{"id":100170,"date":"2026-02-15T20:22:12","date_gmt":"2026-02-15T20:22:12","guid":{"rendered":"https:\/\/vibromera.eu\/?post_type=calculator&#038;p=100170"},"modified":"2026-07-12T23:43:51","modified_gmt":"2026-07-12T23:43:51","slug":"noise-level-addition","status":"publish","type":"calculator","link":"https:\/\/vibromera.eu\/zh\/calculators\/noise-level-addition\/","title":{"rendered":"Acoustic Level Summation Worksheet | Vibromera"},"content":{"rendered":"\n<script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"WebApplication\",\"name\":\"Acoustic Level Summation Worksheet\",\"description\":\"Sum compatible incoherent sound-pressure levels, independent sound-power levels, or coherent same-frequency pressure levels with documented phases.\",\"url\":\"https:\/\/vibromera.eu\/calculators\/noise-level-addition\/\",\"applicationCategory\":\"EngineeringApplication\",\"operatingSystem\":\"Any\",\"offers\":{\"@type\":\"Offer\",\"price\":\"0\",\"priceCurrency\":\"EUR\"},\"creator\":{\"@type\":\"Organization\",\"name\":\"Vibromera\",\"url\":\"https:\/\/vibromera.eu\/\"},\"dateModified\":\"2026-07-13\",\"inLanguage\":\"en\",\"isAccessibleForFree\":true}<\/script>\n\n<script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"FAQPage\",\"mainEntity\":[{\"@type\":\"Question\",\"name\":\"Can any values expressed in dB be added together?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"No. Inputs must represent the same physical level quantity, reference, frequency weighting or band, time basis and operating condition. Sound-pressure, sound-power, exposure, maximum and equivalent-continuous levels are not interchangeable merely because all use decibels.\"}},{\"@type\":\"Question\",\"name\":\"When is 10 log10 summation valid for sound-pressure levels?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"It is valid for compatible mean-square pressure contributions at the same receiver and time basis when the sources are mutually incoherent or uncorrelated and shared background is not counted repeatedly.\"}},{\"@type\":\"Question\",\"name\":\"How are coherent tones combined?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Same-frequency pressure amplitudes with stable relative phases are combined as complex vectors. Two equal in-phase tones add about 6.0206 dB, while two ideal equal tones 180 degrees apart cancel in the mathematical model.\"}},{\"@type\":\"Question\",\"name\":\"Can combined sound-power level predict receiver sound-pressure level?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"No. Combined sound-power level describes total source emission under the stated independence assumptions. Receiver sound-pressure level additionally depends on directivity, distance, environment and propagation.\"}},{\"@type\":\"Question\",\"name\":\"Does this worksheet determine occupational compliance?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"No. It performs level-domain summation only. Exposure metrics require durations and the applicable framework, and no universal 85 dBA decision line is applied here.\"}}]}<\/script>\n\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\":\"Acoustic Level Summation\",\"item\":\"https:\/\/vibromera.eu\/calculators\/noise-level-addition\/\"}]}<\/script>\n\n<style>\n:root{--ls-bg:#f3f5f6;--ls-card:#fff;--ls-ink:#17212b;--ls-muted:#53616d;--ls-line:#ccd5dc;--ls-soft:#edf3f5;--ls-accent:#176b87;--ls-accent-dark:#0e5268;--ls-ok:#17683c;--ls-warn:#8a4b08;--ls-danger:#a22c2c;--ls-radius:10px;--ls-shadow:0 1px 2px rgba(23,33,43,.05),0 8px 24px 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12px;color:var(--ls-muted)}.ls-formula{margin:15px 0;padding:16px;border:1px solid var(--ls-line);border-radius:7px;background:var(--ls-soft);text-align:center;font:700 clamp(14px,2.8vw,19px)\/1.8 var(--ls-mono);overflow-x:auto}.ls-table-wrap{overflow-x:auto}.ls-table{width:100%;border-collapse:collapse;font-size:14px}.ls-table th,.ls-table td{padding:10px 11px;border:1px solid var(--ls-line);text-align:left;vertical-align:top}.ls-table th{background:var(--ls-soft)}.ls-list{margin:8px 0 0;padding-left:22px;color:var(--ls-muted)}.ls-list li+li{margin-top:7px}.ls-ref{overflow-wrap:anywhere}.ls-ref a{color:var(--ls-accent-dark)}.ls-small{font-size:13px;color:var(--ls-muted)}.ls-faq details{border-top:1px solid var(--ls-line)}.ls-faq details:first-of-type{border-top:0}.ls-faq summary{padding:15px 0;font-weight:700;cursor:pointer}.ls-faq details p{padding:0 0 14px;margin:0}.ls-footer{margin-top:24px;text-align:center;color:var(--ls-muted);font-size:13px}.ls-footer a{color:var(--ls-accent-dark)}@media(max-width:720px){.ls-top-grid,.ls-result-grid{grid-template-columns:1fr}.ls-wide,.ls-result-primary{grid-column:auto}.ls-source{grid-template-columns:1fr}.ls-row-number{grid-column:auto}.ls-header{padding:28px 16px}.ls-card-head,.ls-form,.ls-results,.ls-section{padding-left:16px;padding-right:16px}}@media print{.ls-actions,.ls-error{display:none}.ls-card{box-shadow:none}}\n<\/style>\n\n<main class=\"ls-app\" id=\"ls-app\">\n  <header class=\"ls-header\">\n    <p class=\"ls-kicker\">Level-domain engineering worksheet<\/p>\n    <h1 class=\"ls-title\">Acoustic Level Summation<\/h1>\n    <p class=\"ls-lead\">Choose the physical model before adding decibels: incoherent pressure contributions, independent source sound powers, or coherent same-frequency pressure vectors.<\/p>\n    <div class=\"ls-tags\"><span class=\"ls-tag\">same descriptor<\/span><span class=\"ls-tag\">same reference<\/span><span class=\"ls-tag\">stable log-sum<\/span><span class=\"ls-tag\">optional phase model<\/span><\/div>\n  <\/header>\n\n  <div class=\"ls-notice\"><strong>Compatibility gate:<\/strong> \u201cdB\u201d is only a level unit. Do not mix sound pressure with sound power, dB with dBA, different frequency bands, different time weightings\/averaging intervals, different receiver positions, sequential operating states, or measurements that each contain the same background.<\/div>\n\n  <section class=\"ls-card\" aria-labelledby=\"ls-input-title\">\n    <div class=\"ls-card-head\"><h2 id=\"ls-input-title\">Documented components<\/h2><p>All fields start blank. Use each physical component once; do not count shared background repeatedly.<\/p><\/div>\n    <form class=\"ls-form\" id=\"ls-form\" novalidate>\n      <div class=\"ls-top-grid\">\n        <div>\n          <label class=\"ls-label\" for=\"ls-model\">Summation model<\/label>\n          <select class=\"ls-select\" id=\"ls-model\" aria-describedby=\"ls-model-hint\"><option value=\"\">Select model<\/option><option value=\"incoherent-pressure\">Mutually incoherent sound-pressure contributions<\/option><option value=\"independent-power\">Independent source sound-power levels<\/option><option value=\"coherent-tone\">Coherent same-frequency pressure components<\/option><\/select>\n          <span class=\"ls-hint\" id=\"ls-model-hint\">The selected model changes both the inputs and the equation.<\/span>\n        <\/div>\n        <div>\n          <label class=\"ls-label\" for=\"ls-descriptor\">Exact level descriptor<\/label>\n          <input class=\"ls-input\" id=\"ls-descriptor\" type=\"text\" maxlength=\"100\" autocomplete=\"off\" placeholder=\"e.g. LAeq,15min at receiver R1, or LWA re 1 pW\">\n          <span class=\"ls-hint\">Record quantity, reference, weighting\/band and time basis\u2014not merely \u201cdB\u201d.<\/span>\n        <\/div>\n        <div class=\"ls-wide\">\n          <label class=\"ls-label\" for=\"ls-record\">Measurement\/source and background record<\/label>\n          <input class=\"ls-input\" id=\"ls-record\" type=\"text\" maxlength=\"220\" autocomplete=\"off\" placeholder=\"receiver\/operating state, isolation method, background correction and source record\">\n          <span class=\"ls-hint\">Identify how each component was obtained and how shared background or source interaction was excluded.<\/span>\n        <\/div>\n      <\/div>\n      <p class=\"ls-mode-note\" id=\"ls-mode-note\">Select a model to display its physical prerequisites.<\/p>\n\n      <h3 class=\"ls-source-title\">Components<\/h3>\n      <div class=\"ls-sources\">\n        <div class=\"ls-source\"><div class=\"ls-row-number\">Component 1<\/div><div><label class=\"ls-label\" for=\"ls-name-1\">Source\/component<\/label><input class=\"ls-input\" id=\"ls-name-1\" type=\"text\" maxlength=\"100\" autocomplete=\"off\" placeholder=\"source ID\"><\/div><div><label class=\"ls-label\" for=\"ls-level-1\">Level (dB)<\/label><input class=\"ls-input\" id=\"ls-level-1\" type=\"text\" inputmode=\"decimal\" autocomplete=\"off\" placeholder=\"signed decimal\"><\/div><div id=\"ls-phase-wrap-1\" hidden><label class=\"ls-label\" for=\"ls-phase-1\">Relative phase (\u00b0)<\/label><input class=\"ls-input\" id=\"ls-phase-1\" type=\"text\" inputmode=\"decimal\" autocomplete=\"off\" placeholder=\"degrees\"><\/div><\/div>\n        <div class=\"ls-source\"><div class=\"ls-row-number\">Component 2<\/div><div><label class=\"ls-label\" for=\"ls-name-2\">Source\/component<\/label><input class=\"ls-input\" id=\"ls-name-2\" type=\"text\" maxlength=\"100\" autocomplete=\"off\" placeholder=\"source ID\"><\/div><div><label class=\"ls-label\" for=\"ls-level-2\">Level (dB)<\/label><input class=\"ls-input\" id=\"ls-level-2\" type=\"text\" inputmode=\"decimal\" autocomplete=\"off\" placeholder=\"signed decimal\"><\/div><div id=\"ls-phase-wrap-2\" hidden><label class=\"ls-label\" for=\"ls-phase-2\">Relative phase (\u00b0)<\/label><input class=\"ls-input\" id=\"ls-phase-2\" type=\"text\" inputmode=\"decimal\" autocomplete=\"off\" placeholder=\"degrees\"><\/div><\/div>\n        <div class=\"ls-source\"><div class=\"ls-row-number\">Component 3<\/div><div><label class=\"ls-label\" for=\"ls-name-3\">Source\/component<\/label><input class=\"ls-input\" id=\"ls-name-3\" type=\"text\" maxlength=\"100\" autocomplete=\"off\" placeholder=\"source ID\"><\/div><div><label class=\"ls-label\" for=\"ls-level-3\">Level (dB)<\/label><input class=\"ls-input\" id=\"ls-level-3\" type=\"text\" inputmode=\"decimal\" autocomplete=\"off\" placeholder=\"signed decimal\"><\/div><div id=\"ls-phase-wrap-3\" hidden><label class=\"ls-label\" for=\"ls-phase-3\">Relative phase (\u00b0)<\/label><input class=\"ls-input\" id=\"ls-phase-3\" type=\"text\" inputmode=\"decimal\" autocomplete=\"off\" placeholder=\"degrees\"><\/div><\/div>\n        <div class=\"ls-source\"><div class=\"ls-row-number\">Component 4<\/div><div><label class=\"ls-label\" for=\"ls-name-4\">Source\/component<\/label><input class=\"ls-input\" id=\"ls-name-4\" type=\"text\" maxlength=\"100\" autocomplete=\"off\" placeholder=\"source ID\"><\/div><div><label class=\"ls-label\" for=\"ls-level-4\">Level (dB)<\/label><input class=\"ls-input\" id=\"ls-level-4\" type=\"text\" inputmode=\"decimal\" autocomplete=\"off\" placeholder=\"signed decimal\"><\/div><div id=\"ls-phase-wrap-4\" hidden><label class=\"ls-label\" for=\"ls-phase-4\">Relative phase (\u00b0)<\/label><input class=\"ls-input\" id=\"ls-phase-4\" type=\"text\" inputmode=\"decimal\" autocomplete=\"off\" placeholder=\"degrees\"><\/div><\/div>\n        <div class=\"ls-source\"><div class=\"ls-row-number\">Component 5<\/div><div><label class=\"ls-label\" for=\"ls-name-5\">Source\/component<\/label><input class=\"ls-input\" id=\"ls-name-5\" type=\"text\" maxlength=\"100\" autocomplete=\"off\" placeholder=\"source ID\"><\/div><div><label class=\"ls-label\" for=\"ls-level-5\">Level (dB)<\/label><input class=\"ls-input\" id=\"ls-level-5\" type=\"text\" inputmode=\"decimal\" autocomplete=\"off\" placeholder=\"signed decimal\"><\/div><div id=\"ls-phase-wrap-5\" hidden><label class=\"ls-label\" for=\"ls-phase-5\">Relative phase (\u00b0)<\/label><input class=\"ls-input\" id=\"ls-phase-5\" type=\"text\" inputmode=\"decimal\" autocomplete=\"off\" placeholder=\"degrees\"><\/div><\/div>\n        <div class=\"ls-source\"><div class=\"ls-row-number\">Component 6<\/div><div><label class=\"ls-label\" for=\"ls-name-6\">Source\/component<\/label><input class=\"ls-input\" id=\"ls-name-6\" type=\"text\" maxlength=\"100\" autocomplete=\"off\" placeholder=\"source ID\"><\/div><div><label class=\"ls-label\" for=\"ls-level-6\">Level (dB)<\/label><input class=\"ls-input\" id=\"ls-level-6\" type=\"text\" inputmode=\"decimal\" autocomplete=\"off\" placeholder=\"signed decimal\"><\/div><div id=\"ls-phase-wrap-6\" hidden><label class=\"ls-label\" for=\"ls-phase-6\">Relative phase (\u00b0)<\/label><input class=\"ls-input\" id=\"ls-phase-6\" type=\"text\" inputmode=\"decimal\" autocomplete=\"off\" placeholder=\"degrees\"><\/div><\/div>\n        <div class=\"ls-source\"><div class=\"ls-row-number\">Component 7<\/div><div><label class=\"ls-label\" for=\"ls-name-7\">Source\/component<\/label><input class=\"ls-input\" id=\"ls-name-7\" type=\"text\" maxlength=\"100\" autocomplete=\"off\" placeholder=\"source ID\"><\/div><div><label class=\"ls-label\" for=\"ls-level-7\">Level (dB)<\/label><input class=\"ls-input\" id=\"ls-level-7\" type=\"text\" inputmode=\"decimal\" autocomplete=\"off\" placeholder=\"signed decimal\"><\/div><div id=\"ls-phase-wrap-7\" hidden><label class=\"ls-label\" for=\"ls-phase-7\">Relative phase (\u00b0)<\/label><input class=\"ls-input\" id=\"ls-phase-7\" type=\"text\" inputmode=\"decimal\" autocomplete=\"off\" placeholder=\"degrees\"><\/div><\/div>\n        <div class=\"ls-source\"><div class=\"ls-row-number\">Component 8<\/div><div><label class=\"ls-label\" for=\"ls-name-8\">Source\/component<\/label><input class=\"ls-input\" id=\"ls-name-8\" type=\"text\" maxlength=\"100\" autocomplete=\"off\" placeholder=\"source ID\"><\/div><div><label class=\"ls-label\" for=\"ls-level-8\">Level (dB)<\/label><input class=\"ls-input\" id=\"ls-level-8\" type=\"text\" inputmode=\"decimal\" autocomplete=\"off\" placeholder=\"signed decimal\"><\/div><div id=\"ls-phase-wrap-8\" hidden><label class=\"ls-label\" for=\"ls-phase-8\">Relative phase (\u00b0)<\/label><input class=\"ls-input\" id=\"ls-phase-8\" type=\"text\" inputmode=\"decimal\" autocomplete=\"off\" placeholder=\"degrees\"><\/div><\/div>\n      <\/div>\n\n      <div class=\"ls-check\"><input id=\"ls-basis\" type=\"checkbox\"><label for=\"ls-basis\"><strong>I checked compatibility:<\/strong> all components use the exact recorded descriptor and reference; pressure components refer to the same receiver and simultaneous time basis; shared background is removed or negligible; no source is already contained in another input; and the selected incoherence, independent-power or coherent-tone assumptions are supported.<\/label><\/div>\n      <div class=\"ls-actions\"><button class=\"ls-button\" type=\"submit\">Calculate sum<\/button><button class=\"ls-button ls-button-secondary\" type=\"reset\" id=\"ls-reset\">Clear<\/button><\/div>\n      <p class=\"ls-error\" id=\"ls-error\" role=\"alert\" aria-live=\"polite\"><\/p>\n    <\/form>\n\n    <div class=\"ls-results\" id=\"ls-results\" aria-live=\"polite\" hidden data-json=\"\">\n      <h2>Conditional result<\/h2>\n      <div class=\"ls-result-grid\">\n        <div class=\"ls-result ls-result-primary\"><span class=\"ls-result-label\" id=\"ls-primary-label\">Combined level<\/span><output class=\"ls-result-value\" id=\"ls-primary-value\">\u2014<\/output><\/div>\n        <div class=\"ls-result\"><span class=\"ls-result-label\">Components used<\/span><output class=\"ls-result-value\" id=\"ls-count\">\u2014<\/output><\/div>\n        <div class=\"ls-result\"><span class=\"ls-result-label\">Highest individual level<\/span><output class=\"ls-result-value\" id=\"ls-highest\">\u2014<\/output><\/div>\n        <div class=\"ls-result\"><span class=\"ls-result-label\">Change from highest<\/span><output class=\"ls-result-value\" id=\"ls-change\">\u2014<\/output><\/div>\n        <div class=\"ls-result\"><span class=\"ls-result-label\">Resultant phase<\/span><output class=\"ls-result-value\" id=\"ls-result-phase\">\u2014<\/output><\/div>\n        <div class=\"ls-result\"><span class=\"ls-result-label\">Model<\/span><output class=\"ls-result-value\" id=\"ls-model-output\">\u2014<\/output><\/div>\n      <\/div>\n      <p class=\"ls-summary\" id=\"ls-summary\"><\/p>\n      <ol class=\"ls-breakdown\"><li id=\"ls-row-out-1\" hidden><\/li><li id=\"ls-row-out-2\" hidden><\/li><li id=\"ls-row-out-3\" hidden><\/li><li id=\"ls-row-out-4\" hidden><\/li><li id=\"ls-row-out-5\" hidden><\/li><li id=\"ls-row-out-6\" hidden><\/li><li id=\"ls-row-out-7\" hidden><\/li><li id=\"ls-row-out-8\" hidden><\/li><\/ol>\n      <div class=\"ls-actions\"><button class=\"ls-button ls-button-secondary\" id=\"ls-copy\" type=\"button\" disabled>Copy recorded result<\/button><\/div>\n    <\/div>\n  <\/section>\n\n  <section class=\"ls-card\">\n    <div class=\"ls-section\">\n      <h2>Model 1 \u2014 mutually incoherent pressure contributions<\/h2>\n      <p>For compatible mean-square sound-pressure levels from mutually incoherent simultaneous components at one receiver, the cross terms average to zero:<\/p>\n      <div class=\"ls-formula\">L<sub>\u03a3<\/sub> = 10 log\u2081\u2080[\u03a3 10<sup>L\u1d62\/10<\/sup>]<\/div>\n      <p>Every L\u1d62 must be the same descriptor: for example, all L<sub>Aeq,15min<\/sub> at one receiver over the same interval, or all levels in the same one-third-octave band. Two equal incoherent components add exactly 10 log\u2081\u2080(2) = 3.0103 dB.<\/p>\n    <\/div>\n    <div class=\"ls-section\">\n      <h2>Model 2 \u2014 independent source sound powers<\/h2>\n      <p>Independent acoustic powers add linearly, so compatible sound-power levels use the same 10 log\u2081\u2080 expression:<\/p>\n      <div class=\"ls-formula\">L<sub>W,\u03a3<\/sub> = 10 log\u2081\u2080[\u03a3 10<sup>L<sub>W,i<\/sub>\/10<\/sup>]<\/div>\n      <p>The output remains a sound-power level. It is not a receiver sound-pressure level and does not include directivity, distance, propagation, reflections or source interaction. If operating sources change one another\u2019s emission, separately measured powers are not an independent-source model.<\/p>\n    <\/div>\n    <div class=\"ls-section\">\n      <h2>Model 3 \u2014 coherent same-frequency pressure components<\/h2>\n      <p>For stable coherent tones at the same frequency and receiver, convert each pressure level to a relative amplitude and add complex pressure vectors:<\/p>\n      <div class=\"ls-formula\">p<sub>\u03a3<\/sub>\/p\u2080 = \u03a3 10<sup>L<sub>p,i<\/sub>\/20<\/sup> e<sup>j\u03c6\u1d62<\/sup><br>L<sub>p,\u03a3<\/sub> = 20 log\u2081\u2080|p<sub>\u03a3<\/sub>\/p\u2080|<\/div>\n      <p>Two equal in-phase components add 6.0206 dB; equal quadrature components add 3.0103 dB; ideal equal components 180\u00b0 apart cancel. Real acoustic phase varies with frequency and position, so this mode is not valid for broadband levels, unstable phase, partial coherence or spatial averaging.<\/p>\n    <\/div>\n    <div class=\"ls-section\">\n      <h2>Compatibility and exclusion table<\/h2>\n      <div class=\"ls-table-wrap\"><table class=\"ls-table\"><thead><tr><th>Question<\/th><th>Required answer<\/th><th>If not established<\/th><\/tr><\/thead><tbody><tr><td>Same physical quantity and reference?<\/td><td>Yes: Lp with Lp, or Lw with Lw<\/td><td>Do not sum<\/td><\/tr><tr><td>Same weighting\/band and time descriptor?<\/td><td>Yes<\/td><td>Reprocess the underlying data first<\/td><\/tr><tr><td>Same receiver and simultaneous pressure basis?<\/td><td>Yes for pressure modes<\/td><td>Do not present the result as a receiver total<\/td><\/tr><tr><td>Shared background counted once?<\/td><td>Removed, negligible, or explicitly isolated<\/td><td>Inputs can double-count energy<\/td><\/tr><tr><td>Correlation\/coherence known?<\/td><td>Supported by the selected model<\/td><td>Cross-spectral information is required<\/td><\/tr><tr><td>Occupational exposure decision intended?<\/td><td>No\u2014this is level summation only<\/td><td>Use a duration-based framework-specific exposure assessment<\/td><\/tr><\/tbody><\/table><\/div>\n    <\/div>\n    <div class=\"ls-section\">\n      <h2>Sources and standards boundary<\/h2>\n      <p><strong>Equation classification:<\/strong> general logarithmic level relations derived from linear energy\/power addition or coherent pressure superposition. They are not labelled as an ISO compliance calculation.<\/p>\n      <ul class=\"ls-list ls-ref\">\n        <li><a href=\"https:\/\/www.osha.gov\/otm\/section-3-health-hazards\/chapter-5\" target=\"_blank\" rel=\"noopener noreferrer\">OSHA Technical Manual, Section III, Chapter 5, Appendix B.3<\/a> \u2014 official 10 log\u2081\u2080 summation of compatible pressure, intensity or power levels.<\/li>\n        <li><a href=\"https:\/\/www.cdc.gov\/niosh\/docs\/75-183\/pdfs\/75-183.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">NIOSH Industrial Noise Control Manual<\/a> \u2014 random-noise assumption and simultaneous-source energy addition.<\/li>\n        <li><a href=\"https:\/\/physics.nist.gov\/cuu\/pdf\/sp811.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">NIST Special Publication 811<\/a> \u2014 20 log\u2081\u2080 field-quantity and 10 log\u2081\u2080 power-quantity level definitions and the requirement to state the reference.<\/li>\n        <li><a href=\"https:\/\/physics.bu.edu\/py231\/db3.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">Boston University, The Decibel Scale<\/a> \u2014 public instructional derivation distinguishing coherent amplitude addition from incoherent intensity addition.<\/li>\n        <li><a href=\"https:\/\/www.iso.org\/standard\/64978.html\" target=\"_blank\" rel=\"noopener noreferrer\">ISO 80000-8:2020, Edition 2 + Amendment 1:2025<\/a> \u2014 current names, symbols, definitions and units for acoustical quantities.<\/li>\n        <li><a href=\"https:\/\/webstore.iec.ch\/en\/publication\/5708\" target=\"_blank\" rel=\"noopener noreferrer\">IEC 61672-1:2013, Edition 2<\/a> \u2014 distinguishes frequency-weighted, time-weighted, time-averaged and exposure sound-level measurements.<\/li>\n      <\/ul>\n      <p class=\"ls-small\">Official records checked 13 July 2026. Partial-coherence cross terms, background-correction procedures and closed standard clauses are not guessed here.<\/p>\n    <\/div>\n    <div class=\"ls-section ls-faq\">\n      <h2>Questions that prevent common errors<\/h2>\n      <details><summary>Can I mix dB and dBA?<\/summary><p>No. \u201cdB\u201d alone does not identify the measured quantity or weighting. All inputs must have the same explicitly recorded descriptor.<\/p><\/details>\n      <details><summary>Can I add measurements made with each machine on while the same background remains?<\/summary><p>Not directly. Each reading then contains the background, so adding them counts that energy repeatedly. Use source-only contributions obtained through a justified isolation\/background method, or measure the simultaneous total.<\/p><\/details>\n      <details><summary>Can I add sequential tasks to obtain daily exposure?<\/summary><p>Not with this simultaneous-source worksheet. Sequential exposure periods require duration-weighted energy integration or the formula specified by the governing exposure framework.<\/p><\/details>\n      <details><summary>Why can a coherent result be below every component?<\/summary><p>Coherent pressures can interfere destructively. The result depends on relative phase at the specific receiver and frequency; it is not an energy sum.<\/p><\/details>\n      <details><summary>Is there an 85 dBA hearing-protection line?<\/summary><p>No. A source-level sum is not automatically an eight-hour occupational exposure. OSHA, NIOSH and EU action\/limit quantities differ and require duration and framework-specific assessment.<\/p><\/details>\n    <\/div>\n  <\/section>\n\n  <p class=\"ls-footer\">Level-domain worksheet by <a href=\"https:\/\/vibromera.eu\/\">Vibromera<\/a> \u00b7 conditional on the documented compatibility assumptions.<\/p>\n<\/main>\n\n<script>\n(function(){\n  'use strict';\n  function byId(id){return document.getElementById(id)}\n  var ids=[1,2,3,4,5,6,7,8],form=byId('ls-form'),model=byId('ls-model'),descriptor=byId('ls-descriptor'),record=byId('ls-record'),basis=byId('ls-basis'),error=byId('ls-error'),results=byId('ls-results'),copy=byId('ls-copy'),modeNote=byId('ls-mode-note');\n  function parseDecimal(raw){var s=String(raw).trim().replace(\/\\u2212\/g,'-');if(!\/^[+-]?(?:\\d+(?:[.,]\\d*)?|[.,]\\d+)$\/.test(s))return null;if(s.indexOf('.')!==-1&&s.indexOf(',')!==-1)return null;var n=Number(s.replace(',','.'));return Number.isFinite(n)?n:null}\n  function fixed(n,d){var z=Math.abs(n)<Math.pow(10,-d)\/2?0:n;return z.toFixed(d)}\n  function signed(n){var z=Math.abs(n)<.00000005?0:n;return(z>0?'+':'')+fixed(z,4)+' dB'}\n  function hide(){results.hidden=true;results.dataset.json='';copy.disabled=true}\n  function fail(message,field){hide();error.textContent=message;if(field)field.focus();return false}\n  function updateMode(){var coherent=model.value==='coherent-tone';ids.forEach(function(i){byId('ls-phase-wrap-'+i).hidden=!coherent});if(model.value==='incoherent-pressure')modeNote.textContent='Use compatible simultaneous mean-square pressure levels at one receiver only when sources are mutually incoherent and shared background is not repeated.';else if(model.value==='independent-power')modeNote.textContent='Use compatible independent source sound-power levels. The output remains sound power and does not predict receiver sound pressure.';else if(coherent)modeNote.textContent='Use same-frequency pressure levels at one receiver with stable documented relative phases in degrees.';else modeNote.textContent='Select a model to display its physical prerequisites.'}\n  function collect(){var coherent=model.value==='coherent-tone',out=[];for(var j=0;j<ids.length;j++){var i=ids[j],name=byId('ls-name-'+i).value.trim(),levelRaw=byId('ls-level-'+i).value.trim(),phaseRaw=byId('ls-phase-'+i).value.trim(),started=Boolean(name||levelRaw||(coherent&&phaseRaw));if(!started)continue;if(!name)return{error:'Complete the source\/component record for row '+i+'.',field:byId('ls-name-'+i)};var level=parseDecimal(levelRaw);if(level===null)return{error:'Component '+i+' level must be one finite decimal number without units or extra text.',field:byId('ls-level-'+i)};var item={row:i,name:name,level_db:level};if(coherent){var phase=parseDecimal(phaseRaw);if(phase===null)return{error:'Component '+i+' phase must be one finite decimal number in degrees.',field:byId('ls-phase-'+i)};item.phase_deg=((phase%360)+360)%360}out.push(item)}return{components:out}}\n  function energySum(components){var max=Math.max.apply(null,components.map(function(x){return x.level_db})),sum=0;components.forEach(function(x){x.scaled_power=Math.pow(10,(x.level_db-max)\/10);sum+=x.scaled_power});components.forEach(function(x){x.contribution_percent=100*x.scaled_power\/sum});var total=max+10*Math.log10(sum);return{total:total,max:max,delta:total-max}}\n  function coherentSum(components){var max=Math.max.apply(null,components.map(function(x){return x.level_db})),real=0,imag=0,sumAmp=0;components.forEach(function(x){x.scaled_amplitude=Math.pow(10,(x.level_db-max)\/20);var rad=x.phase_deg*Math.PI\/180;real+=x.scaled_amplitude*Math.cos(rad);imag+=x.scaled_amplitude*Math.sin(rad);sumAmp+=x.scaled_amplitude});var mag=Math.hypot(real,imag),tol=64*Number.EPSILON*sumAmp;if(mag<=tol)return{total:null,max:max,delta:null,resultant_phase_deg:null,cancellation:true,scaled_magnitude:mag,numerical_zero_tolerance:tol};var total=max+20*Math.log10(mag),phase=Math.atan2(imag,real)*180\/Math.PI;if(Math.abs(phase)<1e-12)phase=0;return{total:total,max:max,delta:total-max,resultant_phase_deg:phase,cancellation:false,scaled_magnitude:mag,numerical_zero_tolerance:tol}}\n  function clearRows(){ids.forEach(function(i){var el=byId('ls-row-out-'+i);el.hidden=true;el.textContent=''})}\n  function modelName(value){return value==='incoherent-pressure'?'INCOHERENT PRESSURE':value==='independent-power'?'INDEPENDENT SOUND POWER':'COHERENT TONE'}\n  function render(data){byId('ls-primary-label').textContent='Combined level \u2014 '+descriptor.value.trim();byId('ls-count').textContent=String(data.components.length);byId('ls-highest').textContent=fixed(data.max_level_db,4)+' dB';byId('ls-model-output').textContent=modelName(data.model);var coherent=data.model==='coherent-tone';if(data.cancellation){byId('ls-primary-value').textContent='IDEAL ZERO (\u2212\u221e dB limit)';byId('ls-change').textContent='not finite';byId('ls-result-phase').textContent='undefined';byId('ls-summary').className='ls-summary ls-warning';byId('ls-summary').textContent='The entered coherent vectors cancel to numerical zero in the ideal model. Real residual level depends on phase\/amplitude uncertainty, position, frequency and background.'}else{byId('ls-primary-value').textContent=fixed(data.total_level_db,4)+' dB';byId('ls-change').textContent=signed(data.change_from_highest_db);byId('ls-result-phase').textContent=coherent?fixed(data.resultant_phase_deg,4)+'\u00b0':'not applicable';byId('ls-summary').className='ls-summary';byId('ls-summary').textContent=coherent?'Coherent vector sum at the recorded frequency and receiver; phase or position changes can alter the result.':data.model==='independent-power'?'Independent-power sum; the result is sound power, not receiver sound pressure.':'Incoherent mean-square pressure sum at the recorded receiver and time basis.'}data.components.forEach(function(x){var el=byId('ls-row-out-'+x.row);el.textContent=coherent?'Component '+x.row+' \u2014 '+x.name+': '+fixed(x.level_db,4)+' dB at '+fixed(x.phase_deg,4)+'\u00b0; scaled pressure amplitude '+fixed(x.scaled_amplitude,8)+'.':'Component '+x.row+' \u2014 '+x.name+': '+fixed(x.level_db,4)+' dB; linear-domain contribution '+fixed(x.contribution_percent,6)+'% of the summed quantity.';el.hidden=false})}\n  function calculate(event){if(event)event.preventDefault();error.textContent='';if(!['incoherent-pressure','independent-power','coherent-tone'].includes(model.value))return fail('Select the physical summation model.',model);if(!descriptor.value.trim())return fail('Record the exact level descriptor, reference, weighting\/band and time basis.',descriptor);if(!record.value.trim())return fail('Record the measurement\/source, receiver\/operation and background basis.',record);var collected=collect();if(collected.error)return fail(collected.error,collected.field);if(collected.components.length<2)return fail('Enter at least two complete compatible components.',byId('ls-name-1'));if(!basis.checked)return fail('Confirm the compatibility checklist before calculating.',basis);var calc=model.value==='coherent-tone'?coherentSum(collected.components):energySum(collected.components);if(calc.total!==null&&!Number.isFinite(calc.total))return fail('The entered values exceed the worksheet\u2019s finite numerical range.',byId('ls-level-1'));var data={model:model.value,descriptor:descriptor.value.trim(),record:record.value.trim(),components:collected.components,total_level_db:calc.total,max_level_db:calc.max,change_from_highest_db:calc.delta,resultant_phase_deg:calc.resultant_phase_deg===undefined?null:calc.resultant_phase_deg,cancellation:Boolean(calc.cancellation),numerical_zero_tolerance:calc.numerical_zero_tolerance===undefined?null:calc.numerical_zero_tolerance,occupational_exposure_assessed:false,background_correction_performed:false,partial_coherence_assessed:false};clearRows();render(data);results.dataset.json=JSON.stringify(data);results.hidden=false;copy.disabled=false;return true}\n  form.addEventListener('submit',calculate);form.addEventListener('input',function(){hide();error.textContent=''});form.addEventListener('change',function(){hide();error.textContent='';updateMode()});form.addEventListener('reset',function(){window.setTimeout(function(){hide();clearRows();error.textContent='';updateMode();model.focus()},0)});\n  copy.addEventListener('click',function(){var data=results.dataset.json?JSON.parse(results.dataset.json):null;if(!data)return;var lines=['Acoustic level summation','Model: '+modelName(data.model),'Descriptor: '+data.descriptor,'Record: '+data.record];data.components.forEach(function(x){lines.push('Component '+x.row+': '+x.name+'; 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