{"id":100074,"date":"2026-02-15T20:15:11","date_gmt":"2026-02-15T20:15:11","guid":{"rendered":"https:\/\/vibromera.eu\/?post_type=calculator&#038;p=100074"},"modified":"2026-07-12T01:18:00","modified_gmt":"2026-07-12T01:18:00","slug":"density-mass-volume","status":"publish","type":"calculator","link":"https:\/\/vibromera.eu\/fa\/calculators\/density-mass-volume\/","title":{"rendered":"\u0686\u06af\u0627\u0644\u06cc\u060c \u062c\u0631\u0645 \u0648 \u062d\u062c\u0645 | \u062a\u0628\u062f\u06cc\u0644 \u062f\u0642\u06cc\u0642 \u0648\u0627\u062d\u062f"},"content":{"rendered":"\r\n<script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"WebApplication\",\"name\":\"Density, Mass and Volume Arithmetic\",\"description\":\"Solve rho=m\/V in metric or international-foot\/pound units with exact unit conversions and optional geometric volume from traceable dimensions.\",\"url\":\"https:\/\/vibromera.eu\/calculators\/density-mass-volume\/\",\"applicationCategory\":\"Engineering Calculator\",\"operatingSystem\":\"Any\",\"offers\":{\"@type\":\"Offer\",\"price\":\"0\",\"priceCurrency\":\"EUR\"},\"creator\":{\"@type\":\"Organization\",\"name\":\"Vibromera\",\"url\":\"https:\/\/vibromera.eu\/\"},\"dateModified\":\"2026-07-12\",\"inLanguage\":\"en\",\"isAccessibleForFree\":true}<\/script>\r\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\":\"Density, mass and volume\",\"item\":\"https:\/\/vibromera.eu\/calculators\/density-mass-volume\/\"}]}<\/script>\r\n<link rel=\"preconnect\" href=\"https:\/\/fonts.googleapis.com\">\r\n<style>\r\n:root{--vc-bg:#f4f1ec;--vc-surface:#fff;--vc-surface-alt:#f8f6f2;--vc-ink:#1a1a1a;--vc-ink-secondary:#5a5650;--vc-ink-muted:#8a857e;--vc-accent:#c85a2a;--vc-accent-hover:#b04d22;--vc-accent-light:#fdf0ea;--vc-blue:#2a5c8c;--vc-blue-light:#eaf1f8;--vc-green:#2a7a4b;--vc-green-light:#eaf8ef;--vc-yellow:#a67c00;--vc-yellow-light:#fef9e8;--vc-border:#d9d4cc;--vc-border-light:#e8e4dd;--vc-shadow:0 1px 3px rgba(26,26,26,.06),0 4px 12px rgba(26,26,26,.04);--vc-radius:8px;--vc-radius-lg:12px;--vc-font:'DM Sans',-apple-system,BlinkMacSystemFont,'Segoe UI',sans-serif;--vc-mono:'JetBrains Mono',Consolas,Monaco,monospace;--vc-display:'Fraunces',Georgia,serif}\r\n.vc-calculator{font-family:var(--vc-font);font-size:15px;line-height:1.65;color:var(--vc-ink);max-width:960px;margin:0 auto;padding:20px 16px 40px;-webkit-font-smoothing:antialiased}\r\n.vc-calculator *,.vc-calculator *::before,.vc-calculator *::after{box-sizing:border-box}\r\n.vc-header{text-align:center;padding:48px 24px 40px;position:relative}\r\n.vc-header::after{content:'';position:absolute;bottom:0;left:50%;transform:translateX(-50%);width:80px;height:3px;background:var(--vc-accent);border-radius:2px}\r\n.vc-header-eyebrow{font-family:var(--vc-mono);font-size:11px;font-weight:500;letter-spacing:.15em;text-transform:uppercase;color:var(--vc-accent);margin:0 0 12px}\r\n.vc-header-title{font-family:var(--vc-display);font-size:clamp(24px,4vw,36px);font-weight:800;line-height:1.15;color:var(--vc-ink);margin:0 0 16px;letter-spacing:-.02em}\r\n.vc-header-subtitle{font-size:15px;color:var(--vc-ink-secondary);margin:0 auto 20px;max-width:600px}\r\n.vc-badges{display:inline-flex;gap:8px;flex-wrap:wrap;justify-content:center}\r\n.vc-badge{font-family:var(--vc-mono);font-size:11px;font-weight:500;padding:4px 10px;border-radius:4px;background:var(--vc-surface);border:1px solid var(--vc-border);color:var(--vc-ink-secondary)}\r\n.vc-card{background:var(--vc-surface);border:1px solid var(--vc-border);border-radius:var(--vc-radius-lg);box-shadow:var(--vc-shadow);overflow:hidden;margin-top:32px}\r\n.vc-unit-bar{display:flex;border-bottom:1px solid var(--vc-border-light);background:var(--vc-surface-alt)}\r\n.vc-unit-btn{flex:1;padding:12px;border:none;background:transparent;font-family:var(--vc-font);font-size:13px;font-weight:600;color:var(--vc-ink-muted);cursor:pointer;transition:all .2s;position:relative}\r\n.vc-unit-btn:hover{color:var(--vc-ink-secondary);background:rgba(200,90,42,.04)}\r\n.vc-unit-btn.vc-active{color:var(--vc-accent);background:var(--vc-surface)}\r\n.vc-unit-btn.vc-active::after{content:'';position:absolute;bottom:-1px;left:16px;right:16px;height:2px;background:var(--vc-accent);border-radius:1px 1px 0 0}\r\n.vc-form{padding:24px}\r\n.vc-form-grid{display:grid;grid-template-columns:1fr 1fr;gap:18px}\r\n@media(max-width:600px){.vc-form-grid{grid-template-columns:1fr}}\r\n.vc-field{display:flex;flex-direction:column}\r\n.vc-field-full{grid-column:1\/-1}\r\n.vc-label{font-size:12px;font-weight:600;letter-spacing:.04em;text-transform:uppercase;color:var(--vc-ink-secondary);margin-bottom:6px}\r\n.vc-label-hint{font-weight:400;text-transform:none;letter-spacing:0;color:var(--vc-ink-muted);font-size:11px}\r\n.vc-select,.vc-input{width:100%;padding:10px 12px;border:1.5px solid var(--vc-border);border-radius:6px;font-family:var(--vc-font);font-size:14px;color:var(--vc-ink);background:var(--vc-surface);transition:border-color .15s,box-shadow .15s}\r\n.vc-select{padding-right:36px;appearance:none;-webkit-appearance:none;cursor:pointer;background-image:url(\"data:image\/svg+xml,%3Csvg xmlns='http:\/\/www.w3.org\/2000\/svg' width='16' height='16' fill='none' stroke='%235a5650' stroke-width='2'%3E%3Cpath d='M4 6l4 4 4-4'\/%3E%3C\/svg%3E\");background-repeat:no-repeat;background-position:right 10px center}\r\n.vc-select:focus,.vc-input:focus{outline:none;border-color:var(--vc-accent);box-shadow:0 0 0 3px rgba(200,90,42,.12)}\r\n.vc-presets{display:flex;flex-wrap:wrap;gap:8px;margin-top:18px;padding-top:18px;border-top:1px solid var(--vc-border-light)}\r\n.vc-presets-label{font-family:var(--vc-mono);font-size:11px;font-weight:500;letter-spacing:.1em;text-transform:uppercase;color:var(--vc-ink-muted);width:100%;margin-bottom:2px}\r\n.vc-preset-btn{padding:5px 12px;font-family:var(--vc-font);font-size:12px;font-weight:500;border:1px solid var(--vc-border);border-radius:6px;background:var(--vc-surface-alt);color:var(--vc-ink-secondary);cursor:pointer;transition:all .15s}\r\n.vc-preset-btn:hover{border-color:var(--vc-accent);color:var(--vc-accent);background:var(--vc-accent-light)}\r\n.vc-results{border-top:1px solid var(--vc-border-light);background:var(--vc-surface-alt);padding:0;max-height:0;overflow:hidden;transition:max-height .5s cubic-bezier(.4,0,.2,1),padding .3s}\r\n.vc-results.vc-visible{max-height:3000px;padding:24px}\r\n.vc-results-head{display:flex;align-items:center;justify-content:space-between;margin-bottom:18px}\r\n.vc-results-title{font-family:var(--vc-display);font-size:20px;font-weight:700;color:var(--vc-ink);margin:0}\r\n.vc-copy-btn{display:inline-flex;align-items:center;gap:5px;padding:6px 12px;border:1px solid var(--vc-border);border-radius:6px;background:var(--vc-surface);font-family:var(--vc-font);font-size:12px;font-weight:500;color:var(--vc-ink-secondary);cursor:pointer;transition:all .15s}\r\n.vc-copy-btn:hover{border-color:var(--vc-accent);color:var(--vc-accent)}\r\n.vc-copy-btn.vc-copied{background:var(--vc-green-light);border-color:var(--vc-green);color:var(--vc-green)}\r\n.vc-result-grid{display:grid;grid-template-columns:1fr 1fr 1fr;gap:12px;margin-bottom:20px}\r\n@media(max-width:500px){.vc-result-grid{grid-template-columns:1fr}}\r\n.vc-rcard{background:var(--vc-surface);border:1px solid var(--vc-border-light);border-radius:var(--vc-radius);padding:16px;transition:transform .2s}\r\n.vc-rcard:hover{transform:translateY(-1px)}\r\n.vc-rcard-primary{border-color:var(--vc-accent);border-width:2px;background:linear-gradient(135deg,#fdf6f2,var(--vc-surface))}\r\n.vc-rcard-label{font-family:var(--vc-mono);font-size:10px;font-weight:500;letter-spacing:.1em;text-transform:uppercase;color:var(--vc-ink-muted);margin-bottom:4px}\r\n.vc-rcard-value{font-family:var(--vc-mono);font-size:22px;font-weight:600;color:var(--vc-ink);line-height:1.2}\r\n.vc-rcard-primary .vc-rcard-value{font-size:26px;color:var(--vc-accent)}\r\n.vc-rcard-unit{font-size:13px;font-weight:400;color:var(--vc-ink-secondary)}\r\n.vc-section{margin-top:24px;border:1px solid var(--vc-border);border-radius:var(--vc-radius-lg);background:var(--vc-surface);box-shadow:var(--vc-shadow);overflow:hidden}\r\n.vc-section-toggle{width:100%;display:flex;align-items:center;justify-content:space-between;padding:18px 24px;border:none;background:transparent;cursor:pointer;font-family:var(--vc-font);text-align:left;transition:background .15s}\r\n.vc-section-toggle:hover{background:var(--vc-surface-alt)}\r\n.vc-section-toggle-text{display:flex;align-items:center;gap:10px}\r\n.vc-section-icon{font-size:20px;line-height:1}\r\n.vc-section-title{font-family:var(--vc-display);font-size:18px;font-weight:700;color:var(--vc-ink);margin:0}\r\n.vc-section-chevron{width:20px;height:20px;color:var(--vc-ink-muted);transition:transform .3s;flex-shrink:0}\r\n.vc-section.vc-open .vc-section-chevron{transform:rotate(180deg)}\r\n.vc-section-body{max-height:0;overflow:hidden;transition:max-height .4s cubic-bezier(.4,0,.2,1)}\r\n.vc-section.vc-open .vc-section-body{max-height:20000px}\r\n.vc-section-inner{padding:0 24px 24px;border-top:1px solid var(--vc-border-light)}\r\n.vc-theory h3{font-family:var(--vc-display);font-size:17px;font-weight:700;color:var(--vc-ink);margin:28px 0 10px}\r\n.vc-theory h3:first-child{margin-top:20px}\r\n.vc-theory p{font-size:14px;color:var(--vc-ink-secondary);margin:0 0 10px}\r\n.vc-formula-box{background:var(--vc-surface-alt);border:2px solid var(--vc-border);border-radius:6px;padding:14px 20px;font-family:var(--vc-mono);font-size:16px;font-weight:500;text-align:center;margin:14px 0;color:var(--vc-ink);overflow-x:auto}\r\n.vc-info-box{background:var(--vc-blue-light);border-left:3px solid var(--vc-blue);padding:14px 16px;border-radius:0 6px 6px 0;margin:14px 0}\r\n.vc-info-box p{margin:0;font-size:14px;color:var(--vc-ink-secondary)}\r\n.vc-example-box{background:var(--vc-surface-alt);border:1px solid var(--vc-border-light);border-radius:6px;padding:16px;margin:14px 0}\r\n.vc-example-title{font-family:var(--vc-mono);font-size:13px;font-weight:600;color:var(--vc-accent);margin-bottom:8px}\r\n.vc-table{width:100%;border-collapse:collapse;margin:14px 0;font-size:13px}\r\n.vc-table th,.vc-table td{padding:10px 12px;border:1px solid var(--vc-border-light);text-align:left}\r\n.vc-table th{background:var(--vc-surface-alt);font-size:11px;font-weight:600;text-transform:uppercase;letter-spacing:.05em;color:var(--vc-ink-secondary)}\r\n.vc-table tr:nth-child(even){background:var(--vc-surface-alt)}\r\n@media(max-width:600px){.vc-table{font-size:12px}.vc-table th,.vc-table td{padding:8px}}\r\n.vc-faq-list{display:flex;flex-direction:column;gap:8px;margin-top:20px}\r\n.vc-faq-item{border:1px solid var(--vc-border-light);border-radius:6px;overflow:hidden}\r\n.vc-faq-q{width:100%;display:flex;align-items:center;justify-content:space-between;gap:12px;padding:14px 16px;border:none;background:var(--vc-surface-alt);cursor:pointer;font-family:var(--vc-font);font-size:15px;font-weight:600;color:var(--vc-ink);text-align:left;transition:background .15s}\r\n.vc-faq-q:hover{background:#ede9e3}\r\n.vc-faq-chevron{width:16px;height:16px;color:var(--vc-ink-muted);flex-shrink:0;transition:transform .25s}\r\n.vc-faq-item.vc-open .vc-faq-chevron{transform:rotate(180deg)}\r\n.vc-faq-a{max-height:0;overflow:hidden;transition:max-height .35s}\r\n.vc-faq-item.vc-open .vc-faq-a{max-height:1200px}\r\n.vc-faq-a-inner{padding:14px 16px;border-top:1px solid var(--vc-border-light);font-size:14px;color:var(--vc-ink-secondary)}\r\n.vc-faq-a-inner p{margin:0 0 8px}\r\n.vc-faq-a-inner p:last-child{margin-bottom:0}\r\n.vc-faq-a-inner ul{margin:4px 0 8px 16px;padding:0}\r\n.vc-faq-a-inner li{margin-bottom:3px}\r\n.vc-related{display:flex;flex-wrap:wrap;gap:10px;margin-top:16px}\r\n.vc-related-link{display:inline-block;padding:8px 16px;font-family:var(--vc-font);font-size:13px;font-weight:600;background:var(--vc-surface-alt);color:var(--vc-ink-secondary);border:1px solid var(--vc-border);border-radius:var(--vc-radius);text-decoration:none;transition:all .15s}\r\n.vc-related-link:hover{border-color:var(--vc-accent);color:var(--vc-accent);background:var(--vc-accent-light)}\r\n.vc-promo{margin-top:24px;padding:20px;background:linear-gradient(135deg,var(--vc-accent-light),var(--vc-surface));border:1px solid var(--vc-border);border-radius:var(--vc-radius-lg);display:flex;align-items:center;gap:16px}\r\n.vc-promo-text{flex:1;font-size:14px;color:var(--vc-ink-secondary)}\r\n.vc-promo-text strong{color:var(--vc-ink)}\r\n.vc-promo-link{padding:8px 20px;font-size:13px;font-weight:700;color:#fff;background:var(--vc-accent);border-radius:var(--vc-radius);text-decoration:none;white-space:nowrap;transition:background .15s}\r\n.vc-promo-link:hover{background:var(--vc-accent-hover)}\r\n.vc-footer{text-align:center;padding:32px 16px;font-size:13px;color:var(--vc-ink-muted)}\r\n.vc-footer a{color:var(--vc-accent);text-decoration:none}\r\n.vc-footer a:hover{text-decoration:underline}\r\n.vc-footer-links{margin-top:8px;font-size:12px}\r\n.vc-footer-links a{margin:0 8px}\r\n.vc-shape-fields{display:none;margin-top:12px;padding:12px;background:var(--vc-surface-alt);border:1px solid var(--vc-border-light);border-radius:6px}\r\n.vc-shape-fields.vc-active{display:grid;grid-template-columns:1fr 1fr;gap:12px}\r\n@media(max-width:500px){.vc-shape-fields.vc-active{grid-template-columns:1fr}}\r\n@media print{.vc-section-body{max-height:none!important}.vc-faq-a{max-height:none!important}.vc-results{max-height:none!important;padding:24px!important}.vc-copy-btn,.vc-section-chevron,.vc-faq-chevron,.vc-presets,.vc-promo{display:none!important}}\r\n<\/style>\r\n<div class=\"vc-calculator\" id=\"vc-density\"><header class=\"vc-header\"><p class=\"vc-header-eyebrow\">SI-core dimensional arithmetic<\/p><h1 class=\"vc-header-title\">Density, Mass and Volume<\/h1><p class=\"vc-header-subtitle\">Solve \u03c1=m\/V using metric or international-foot\/avoirdupois-pound inputs. Optional geometric volume uses dimensions in millimetres or inches and is converted through one SI calculation core.<\/p><div class=\"vc-badges\"><span class=\"vc-badge\">\u03c1=m\/V<\/span><span class=\"vc-badge\">Exact unit definitions<\/span><span class=\"vc-badge\">Traceable density required<\/span><\/div><\/header>\r\n<div class=\"vc-card\"><form class=\"vc-form\" id=\"vc-form\" autocomplete=\"off\"><div class=\"vc-form-grid\"><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-units\">Input unit system<\/label><select class=\"vc-select\" id=\"vc-units\"><option value=\"metric\">Metric: kg\/m\u00b3, kg, m\u00b3, mm<\/option><option value=\"imperial\">International foot\/pound: lb\/ft\u00b3, lb, ft\u00b3, in<\/option><\/select><\/div><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-solve\">Solve for<\/label><select class=\"vc-select\" id=\"vc-solve\"><option value=\"mass\">Mass m=\u03c1V<\/option><option value=\"volume\">Volume V=m\/\u03c1<\/option><option value=\"density\">Density \u03c1=m\/V<\/option><\/select><\/div><div class=\"vc-field\" id=\"vc-density-row\"><label class=\"vc-label\" for=\"vc-density-in\">Density \u03c1 <span class=\"vc-label-hint\" id=\"vc-density-unit\">(kg\/m\u00b3; &gt;0)<\/span><\/label><input class=\"vc-input\" id=\"vc-density-in\" type=\"text\" inputmode=\"decimal\"><\/div><div class=\"vc-field\" id=\"vc-mass-row\" style=\"display:none\"><label class=\"vc-label\" for=\"vc-mass-in\">Mass m <span class=\"vc-label-hint\" id=\"vc-mass-unit\">(kg; &gt;0)<\/span><\/label><input class=\"vc-input\" id=\"vc-mass-in\" type=\"text\" inputmode=\"decimal\"><\/div><div class=\"vc-field\" id=\"vc-volume-row\"><label class=\"vc-label\" for=\"vc-volume-in\">Volume V <span class=\"vc-label-hint\" id=\"vc-volume-unit\">(m\u00b3; &gt;0)<\/span><\/label><input class=\"vc-input\" id=\"vc-volume-in\" type=\"text\" inputmode=\"decimal\"><\/div><div class=\"vc-field\" id=\"vc-shape-row\"><label class=\"vc-label\" for=\"vc-shape\">Volume source<\/label><select class=\"vc-select\" id=\"vc-shape\"><option value=\"manual\">Enter volume manually<\/option><option value=\"rect\">Rectangular block<\/option><option value=\"cylinder\">Solid cylinder<\/option><option value=\"hollow\">Hollow cylinder<\/option><option value=\"sphere\">Sphere<\/option><option value=\"cone\">Cone<\/option><\/select><\/div><\/div><div class=\"vc-shape-fields\" id=\"vc-shape-dims\"><div class=\"vc-field vc-dim vc-dim-a\"><label class=\"vc-label\" for=\"vc-a\">Length\/side a <span class=\"vc-label-hint vc-dim-unit\">(mm)<\/span><\/label><input class=\"vc-input\" id=\"vc-a\" type=\"text\" inputmode=\"decimal\"><\/div><div class=\"vc-field vc-dim vc-dim-b\"><label class=\"vc-label\" for=\"vc-b\">Width b <span class=\"vc-label-hint vc-dim-unit\">(mm)<\/span><\/label><input class=\"vc-input\" id=\"vc-b\" type=\"text\" inputmode=\"decimal\"><\/div><div class=\"vc-field vc-dim vc-dim-h\"><label class=\"vc-label\" for=\"vc-h\">Height\/length h <span class=\"vc-label-hint vc-dim-unit\">(mm)<\/span><\/label><input class=\"vc-input\" id=\"vc-h\" type=\"text\" inputmode=\"decimal\"><\/div><div class=\"vc-field vc-dim vc-dim-r\"><label class=\"vc-label\" for=\"vc-r\">Outer radius R <span class=\"vc-label-hint vc-dim-unit\">(mm)<\/span><\/label><input class=\"vc-input\" id=\"vc-r\" type=\"text\" inputmode=\"decimal\"><\/div><div class=\"vc-field vc-dim vc-dim-ri\"><label class=\"vc-label\" for=\"vc-ri\">Inner radius r <span class=\"vc-label-hint vc-dim-unit\">(mm)<\/span><\/label><input class=\"vc-input\" id=\"vc-ri\" type=\"text\" inputmode=\"decimal\"><\/div><\/div><div style=\"padding:0 24px 24px\"><div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-source\">Density or measurement source, material condition\/temperature and dimension basis<\/label><input class=\"vc-input\" id=\"vc-source\" type=\"text\" maxlength=\"300\"><\/div><p id=\"vc-error\" role=\"alert\" style=\"margin:.75rem 0 0;color:#b42318\"><\/p><div class=\"vc-warning-box\"><p style=\"margin:0\"><strong>Data gate:<\/strong> density depends on composition, porosity, moisture, temperature and pressure. Enter a value traceable to the actual batch\/specification or measurement. No generic material preset is selected by this calculator.<\/p><\/div><\/div><\/form><div class=\"vc-results\" id=\"vc-results\"><div class=\"vc-results-head\"><h2 class=\"vc-results-title\">Physical result<\/h2><button type=\"button\" class=\"vc-copy-btn\" id=\"vc-copy-btn\">Copy<\/button><\/div><div class=\"vc-result-grid\"><div class=\"vc-rcard vc-rcard-primary\"><div class=\"vc-rcard-label\">Density<\/div><div class=\"vc-rcard-value\" id=\"vc-r-density\">\u2014<\/div><\/div><div class=\"vc-rcard vc-rcard-primary\"><div class=\"vc-rcard-label\">Mass<\/div><div class=\"vc-rcard-value\" id=\"vc-r-mass\">\u2014<\/div><\/div><div class=\"vc-rcard vc-rcard-primary\"><div class=\"vc-rcard-label\">Volume<\/div><div class=\"vc-rcard-value\" id=\"vc-r-volume\">\u2014<\/div><\/div><div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Density conversions<\/div><div class=\"vc-rcard-value\" id=\"vc-r-density-alt\">\u2014<\/div><\/div><div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Mass conversion<\/div><div class=\"vc-rcard-value\" id=\"vc-r-mass-alt\">\u2014<\/div><\/div><div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Volume conversions<\/div><div class=\"vc-rcard-value\" id=\"vc-r-volume-alt\">\u2014<\/div><\/div><\/div><p id=\"vc-r-note\" style=\"margin:0;color:var(--vc-ink-secondary)\"><\/p><\/div><\/div>\r\n<div class=\"vc-section vc-open\"><button type=\"button\" class=\"vc-section-toggle\" aria-expanded=\"true\"><span class=\"vc-section-toggle-text\"><span class=\"vc-section-icon\">\ud83d\udcd8<\/span><span class=\"vc-section-title\">Equations, geometry and exact conversions<\/span><\/span><\/button><div class=\"vc-section-body\"><div class=\"vc-section-inner vc-theory\"><div class=\"vc-formula-box\">\u03c1=m\/V; &nbsp; m=\u03c1V; &nbsp; V=m\/\u03c1<\/div><div class=\"vc-formula-box\">V<sub>rect<\/sub>=abh; &nbsp; V<sub>cyl<\/sub>=\u03c0R\u00b2h; &nbsp; V<sub>hollow<\/sub>=\u03c0(R\u00b2\u2212r\u00b2)h<\/div><div class=\"vc-formula-box\">V<sub>sphere<\/sub>=4\u03c0R\u00b3\/3; &nbsp; V<sub>cone<\/sub>=\u03c0R\u00b2h\/3<\/div><p>The <a href=\"https:\/\/www.bipm.org\/en\/publications\/si-brochure\/\" target=\"_blank\" rel=\"noopener\">BIPM SI Brochure, ninth edition updated in 2026<\/a> identifies kg\/m\u00b3 as the coherent SI unit of mass density. <a href=\"https:\/\/www.nist.gov\/glossary-term\/21726\" target=\"_blank\" rel=\"noopener\">NIST defines density<\/a> as mass per unit volume and notes that a substance density is normally stated with conditions.<\/p><p><a href=\"https:\/\/www.nist.gov\/pml\/special-publication-811\/nist-guide-si-appendix-b-conversion-factors\" target=\"_blank\" rel=\"noopener\">NIST SP 811 conversion guidance<\/a> uses the international foot 1 ft=0.3048 m exactly and avoirdupois pound 1 lb=0.45359237 kg exactly. Therefore 1 ft\u00b3=0.028316846592 m\u00b3 and 1 lb\/ft\u00b3=16.01846337396 kg\/m\u00b3. Shape equations are general geometric identities, not ISO formulas.<\/p><div class=\"vc-warning-box\"><p style=\"margin:0\"><strong>Removed claims:<\/strong> the former material table was unsourced and internally inconsistent (PTFE appeared as both 1300 and 2200 kg\/m\u00b3). The water-buoyancy\/floating decision used full object volume even for partial immersion and has been removed. Kilograms, pounds and tonnes are mass units\u2014not weight-force units.<\/p><\/div><\/div><\/div><\/div><footer class=\"vc-footer\"><p>\u00a9 2024\u20132026 <a href=\"https:\/\/vibromera.eu\/\">Vibromera<\/a><\/p><p>SI-core mass-density arithmetic with exact international-foot\/pound conversions. Scientific review: July 2026.<\/p><\/footer><\/div>\r\n<script>(function(){'use strict';var LBKG=0.45359237,FTM=0.3048,FT3=FTM*FTM*FTM,INM=0.0254,LBFT3=LBKG\/FT3,unit='metric';function $(i){return document.getElementById(i)}function raw(v){var s=String(v).trim().replace(\/\\s+\/g,'');if(!\/^[+]?(?:\\d+(?:[.,]\\d*)?|[.,]\\d+)$\/.test(s))return NaN;return Number(s.replace(',','.'))}function pos(v){var x=raw(v);return Number.isFinite(x)&&x>0?x:NaN}function f(x){var y=Math.round(x*1e9)\/1e9;if(Math.abs(x-y)<=2e-12*Math.max(1,Math.abs(x)))x=y;return Number(x.toPrecision(12)).toString()}function put(id,x){if(Number.isFinite(x))$(id).value=Number(x.toPrecision(15)).toString()}function clearResult(){['vc-r-density','vc-r-mass','vc-r-volume','vc-r-density-alt','vc-r-mass-alt','vc-r-volume-alt'].forEach(function(id){$(id).textContent='\u2014'});$('vc-r-note').textContent=''}function convertInputs(next){if(next===unit)return;var toImp=next==='imperial',map=[['vc-density-in',toImp?1\/LBFT3:LBFT3],['vc-mass-in',toImp?1\/LBKG:LBKG],['vc-volume-in',toImp?1\/FT3:FT3]];map.forEach(function(q){var x=raw($(q[0]).value);if(Number.isFinite(x))put(q[0],x*q[1])});['vc-a','vc-b','vc-h','vc-r','vc-ri'].forEach(function(id){var x=raw($(id).value);if(Number.isFinite(x))put(id,x*(toImp?1\/25.4:25.4))});unit=next}function req(shape){return shape==='rect'?['a','b','h']:shape==='cylinder'||shape==='cone'?['r','h']:shape==='hollow'?['r','ri','h']:shape==='sphere'?['r']:[]}function shapeVol(){var shape=$('vc-shape').value,fac=unit==='metric'?0.001:INM,o={};for(var id of req(shape)){o[id]=pos($('vc-'+id).value);if(!Number.isFinite(o[id]))return NaN}if(shape==='rect')return o.a*o.b*o.h*fac*fac*fac;if(shape==='cylinder')return Math.PI*(o.r*fac)**2*(o.h*fac);if(shape==='hollow')return o.r>o.ri?Math.PI*((o.r*fac)**2-(o.ri*fac)**2)*(o.h*fac):NaN;if(shape==='sphere')return 4*Math.PI*(o.r*fac)**3\/3;if(shape==='cone')return Math.PI*(o.r*fac)**2*(o.h*fac)\/3;return NaN}function toggle(){var solve=$('vc-solve').value,shape=$('vc-shape').value;if(solve==='volume'){shape='manual';$('vc-shape').value='manual';$('vc-shape').disabled=true}else $('vc-shape').disabled=false;$('vc-density-row').style.display=solve==='density'?'none':'flex';$('vc-mass-row').style.display=solve==='mass'?'none':'flex';$('vc-volume-row').style.display=solve==='volume'?'none':'flex';$('vc-shape-row').style.display=solve==='volume'?'none':'flex';var active=shape!=='manual'&&solve!=='volume';$('vc-shape-dims').classList.toggle('vc-active',active);document.querySelectorAll('.vc-dim').forEach(function(x){x.style.display='none'});if(active)req(shape).forEach(function(id){document.querySelector('.vc-dim-'+id).style.display='flex'});$('vc-volume-in').readOnly=active;$('vc-density-unit').textContent=unit==='metric'?'(kg\/m\u00b3; >0)':'(lb\/ft\u00b3; >0)';$('vc-mass-unit').textContent=unit==='metric'?'(kg; >0)':'(lb; >0)';$('vc-volume-unit').textContent=unit==='metric'?'(m\u00b3; >0)':'(ft\u00b3; >0)';document.querySelectorAll('.vc-dim-unit').forEach(function(x){x.textContent=unit==='metric'?'(mm)':'(in)'})}function calc(){toggle();var solve=$('vc-solve').value,shape=$('vc-shape').value,source=$('vc-source').value.trim(),rho=pos($('vc-density-in').value),m=pos($('vc-mass-in').value),v=shape==='manual'?pos($('vc-volume-in').value):shapeVol();if(shape!=='manual'&&Number.isFinite(v))put('vc-volume-in',unit==='metric'?v:v\/FT3);if(unit==='imperial'){if(Number.isFinite(rho))rho*=LBFT3;if(Number.isFinite(m))m*=LBKG;if(shape==='manual'&&Number.isFinite(v))v*=FT3}var bad=solve==='mass'?(!Number.isFinite(rho)||!Number.isFinite(v)):solve==='volume'?(!Number.isFinite(rho)||!Number.isFinite(m)):(!Number.isFinite(m)||!Number.isFinite(v));if(!bad){if(solve==='mass')m=rho*v;else if(solve==='volume')v=m\/rho;else rho=m\/v}var any=Array.from(document.querySelectorAll('#vc-form input')).some(function(x){return x.value.trim()});if(bad||!source){$('vc-error').textContent=any?'Enter all required positive values,valid shape dimensions,and a traceable data\/measurement basis.':'';clearResult();$('vc-results').classList.remove('vc-visible');return}$('vc-error').textContent='';$('vc-r-density').textContent=f(rho)+' kg\/m\u00b3';$('vc-r-mass').textContent=f(m)+' kg';$('vc-r-volume').textContent=f(v)+' m\u00b3';$('vc-r-density-alt').textContent=f(rho\/1000)+' g\/cm\u00b3 | '+f(rho\/LBFT3)+' lb\/ft\u00b3';$('vc-r-mass-alt').textContent=f(m\/LBKG)+' lb';$('vc-r-volume-alt').textContent=f(v*1000)+' L | '+f(v\/FT3)+' ft\u00b3';$('vc-r-note').textContent='Basis: '+source+' | Density and dimensions are treated as supplied measurement data.';$('vc-results').classList.add('vc-visible');var u=new URL(location),vals={unit_system:unit,solve_for:solve,volume_source:shape,data_basis:source},map={density:'vc-density-in',mass:'vc-mass-in',volume:'vc-volume-in',dim_a:'vc-a',dim_b:'vc-b',dim_h:'vc-h',outer_radius:'vc-r',inner_radius:'vc-ri'},rel=[];if(solve!=='density')rel.push('density');if(solve!=='mass')rel.push('mass');if(solve!=='volume'&&shape==='manual')rel.push('volume');var dimKey={a:'dim_a',b:'dim_b',h:'dim_h',r:'outer_radius',ri:'inner_radius'};if(solve!=='volume'&&shape!=='manual')req(shape).forEach(function(q){rel.push(dimKey[q])});Object.keys(map).forEach(function(q){u.searchParams.delete(q);if(rel.indexOf(q)>=0){var s=$(map[q]).value.trim();if(s)vals[q]=s.replace(',','.')}});Object.keys(vals).forEach(function(q){u.searchParams.set(q,vals[q])});history.replaceState(null,'',u.toString())}$('vc-units').addEventListener('change',function(){convertInputs(this.value);calc()});$('vc-form').addEventListener('input',calc);$('vc-form').addEventListener('change',function(e){if(e.target.id!=='vc-units')calc()});$('vc-copy-btn').addEventListener('click',function(){if(navigator.clipboard)navigator.clipboard.writeText($('vc-results').innerText)});document.querySelectorAll('.vc-section-toggle').forEach(function(b){b.addEventListener('click',function(){var s=this.closest('.vc-section');s.classList.toggle('vc-open');this.setAttribute('aria-expanded',s.classList.contains('vc-open'))})});var p=new URLSearchParams(location.search),map={unit_system:'vc-units',solve_for:'vc-solve',volume_source:'vc-shape',density:'vc-density-in',mass:'vc-mass-in',volume:'vc-volume-in',dim_a:'vc-a',dim_b:'vc-b',dim_h:'vc-h',outer_radius:'vc-r',inner_radius:'vc-ri',data_basis:'vc-source'};Object.keys(map).forEach(function(q){if(p.has(q))$(map[q]).value=p.get(q)});unit=$('vc-units').value;calc()})();<\/script>\r\n","protected":false},"excerpt":{"rendered":"<p>Solve density, mass or volume through one SI calculation core with exact international-foot\/pound conversions and optional validated geometric volume.<\/p>","protected":false},"featured_media":0,"template":"","meta":{"ai_generated_summary":"","footnotes":""},"categories":[],"tags":[],"class_list":["post-100074","calculator","type-calculator","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/vibromera.eu\/fa\/wp-json\/wp\/v2\/calculator\/100074","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/vibromera.eu\/fa\/wp-json\/wp\/v2\/calculator"}],"about":[{"href":"https:\/\/vibromera.eu\/fa\/wp-json\/wp\/v2\/types\/calculator"}],"version-history":[{"count":6,"href":"https:\/\/vibromera.eu\/fa\/wp-json\/wp\/v2\/calculator\/100074\/revisions"}],"predecessor-version":[{"id":102369,"href":"https:\/\/vibromera.eu\/fa\/wp-json\/wp\/v2\/calculator\/100074\/revisions\/102369"}],"wp:attachment":[{"href":"https:\/\/vibromera.eu\/fa\/wp-json\/wp\/v2\/media?parent=100074"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/vibromera.eu\/fa\/wp-json\/wp\/v2\/categories?post=100074"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/vibromera.eu\/fa\/wp-json\/wp\/v2\/tags?post=100074"}],"curies":[{"name":"\u0648\u0631\u062f\u067e\u0631\u0633","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}