:#fff3d6;--si-bad:#9a2f2f;--si-badbg:#fff0ef;--si-good:#17663d;--si-goodbg:#e8f7ee;max-width:1160px;margin:24px auto;font:16px\/1.55 Arial,sans-serif;color:var(--si-ink);background:var(--si-white);border:1px solid var(--si-line);border-radius:18px;overflow:hidden;box-shadow:0 12px 34px rgba(23,49,58,.12)}\n#vbm-si *{box-sizing:border-box}#vbm-si h1,#vbm-si h2,#vbm-si h3{line-height:1.2;margin:0 0 12px}#vbm-si p{margin:0 0 12px}#vbm-si a{color:#075f75;text-decoration:underline;text-underline-offset:2px}#vbm-si .si-hero{padding:34px;background:linear-gradient(135deg,var(--si-blue2),var(--si-blue));color:#fff}#vbm-si .si-hero h1{color:#fff;font-size:clamp(29px,5vw,46px);max-width:940px}#vbm-si .si-kicker{font-weight:700;letter-spacing:.08em;text-transform:uppercase;font-size:13px;margin-bottom:10px}#vbm-si .si-hero p{max-width:940px;font-size:18px;color:#effcfd}#vbm-si .si-tags{display:flex;flex-wrap:wrap;gap:8px;margin-top:16px}#vbm-si .si-tag{padding:6px 10px;border:1px solid rgba(255,255,255,.48);border-radius:999px;font-size:13px;font-weight:700}\n#vbm-si .si-body{padding:28px}#vbm-si .si-alert{padding:16px 18px;border-left:5px solid var(--si-warn);background:var(--si-warnbg);border-radius:8px;margin-bottom:22px}#vbm-si .si-alert strong{display:block;margin-bottom:4px}#vbm-si form,#vbm-si .si-grid,#vbm-si .si-card,#vbm-si .si-section,#vbm-si .si-field{min-width:0}#vbm-si .si-grid{display:grid;grid-template-columns:minmax(0,1fr) minmax(0,1fr);gap:16px}#vbm-si .si-card{border:1px solid var(--si-line);border-radius:12px;padding:20px;background:var(--si-white)}#vbm-si .si-card h2{font-size:24px}#vbm-si .si-field{display:grid;align-content:start;gap:6px}#vbm-si .si-field label,#vbm-si .si-label,#vbm-si legend{font-weight:700}#vbm-si .si-field input,#vbm-si .si-field select,#vbm-si .si-field textarea,#vbm-si .si-data-input{width:100%;min-width:0;max-width:100%;border:1px solid #9fb5bc;border-radius:7px;padding:10px 11px;background:#fff;color:#17313a;font:inherit}#vbm-si input:focus,#vbm-si select:focus,#vbm-si textarea:focus{outline:3px solid rgba(11,100,119,.2);border-color:var(--si-blue)}#vbm-si input:disabled{background:#edf1f2;color:#75868c}#vbm-si .si-field textarea{min-height:92px;resize:vertical}#vbm-si .si-hint{font-size:13px;color:var(--si-muted)}#vbm-si .si-wide{grid-column:1\/-1}#vbm-si fieldset{border:0;padding:0;margin:0;min-width:0}#vbm-si legend{font-size:24px;line-height:1.2;margin-bottom:10px}\n#vbm-si .si-table-wrap{width:100%;max-width:100%;min-width:0;overflow-x:auto;overscroll-behavior-x:contain;border:1px solid var(--si-line);border-radius:10px;margin-top:14px}#vbm-si table{width:100%;min-width:800px;border-collapse:collapse;background:#fff}#vbm-si th,#vbm-si td{padding:10px 11px;border-bottom:1px solid #d9e3e5;text-align:left;vertical-align:middle}#vbm-si th{background:#e8f1f2}#vbm-si tbody tr:last-child th,#vbm-si tbody tr:last-child td{border-bottom:0}#vbm-si .si-row-number{width:58px;text-align:center}#vbm-si .si-row-label{min-width:190px}#vbm-si .si-row-value,#vbm-si .si-row-width{min-width:185px}#vbm-si .si-sr{position:absolute;width:1px;height:1px;padding:0;margin:-1px;overflow:hidden;clip:rect(0,0,0,0);white-space:nowrap;border:0}\n#vbm-si .si-checks{display:grid;gap:10px;margin-top:10px}#vbm-si .si-check{display:grid;grid-template-columns:22px 1fr;gap:9px;align-items:start;padding:10px;border:1px solid #d5e1e4;border-radius:8px;background:var(--si-bg)}#vbm-si .si-check input{width:18px;height:18px;margin-top:3px}#vbm-si .si-actions{display:flex;flex-wrap:wrap;gap:10px;margin-top:18px}#vbm-si button{border:0;border-radius:8px;padding:11px 18px;font:700 15px Arial,sans-serif;cursor:pointer}#vbm-si .si-primary{background:var(--si-blue);color:#fff}#vbm-si .si-secondary{background:#e7eff1;color:var(--si-ink)}\n#vbm-si .si-result{display:none;margin-top:20px;border:2px solid var(--si-line);border-radius:12px;padding:20px;background:var(--si-bg)}#vbm-si .si-result.si-visible{display:block}#vbm-si .si-result.si-error{border-color:var(--si-bad);background:var(--si-badbg)}#vbm-si .si-result.si-incomplete,#vbm-si .si-result.si-stale{border-color:var(--si-warn);background:var(--si-warnbg)}#vbm-si .si-result.si-ready{border-color:var(--si-good);background:var(--si-goodbg)}#vbm-si .si-result h2{font-size:23px}#vbm-si .si-values{display:grid;grid-template-columns:repeat(3,minmax(0,1fr));gap:10px;margin-top:16px}#vbm-si .si-value{background:#fff;border:1px solid var(--si-line);border-radius:8px;padding:13px}#vbm-si .si-value span{display:block;color:var(--si-muted);font-size:13px}#vbm-si .si-value strong{display:block;font-size:19px;overflow-wrap:anywhere}#vbm-si .si-errors{margin:10px 0 0;padding-left:22px}\n#vbm-si .si-section{margin-top:24px}#vbm-si .si-section h2{font-size:26px}#vbm-si .si-formula{font-family:Consolas,monospace;background:#edf6f7;border:1px solid #b8d6dc;border-radius:8px;padding:14px;overflow-x:auto;margin:10px 0}#vbm-si .si-boundary{border-left:5px solid var(--si-blue);background:#eaf6f8;padding:15px 17px;border-radius:8px;margin:14px 0}#vbm-si details{border:1px solid var(--si-line);border-radius:9px;padding:12px 14px;background:#fff;margin:9px 0}#vbm-si summary{font-weight:700;cursor:pointer}#vbm-si .si-footer{margin-top:24px;padding:17px;background:#edf3f4;border-radius:10px;color:var(--si-muted);font-size:14px}\n@media(max-width:760px){#vbm-si{width:100%;max-width:100%;margin:12px 0;border-radius:12px}#vbm-si .si-hero,#vbm-si .si-body{padding:22px 16px}#vbm-si .si-grid{grid-template-columns:minmax(0,1fr)}#vbm-si .si-wide{grid-column:auto}#vbm-si .si-values{grid-template-columns:1fr 1fr}}@media(max-width:430px){#vbm-si .si-values{grid-template-columns:1fr}#vbm-si button{width:100%}}\n<\/style>\n<main id=\"vbm-si\">\n  <header class=\"si-hero\">\n    <div class=\"si-kicker\">Traceable signal-processing worksheet<\/div>\n    <h1>Spectral RMS Integration Worksheet<\/h1>\n    <p>Combine documented non-overlapping RMS contributions or integrate documented PSD\/ASD data over explicit effective bandwidths. The output is the RMS of the entered data&mdash;not automatically a machine overall level, ISO acceptance decision or diagnosis.<\/p>\n    <div class=\"si-tags\"><span class=\"si-tag\">RMS contributions<\/span><span class=\"si-tag\">PSD integration<\/span><span class=\"si-tag\">ASD integration<\/span><span class=\"si-tag\">No peak-list shortcut<\/span><\/div>\n  <\/header>\n  <div class=\"si-body\">\n    <div class=\"si-alert\"><strong>Do not paste a list of displayed peaks<\/strong>A few peak amplitudes do not represent all energy in a frequency band. Do not enter peak, peak-to-peak, max-hold, ESD, mixed-axis, mixed-unit or mixed-record values. Use a documented analyzer export whose scaling and effective integration bandwidth are known.<\/div>\n    <form id=\"si-form\" novalidate>\n      <section class=\"si-card\">\n        <h2>Measurement identity and scaling<\/h2>\n        <p>Blank inputs are deliberate. This worksheet cannot infer the analyzer normalization, window correction, complete frequency band or machine acceptance criterion.<\/p>\n        <div class=\"si-grid\">\n          <div class=\"si-field\"><label for=\"si-case\">Measurement record ID<\/label><input id=\"si-case\" type=\"text\" maxlength=\"120\" required><\/div>\n          <div class=\"si-field\"><label for=\"si-quantity\">Measured quantity<\/label><input id=\"si-quantity\" type=\"text\" maxlength=\"80\" required placeholder=\"e.g. casing vibration velocity\"><\/div>\n          <div class=\"si-field\"><label for=\"si-axis\">Point and direction<\/label><input id=\"si-axis\" type=\"text\" maxlength=\"120\" required placeholder=\"e.g. DE bearing, horizontal\"><\/div>\n          <div class=\"si-field\"><label for=\"si-unit\">Underlying engineering unit<\/label><input id=\"si-unit\" type=\"text\" maxlength=\"40\" required placeholder=\"e.g. mm\/s\"><span class=\"si-hint\">Enter the unit of the resulting RMS quantity, not a density suffix.<\/span><\/div>\n          <div class=\"si-field\"><label for=\"si-band-start\">Intended band start (Hz)<\/label><input id=\"si-band-start\" type=\"text\" inputmode=\"decimal\" required><\/div>\n          <div class=\"si-field\"><label for=\"si-band-end\">Intended band end (Hz)<\/label><input id=\"si-band-end\" type=\"text\" inputmode=\"decimal\" required><\/div>\n          <div class=\"si-field\"><label for=\"si-scaling\">Input scaling<\/label><select id=\"si-scaling\" required><option value=\"\">Select documented scaling<\/option><option value=\"rms\">Non-overlapping RMS contribution \/ integrated RMS band<\/option><option value=\"psd\">Power spectral density (underlying unit squared per Hz)<\/option><option value=\"asd\">Amplitude spectral density (underlying unit per square-root Hz)<\/option><\/select><\/div>\n          <div class=\"si-field si-wide\"><label for=\"si-processing\">Analyzer export and processing record<\/label><textarea id=\"si-processing\" maxlength=\"1000\" required placeholder=\"Instrument\/software, channel, sampling, record length, window, amplitude convention, line spacing\/effective bandwidth, averaging, filters, DC\/Nyquist handling and export identifier\"><\/textarea><\/div>\n        <\/div>\n      <\/section>\n      <section class=\"si-card si-section\">\n        <h2>Documented non-overlapping inputs<\/h2>\n        <p id=\"si-mode-help\">Select an input scaling. For density modes, enter the effective integration width belonging to each density value; do not assume that displayed line spacing and noise bandwidth are interchangeable.<\/p>\n        <div class=\"si-table-wrap\"><table aria-describedby=\"si-mode-help\"><thead><tr><th class=\"si-row-number\" scope=\"col\">Row<\/th><th class=\"si-row-label\" scope=\"col\">Line\/band identifier<\/th><th class=\"si-row-value\" scope=\"col\">Value in selected scaling<\/th><th class=\"si-row-width\" scope=\"col\">Effective integration width, Hz<\/th><\/tr><\/thead><tbody>\n          <tr><th class=\"si-row-number\" scope=\"row\">1<\/th><td><label class=\"si-sr\" for=\"si-label-1\">Row 1 identifier<\/label><input class=\"si-data-input\" id=\"si-label-1\" type=\"text\" maxlength=\"80\"><\/td><td><label class=\"si-sr\" for=\"si-value-1\">Row 1 value<\/label><input class=\"si-data-input si-value-input\" id=\"si-value-1\" type=\"text\" inputmode=\"decimal\"><\/td><td><label class=\"si-sr\" for=\"si-width-1\">Row 1 effective integration width<\/label><input class=\"si-data-input si-width-input\" id=\"si-width-1\" type=\"text\" inputmode=\"decimal\" disabled><\/td><\/tr>\n          <tr><th class=\"si-row-number\" scope=\"row\">2<\/th><td><label class=\"si-sr\" for=\"si-label-2\">Row 2 identifier<\/label><input class=\"si-data-input\" id=\"si-label-2\" type=\"text\" maxlength=\"80\"><\/td><td><label class=\"si-sr\" for=\"si-value-2\">Row 2 value<\/label><input class=\"si-data-input si-value-input\" id=\"si-value-2\" type=\"text\" inputmode=\"decimal\"><\/td><td><label class=\"si-sr\" for=\"si-width-2\">Row 2 effective integration width<\/label><input class=\"si-data-input si-width-input\" id=\"si-width-2\" type=\"text\" inputmode=\"decimal\" disabled><\/td><\/tr>\n          <tr><th class=\"si-row-number\" scope=\"row\">3<\/th><td><label class=\"si-sr\" for=\"si-label-3\">Row 3 identifier<\/label><input class=\"si-data-input\" id=\"si-label-3\" type=\"text\" maxlength=\"80\"><\/td><td><label class=\"si-sr\" for=\"si-value-3\">Row 3 value<\/label><input class=\"si-data-input si-value-input\" id=\"si-value-3\" type=\"text\" inputmode=\"decimal\"><\/td><td><label class=\"si-sr\" for=\"si-width-3\">Row 3 effective integration width<\/label><input class=\"si-data-input si-width-input\" id=\"si-width-3\" type=\"text\" inputmode=\"decimal\" disabled><\/td><\/tr>\n          <tr><th class=\"si-row-number\" scope=\"row\">4<\/th><td><label class=\"si-sr\" for=\"si-label-4\">Row 4 identifier<\/label><input class=\"si-data-input\" id=\"si-label-4\" type=\"text\" maxlength=\"80\"><\/td><td><label class=\"si-sr\" for=\"si-value-4\">Row 4 value<\/label><input class=\"si-data-input si-value-input\" id=\"si-value-4\" type=\"text\" inputmode=\"decimal\"><\/td><td><label class=\"si-sr\" for=\"si-width-4\">Row 4 effective integration width<\/label><input class=\"si-data-input si-width-input\" id=\"si-width-4\" type=\"text\" inputmode=\"decimal\" disabled><\/td><\/tr>\n          <tr><th class=\"si-row-number\" scope=\"row\">5<\/th><td><label class=\"si-sr\" for=\"si-label-5\">Row 5 identifier<\/label><input class=\"si-data-input\" id=\"si-label-5\" type=\"text\" maxlength=\"80\"><\/td><td><label class=\"si-sr\" for=\"si-value-5\">Row 5 value<\/label><input class=\"si-data-input si-value-input\" id=\"si-value-5\" type=\"text\" inputmode=\"decimal\"><\/td><td><label class=\"si-sr\" for=\"si-width-5\">Row 5 effective integration width<\/label><input class=\"si-data-input si-width-input\" id=\"si-width-5\" type=\"text\" inputmode=\"decimal\" disabled><\/td><\/tr>\n          <tr><th class=\"si-row-number\" scope=\"row\">6<\/th><td><label class=\"si-sr\" for=\"si-label-6\">Row 6 identifier<\/label><input class=\"si-data-input\" id=\"si-label-6\" type=\"text\" maxlength=\"80\"><\/td><td><label class=\"si-sr\" for=\"si-value-6\">Row 6 value<\/label><input class=\"si-data-input si-value-input\" id=\"si-value-6\" type=\"text\" inputmode=\"decimal\"><\/td><td><label class=\"si-sr\" for=\"si-width-6\">Row 6 effective integration width<\/label><input class=\"si-data-input si-width-input\" id=\"si-width-6\" type=\"text\" inputmode=\"decimal\" disabled><\/td><\/tr>\n          <tr><th class=\"si-row-number\" scope=\"row\">7<\/th><td><label class=\"si-sr\" for=\"si-label-7\">Row 7 identifier<\/label><input class=\"si-data-input\" id=\"si-label-7\" type=\"text\" maxlength=\"80\"><\/td><td><label class=\"si-sr\" for=\"si-value-7\">Row 7 value<\/label><input class=\"si-data-input si-value-input\" id=\"si-value-7\" type=\"text\" inputmode=\"decimal\"><\/td><td><label class=\"si-sr\" for=\"si-width-7\">Row 7 effective integration width<\/label><input class=\"si-data-input si-width-input\" id=\"si-width-7\" type=\"text\" inputmode=\"decimal\" disabled><\/td><\/tr>\n          <tr><th class=\"si-row-number\" scope=\"row\">8<\/th><td><label class=\"si-sr\" for=\"si-label-8\">Row 8 identifier<\/label><input class=\"si-data-input\" id=\"si-label-8\" type=\"text\" maxlength=\"80\"><\/td><td><label class=\"si-sr\" for=\"si-value-8\">Row 8 value<\/label><input class=\"si-data-input si-value-input\" id=\"si-value-8\" type=\"text\" inputmode=\"decimal\"><\/td><td><label class=\"si-sr\" for=\"si-width-8\">Row 8 effective integration width<\/label><input class=\"si-data-input si-width-input\" id=\"si-width-8\" type=\"text\" inputmode=\"decimal\" disabled><\/td><\/tr>\n        <\/tbody><\/table><\/div>\n      <\/section>\n      <section class=\"si-card si-section\">\n        <fieldset><legend>Evidence gates<\/legend><p>The arithmetic can be shown when a gate is incomplete, but the result must not be reported as a reviewed selected-band RMS until all six are documented.<\/p>\n          <div class=\"si-checks\">\n            <label class=\"si-check\" for=\"si-ev-channel\"><input id=\"si-ev-channel\" type=\"checkbox\"><span><strong>Same channel and quantity.<\/strong> Every row is from the same calibrated channel, point, direction, physical quantity and underlying unit.<\/span><\/label>\n            <label class=\"si-check\" for=\"si-ev-record\"><input id=\"si-ev-record\" type=\"checkbox\"><span><strong>Same record and condition.<\/strong> Rows belong to the same acquisition and operating condition; averaged records are not mixed without a documented method.<\/span><\/label>\n            <label class=\"si-check\" for=\"si-ev-scaling\"><input id=\"si-ev-scaling\" type=\"checkbox\"><span><strong>Scaling identified.<\/strong> The export is the selected RMS\/PSD\/ASD type&mdash;not peak, peak-to-peak, max-hold, ESD or an unknown analyzer magnitude.<\/span><\/label>\n            <label class=\"si-check\" for=\"si-ev-band\"><input id=\"si-ev-band\" type=\"checkbox\"><span><strong>Complete intended band.<\/strong> All relevant lines\/bands between the declared limits are included, with filters, DC and Nyquist treatment recorded.<\/span><\/label>\n            <label class=\"si-check\" for=\"si-ev-overlap\"><input id=\"si-ev-overlap\" type=\"checkbox\"><span><strong>No overlap or selected-peak shortcut.<\/strong> Rows are mutually non-overlapping and do not double-count leakage, sidebands or previously integrated bands.<\/span><\/label>\n            <label class=\"si-check\" for=\"si-ev-window\"><input id=\"si-ev-window\" type=\"checkbox\"><span><strong>Analyzer normalization verified.<\/strong> Window, amplitude convention, density normalization and effective integration widths come from the instrument\/export documentation.<\/span><\/label>\n          <\/div>\n        <\/fieldset>\n        <div class=\"si-actions\"><button class=\"si-primary\" type=\"submit\">Calculate documented inputs<\/button><button class=\"si-secondary\" id=\"si-clear\" type=\"button\">Clear<\/button><\/div>\n      <\/section>\n    <\/form>\n    <section id=\"si-result\" class=\"si-result\" role=\"status\" aria-live=\"polite\">\n      <h2 id=\"si-result-title\">Not calculated<\/h2><p id=\"si-result-summary\"><\/p><ul id=\"si-errors\" class=\"si-errors\"><\/ul>\n      <div id=\"si-values\" class=\"si-values\">\n        <div class=\"si-value\"><span>RMS of entered data<\/span><strong id=\"si-out-rms\">&#8211;<\/strong><\/div>\n        <div class=\"si-value\"><span>Summed mean square<\/span><strong id=\"si-out-ms\">&#8211;<\/strong><\/div>\n        <div class=\"si-value\"><span>Rows used<\/span><strong id=\"si-out-rows\">&#8211;<\/strong><\/div>\n        <div class=\"si-value\"><span>Largest mean-square share<\/span><strong id=\"si-out-largest\">&#8211;<\/strong><\/div>\n        <div class=\"si-value\"><span>Declared intended band<\/span><strong id=\"si-out-band\">&#8211;<\/strong><\/div>\n        <div class=\"si-value\"><span>Input scaling<\/span><strong id=\"si-out-mode\">&#8211;<\/strong><\/div>\n      <\/div>\n    <\/section>\n\n    <section class=\"si-section\">\n      <h2>Equations and dimensional check<\/h2>\n      <p>These are public signal-processing relations, not acceptance formulas issued by ISO. They are valid only for correctly scaled, mutually non-overlapping contributions from the declared measurement.<\/p>\n      <div class=\"si-formula\">Integrated RMS contributions: x_selected,RMS = sqrt( sum( x_i,RMS^2 ) )<\/div>\n      <div class=\"si-formula\">PSD entries: x_selected,RMS = sqrt( sum( G_i * delta_f_i ) )<\/div>\n      <div class=\"si-formula\">ASD entries: x_selected,RMS = sqrt( sum( A_i^2 * delta_f_i ) )<\/div>\n      <p><em>G<\/em><sub>i<\/sub> has underlying-unit squared per hertz, <em>A<\/em><sub>i<\/sub> has underlying-unit per square-root hertz, and delta-f<sub>i<\/sub> is the applicable effective integration width in hertz. Each term therefore has underlying-unit squared; the final square root restores the underlying engineering unit.<\/p>\n      <div class=\"si-boundary\"><strong>Output name:<\/strong> &ldquo;RMS of entered data&rdquo; is intentional. It may be described as a selected-band RMS only when the complete declared band and all evidence gates are satisfied. It is not automatically the broadband overall value used by a machine-specific standard.<\/div>\n      <p><strong>Published behavior cross-check:<\/strong> the Dewesoft FFT Analyzer V26-1 manual states that its RMS marker sums all FFT lines in a selected band. Its example changes the range from 0&ndash;5000 Hz to 0&ndash;3800.05 Hz and the RMS changes from 0.9934 to 0.9902. This demonstrates why the selected band and all lines&mdash;not a few displayed peaks&mdash;matter.<\/p>\n    <\/section>\n\n    <section class=\"si-card si-section\">\n      <h2>Separate time-record crest factor<\/h2>\n      <p>Crest factor requires an absolute instantaneous peak and RMS from the same time record, channel, unit, band and filter. A magnitude-only spectrum does not contain the phase\/time history needed to reconstruct the waveform peak.<\/p>\n      <form id=\"si-cf-form\" novalidate>\n        <div class=\"si-grid\">\n          <div class=\"si-field\"><label for=\"si-cf-case\">Time-record ID<\/label><input id=\"si-cf-case\" type=\"text\" maxlength=\"120\" required><\/div>\n          <div class=\"si-field\"><label for=\"si-cf-unit\">Engineering unit<\/label><input id=\"si-cf-unit\" type=\"text\" maxlength=\"40\" required><\/div>\n          <div class=\"si-field\"><label for=\"si-cf-rms\">Time-record RMS<\/label><input id=\"si-cf-rms\" type=\"text\" inputmode=\"decimal\" required><\/div>\n          <div class=\"si-field\"><label for=\"si-cf-peak\">Largest absolute instantaneous peak<\/label><input id=\"si-cf-peak\" type=\"text\" inputmode=\"decimal\" required><\/div>\n          <div class=\"si-field si-wide\"><label for=\"si-cf-condition\">Band, filter and acquisition note<\/label><textarea id=\"si-cf-condition\" maxlength=\"600\" required><\/textarea><\/div>\n          <label class=\"si-check si-wide\" for=\"si-cf-evidence\"><input id=\"si-cf-evidence\" type=\"checkbox\"><span><strong>Same valid time record.<\/strong> Peak and RMS use the same channel, record, engineering unit, weighting\/filter and time interval, and the acquisition is not clipped.<\/span><\/label>\n        <\/div>\n        <div class=\"si-actions\"><button class=\"si-primary\" type=\"submit\">Calculate crest factor<\/button><button class=\"si-secondary\" id=\"si-cf-clear\" type=\"button\">Clear crest factor<\/button><\/div>\n      <\/form>\n      <section id=\"si-cf-result\" class=\"si-result\" role=\"status\" aria-live=\"polite\"><h3 id=\"si-cf-title\">Not calculated<\/h3><p id=\"si-cf-summary\"><\/p><div class=\"si-values\"><div class=\"si-value\"><span>Crest factor<\/span><strong id=\"si-cf-out\">&#8211;<\/strong><\/div><div class=\"si-value\"><span>Formula<\/span><strong>CF = |peak| \/ RMS<\/strong><\/div><\/div><\/section>\n      <div class=\"si-alert\" style=\"margin-top:18px\"><strong>No diagnostic threshold<\/strong>This worksheet does not label a crest factor &ldquo;normal,&rdquo; identify a bearing fault or set an alarm. Interpretation depends on sensor bandwidth, filtering, operating condition, signal type and a validated diagnostic procedure.<\/div>\n    <\/section>\n\n    <section class=\"si-section\">\n      <h2>Source and standards boundary<\/h2>\n      <div class=\"si-table-wrap\"><table><thead><tr><th>ID<\/th><th>Source<\/th><th>Verified public information<\/th><th>Use on this page<\/th><\/tr><\/thead><tbody>\n        <tr id=\"source-S1\"><td>S1<\/td><td><a href=\"https:\/\/www.iso.org\/standard\/35588.html\" target=\"_blank\" rel=\"noopener\">ISO 18431-1:2005, Edition 1; Cor 1:2009<\/a><\/td><td>Published. Last confirmed in 2019; the official lifecycle shows systematic review\/close of review and &ldquo;to be revised.&rdquo; Its public abstract covers transformations and physical units and warns that signal type must be identified correctly, especially in frequency-domain analysis.<\/td><td>Signal-type and units boundary only; no protected transformation or clause is reproduced.<\/td><\/tr>\n        <tr id=\"source-S2\"><td>S2<\/td><td><a href=\"https:\/\/www.iso.org\/standard\/35589.html\" target=\"_blank\" rel=\"noopener\">ISO 18431-2:2004, Edition 1; Cor 1:2008<\/a><\/td><td>Published. Last confirmed in 2019 and currently shown at stage 90.60 under review. The public abstract covers rectangular, Hanning and flat-top time windows before DFT analysis.<\/td><td>Windowing context only; no protected correction coefficient is inferred.<\/td><\/tr>\n        <tr id=\"source-S3\"><td>S3<\/td><td><a href=\"https:\/\/www.iso.org\/standard\/21831.html\" target=\"_blank\" rel=\"noopener\">ISO 13373-1:2002, Edition 1<\/a><\/td><td>Published and confirmed in 2024. The public scope covers general vibration measurement and data-collection procedures for machinery condition monitoring.<\/td><td>Measurement-record context, not the source of the arithmetic.<\/td><\/tr>\n        <tr id=\"source-S4\"><td>S4<\/td><td><a href=\"https:\/\/www.iso.org\/standard\/68128.html\" target=\"_blank\" rel=\"noopener\">ISO 13373-2:2016, Edition 2<\/a><\/td><td>Published and confirmed in 2021; the official lifecycle currently shows systematic review. Its public scope covers processing, analysis and presentation of vibration data in time and frequency domains.<\/td><td>Processing context, not an ISO acceptance threshold.<\/td><\/tr>\n        <tr id=\"source-S5\"><td>S5<\/td><td><a href=\"https:\/\/downloads.dewesoft.com\/manuals\/dewesoft-fft-analyzer-manual-en.pdf\" target=\"_blank\" rel=\"noopener\">Dewesoft FFT Analyzer Solution User Manual V26-1<\/a><\/td><td>Public full manual: pp. 20&ndash;21 explain window noise bandwidth; pp. 42&ndash;43 distinguish Linear, Power, PSD and ASD units\/scaling; p. 54 states that the RMS marker sums every FFT line in the selected band.<\/td><td>Public implementation evidence for scaling distinctions, effective bandwidth and the published band-RMS behavior.<\/td><\/tr>\n      <\/tbody><\/table><\/div>\n      <div class=\"si-alert\" style=\"margin-top:16px\"><strong>NEEDS_LICENSED_SOURCE<\/strong>The exact normative transformations, window definitions\/corrections and machinery-monitoring procedures in ISO 18431-1, ISO 18431-2 and ISO 13373 are protected. Their official cards verify lifecycle and public scope only. This worksheet does not invent clauses, tolerances, acceptance zones or an ISO &ldquo;overall vibration&rdquo; formula.<\/div>\n    <\/section>\n\n    <section class=\"si-section\">\n      <h2>Corrections made in this audit<\/h2>\n      <details><summary>Selected peaks are no longer called an overall level<\/summary><p>The former calculator accepted ten unlabeled amplitudes and applied RSS without frequencies, bandwidths, spectrum normalization or proof that the intended band was complete. The replacement labels the result as the RMS of entered data and requires measurement identity, scaling, band and processing evidence.<\/p><\/details>\n      <details><summary>RMS, PSD and ASD are separated<\/summary><p>The former page treated any same-unit amplitudes as interchangeable. The replacement has three explicit formulas and requires effective integration widths for density values. Peak, peak-to-peak, max-hold, ESD and unknown analyzer magnitudes are rejected by scope.<\/p><\/details>\n      <details><summary>Peak-to-RMS conversion was removed<\/summary><p>Dividing a peak by the square root of two is valid for a sinusoid, not an arbitrary vibration waveform or peak list. The replacement performs no peak-to-RMS conversion.<\/p><\/details>\n      <details><summary>Crest factor no longer comes from a spectral peak<\/summary><p>The former calculator divided an optional peak by the RSS of selected spectral entries and labeled values above four as a bearing-fault indication. Crest factor is now isolated to a same-record time-domain peak\/RMS pair and has no diagnostic threshold.<\/p><\/details>\n      <details><summary>Input integrity and traceability were rebuilt<\/summary><p>Decimal point and decimal comma are accepted separately. Mixed separators, negative values, incomplete rows, invalid bands, non-finite calculations and density values without bandwidth are rejected. Defaults, presets, auto-calculation, browser history, clipboard export and external formula rendering were removed.<\/p><\/details>\n      <details><summary>ISO claims are bounded to public evidence<\/summary><p>The visible equations are identified as public signal-processing relations rather than ISO acceptance formulas. Official lifecycle cards and the public Dewesoft manual are linked, while protected details remain explicitly NEEDS_LICENSED_SOURCE.<\/p><\/details>\n    <\/section>\n\n    <div class=\"si-footer\">Engineering boundary: this is a traceable arithmetic worksheet, not an analyzer, resampling tool, phase reconstruction, waveform synthesizer, order tracker, octave-band processor, ISO zone evaluator, alarm\/trip setting or machine diagnosis. Verify calibration, acquisition, scaling, bandwidth, window normalization and the applicable machine-specific evaluation standard. Last technical review: 17 July 2026.<\/div>\n  <\/div>\n<\/main>\n<script>\n(function(){\n  'use strict';\n  var root=document.getElementById('vbm-si');if(!root)return;\n  function byId(id){return document.getElementById(id)}\n  function parseDecimal(raw){var s=String(raw).trim();if(!\/^\\+?(?:\\d+(?:[.,]\\d*)?|[.,]\\d+)$\/.test(s)||(\/[.]\/.test(s)&&\/,\/.test(s)))return null;var n=Number(s.replace(',','.'));return Number.isFinite(n)?n:null}\n  function format(n){var a=Math.abs(n);if(n===0)return '0';if(a>=1000000||a<0.0001)return n.toExponential(6);return Number(n.toPrecision(8)).toString()}\n  function setList(id,items){var list=byId(id);while(list.firstChild)list.removeChild(list.firstChild);items.forEach(function(item){var li=document.createElement('li');li.textContent=item;list.appendChild(li)})}\n  function state(box,kind,title,summary){box.className='si-result si-visible si-'+kind;box.querySelector('h2, h3').textContent=title;var p=box.querySelector('p');p.textContent=summary}\n  var form=byId('si-form'),result=byId('si-result'),scaling=byId('si-scaling'),widths=Array.prototype.slice.call(root.querySelectorAll('.si-width-input'));\n  var modeNames={rms:'Integrated RMS contributions',psd:'Power spectral density',asd:'Amplitude spectral density'};\n  function updateMode(){var density=scaling.value==='psd'||scaling.value==='asd';widths.forEach(function(x){x.disabled=!density});var help=byId('si-mode-help');if(scaling.value==='rms')help.textContent='Enter already integrated, mutually non-overlapping RMS line\/band contributions in the underlying unit. Effective-width fields are not used.';else if(scaling.value==='psd')help.textContent='Enter PSD in underlying-unit squared per hertz and the applicable effective integration width in hertz for every row.';else if(scaling.value==='asd')help.textContent='Enter ASD in underlying-unit per square-root hertz and the applicable effective integration width in hertz for every row.';else help.textContent='Select an input scaling. For density modes, enter the effective integration width belonging to each density value; do not assume that displayed line spacing and noise bandwidth are interchangeable.'}\n  function staleMain(){if(result.classList.contains('si-visible')&&!result.classList.contains('si-stale'))state(result,'stale','Result is stale','Inputs or evidence changed. Recalculate before using the displayed values.')}\n  scaling.addEventListener('change',function(){updateMode();staleMain()});form.addEventListener('input',staleMain);form.addEventListener('change',staleMain);updateMode();\n  form.addEventListener('submit',function(event){event.preventDefault();var errors=[],record=byId('si-case').value.trim(),quantity=byId('si-quantity').value.trim(),axis=byId('si-axis').value.trim(),unit=byId('si-unit').value.trim(),start=parseDecimal(byId('si-band-start').value),end=parseDecimal(byId('si-band-end').value),mode=scaling.value,processing=byId('si-processing').value.trim();\n    if(!record)errors.push('Measurement record ID is required.');if(!quantity)errors.push('Measured quantity is required.');if(!axis)errors.push('Point and direction are required.');if(!unit)errors.push('Underlying engineering unit is required.');if(start===null||start<0)errors.push('Band start must be a finite number greater than or equal to zero.');if(end===null||end<=0)errors.push('Band end must be a finite positive number.');if(start!==null&&end!==null&&end<=start)errors.push('Band end must be greater than band start.');if(!mode)errors.push('Select the documented input scaling.');if(!processing)errors.push('Analyzer export and processing record is required.');\n    var terms=[],used=0,positive=false,density=mode==='psd'||mode==='asd';for(var i=1;i<=8;i++){var label=byId('si-label-'+i).value.trim(),valueRaw=byId('si-value-'+i).value.trim(),widthRaw=byId('si-width-'+i).value.trim();if(!label&&!valueRaw&&!widthRaw)continue;if(!valueRaw){errors.push('Row '+i+': value is required for a partially completed row.');continue}var value=parseDecimal(valueRaw);if(value===null||value<0){errors.push('Row '+i+': value must be a finite non-negative decimal.');continue}var width=null;if(density){width=parseDecimal(widthRaw);if(width===null||width<=0){errors.push('Row '+i+': a finite positive effective integration width is required.');continue}}else if(widthRaw){errors.push('Row '+i+': effective width is not used for integrated RMS contributions.');continue}var term=mode==='rms'?value*value:mode==='psd'?value*width:value*value*width;if(!Number.isFinite(term)){errors.push('Row '+i+': the mean-square contribution overflows the numeric range.');continue}terms.push(term);used++;if(term>0)positive=true}\n    if(!used)errors.push('Enter at least one complete data row.');else if(!positive)errors.push('At least one row must have a positive mean-square contribution.');if(errors.length){setList('si-errors',errors);state(result,'error','Cannot calculate','Correct the listed input or traceability errors.');return}\n    var meanSquare=0;terms.forEach(function(x){meanSquare+=x});if(!Number.isFinite(meanSquare)||meanSquare<=0){setList('si-errors',['The summed mean square is outside the finite positive numeric range.']);state(result,'error','Cannot calculate','Reduce the numeric range or verify the exported values.');return}var rms=Math.sqrt(meanSquare),largest=Math.max.apply(null,terms)\/meanSquare*100;if(!Number.isFinite(rms)||!Number.isFinite(largest)){setList('si-errors',['The result is not finite.']);state(result,'error','Cannot calculate','Verify scaling, values and effective widths.');return}\n    byId('si-out-rms').textContent=format(rms)+' '+unit;byId('si-out-ms').textContent=format(meanSquare)+' '+unit+' squared';byId('si-out-rows').textContent=String(used);byId('si-out-largest').textContent=format(largest)+'%';byId('si-out-band').textContent=format(start)+' to '+format(end)+' Hz';byId('si-out-mode').textContent=modeNames[mode];setList('si-errors',[]);var evIds=['si-ev-channel','si-ev-record','si-ev-scaling','si-ev-band','si-ev-overlap','si-ev-window'],done=evIds.filter(function(id){return byId(id).checked}).length;if(done===evIds.length)state(result,'ready','Selected-band arithmetic complete','All six evidence gates are recorded. This is the RMS of the documented entered data; it is not an ISO acceptance judgment or machine diagnosis.');else state(result,'incomplete','Arithmetic complete; evidence incomplete','Only '+done+' of 6 evidence gates are recorded. Do not report this as a reviewed selected-band or machine overall value.');\n  });\n  byId('si-clear').addEventListener('click',function(){form.reset();updateMode();result.className='si-result';setList('si-errors',[]);['si-out-rms','si-out-ms','si-out-rows','si-out-largest','si-out-band','si-out-mode'].forEach(function(id){byId(id).textContent='-'});byId('si-case').focus()});\n  var cfForm=byId('si-cf-form'),cfResult=byId('si-cf-result');function staleCf(){if(cfResult.classList.contains('si-visible')&&!cfResult.classList.contains('si-stale'))state(cfResult,'stale','Crest-factor result is stale','Inputs or evidence changed. Recalculate before using the displayed value.')}cfForm.addEventListener('input',staleCf);cfForm.addEventListener('change',staleCf);\n  cfForm.addEventListener('submit',function(event){event.preventDefault();var errors=[],record=byId('si-cf-case').value.trim(),unit=byId('si-cf-unit').value.trim(),rms=parseDecimal(byId('si-cf-rms').value),peak=parseDecimal(byId('si-cf-peak').value),condition=byId('si-cf-condition').value.trim();if(!record)errors.push('Time-record ID is required.');if(!unit)errors.push('Engineering unit is required.');if(rms===null||rms<=0)errors.push('Time-record RMS must be finite and positive.');if(peak===null||peak<0)errors.push('Absolute peak must be finite and non-negative.');if(rms!==null&&peak!==null&&rms>0&&peak<rms)errors.push('Absolute peak cannot be less than RMS for the same record.');if(!condition)errors.push('Band, filter and acquisition note is required.');if(errors.length){state(cfResult,'error','Cannot calculate crest factor',errors.join(' '));return}var cf=peak\/rms;if(!Number.isFinite(cf)){state(cfResult,'error','Cannot calculate crest factor','The ratio is outside the finite numeric range.');return}byId('si-cf-out').textContent=format(cf);if(byId('si-cf-evidence').checked)state(cfResult,'ready','Crest factor calculated','Same-record evidence is recorded. No diagnostic condition or alarm threshold is assigned.');else state(cfResult,'incomplete','Crest factor arithmetic only','Same-record evidence is incomplete. Do not interpret or report this ratio as a reviewed crest factor.');});\n  byId('si-cf-clear').addEventListener('click',function(){cfForm.reset();cfResult.className='si-result';byId('si-cf-out').textContent='-';byId('si-cf-case').focus()});\n})();\n<\/script>\n\n","protected":false},"excerpt":{"rendered":"<p>Combine documented non-overlapping RMS contributions or integrate PSD\/ASD values over explicit effective bandwidths. Not an ISO acceptance decision or diagnosis.<\/p>","protected":false},"featured_media":0,"template":"","meta":{"ai_generated_summary":"","footnotes":""},"categories":[],"tags":[],"class_list":["post-100293","calculator","type-calculator","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/vibromera.eu\/uk\/wp-json\/wp\/v2\/calculator\/100293","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/vibromera.eu\/uk\/wp-json\/wp\/v2\/calculator"}],"about":[{"href":"https:\/\/vibromera.eu\/uk\/wp-json\/wp\/v2\/types\/calculator"}],"version-history":[{"count":3,"href":"https:\/\/vibromera.eu\/uk\/wp-json\/wp\/v2\/calculator\/100293\/revisions"}],"predecessor-version":[{"id":102642,"href":"https:\/\/vibromera.eu\/uk\/wp-json\/wp\/v2\/calculator\/100293\/revisions\/102642"}],"wp:attachment":[{"href":"https:\/\/vibromera.eu\/uk\/wp-json\/wp\/v2\/media?parent=100293"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/vibromera.eu\/uk\/wp-json\/wp\/v2\/categories?post=100293"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/vibromera.eu\/uk\/wp-json\/wp\/v2\/tags?post=100293"}],"curies":[{"name":"\u0412\u041f","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}