{"id":100154,"date":"2026-02-15T20:21:20","date_gmt":"2026-02-15T20:21:20","guid":{"rendered":"https:\/\/vibromera.eu\/?post_type=calculator&#038;p=100154"},"modified":"2026-07-12T20:31:52","modified_gmt":"2026-07-12T20:31:52","slug":"metric-thread-dimensions","status":"publish","type":"calculator","link":"https:\/\/vibromera.eu\/fa\/calculators\/metric-thread-dimensions\/","title":{"rendered":"\u0648\u0631\u06a9\u200c\u0634\u06cc\u062a \u0647\u0646\u062f\u0633\u0647 \u0648 \u0645\u0633\u0627\u062d\u062a \u062a\u0646\u0634 \u06af\u0631\u062f\u0627\u06cc \u0645\u062a\u0631\u06cc 60\u00b0"},"content":{"rendered":"\n<script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"WebApplication\",\"name\":\"Metric 60\u00b0 Thread Geometry and Stress-Area Worksheet\",\"description\":\"Calculate a documented 60-degree metric-thread basic-profile model and a separately labelled nominal stress-area screening value without implying tolerance or ISO conformity.\",\"url\":\"https:\/\/vibromera.eu\/calculators\/metric-thread-dimensions\/\",\"applicationCategory\":\"Engineering Reference\",\"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>\n<style>:root{--th:#34598a;--thl:#eaf1fa;--ink:#181817;--sec:#595750;--mut:#817e76;--b:#d8d4cc;--bl:#e9e5dd;--alt:#f8f6f1;--red:#b42318;--yel:#fff8df;--amb:#8a6500;--font:'DM Sans',-apple-system,BlinkMacSystemFont,'Segoe UI',sans-serif}.th-wrap{font-family:var(--font);color:var(--ink);max-width:1080px;margin:0 auto;border:1px solid var(--bl);border-radius:16px;overflow:hidden;background:#fff}.th-wrap *,.th-wrap *:before,.th-wrap *:after{box-sizing:border-box}.th-hero{padding:34px 38px 26px;background:linear-gradient(135deg,#fbfcfe,#eaf1fa)}.th-kicker{text-transform:uppercase;letter-spacing:.1em;font-size:12px;font-weight:800;color:var(--th)}.th-hero h1{font-size:clamp(28px,4vw,44px);line-height:1.08;margin:8px 0 12px}.th-lead{font-size:17px;line-height:1.65;color:var(--sec);max-width:960px}.th-badges{display:flex;flex-wrap:wrap;gap:8px;margin-top:18px}.th-badge{padding:6px 10px;border-radius:99px;background:#fff;border:1px solid var(--b);font-size:12px;font-weight:700}.th-main{padding:30px 38px}.th-panel{border:1px solid var(--b);border-radius:14px;padding:24px}.th-panel h2{font-size:22px;margin:0 0 8px}.th-note{font-size:14px;line-height:1.55;color:var(--sec)}.th-grid{display:grid;grid-template-columns:1fr 1fr;gap:18px;margin-top:20px}.th-field{display:flex;flex-direction:column;gap:7px}.th-wide{grid-column:1\/-1}.th-label{font-size:13px;font-weight:800}.th-input,.th-textarea{width:100%;border:1px solid var(--b);border-radius:9px;background:#fff;color:var(--ink);font:inherit;padding:11px 12px}.th-input:focus,.th-textarea:focus{outline:3px solid #b8cdf0;outline-offset:1px;border-color:var(--th)}.th-textarea{min-height:92px;resize:vertical}.th-help{font-size:12px;line-height:1.45;color:var(--mut)}.th-error{min-height:22px;margin:14px 0 0;color:var(--red);font-size:13px;font-weight:800}.th-results{margin-top:22px;border:1px solid var(--b);border-radius:12px;overflow:hidden}.th-rhead{background:var(--thl);padding:18px 20px}.th-rtitle{font-size:20px;font-weight:900;color:var(--th)}.th-rsub{font-size:13px;color:var(--sec);margin-top:4px}.th-rgrid{display:grid;grid-template-columns:repeat(3,1fr);gap:1px;background:var(--bl)}.th-card{background:#fff;padding:18px}.th-card h3{font-size:12px;text-transform:uppercase;letter-spacing:.06em;color:var(--mut);margin:0 0 8px}.th-val{font-size:20px;font-weight:900;overflow-wrap:anywhere}.th-unit{font-size:12px;color:var(--mut);margin-top:4px}.th-alert{border-left:4px solid var(--amb);background:var(--yel);padding:14px 16px;margin-top:18px;font-size:14px;line-height:1.55}.th-section{border-top:1px solid var(--bl);padding:28px 38px}.th-section h2{font-size:24px;margin:0 0 10px}.th-section h3{font-size:18px;margin:22px 0 8px}.th-section p,.th-section li{font-size:14px;line-height:1.65;color:var(--sec)}.th-table-wrap{overflow-x:auto;border:1px solid var(--b);border-radius:10px}.th-table{width:100%;border-collapse:collapse;min-width:800px}.th-table th,.th-table td{padding:12px 13px;text-align:left;vertical-align:top;border-bottom:1px solid var(--bl);font-size:13px;line-height:1.45}.th-table th{background:var(--alt);font-weight:900}.th-table tr:last-child td{border-bottom:0}.th-code{font-family:ui-monospace,SFMono-Regular,Consolas,monospace}.th-footer{padding:20px 38px;background:var(--alt);font-size:12px;color:var(--mut)}.th-footer a,.th-section a{color:var(--th)}@media(max-width:700px){.th-hero,.th-main,.th-section{padding-left:20px;padding-right:20px}.th-grid,.th-rgrid{grid-template-columns:1fr}.th-wide{grid-column:auto}.th-panel{padding:18px}.th-table{min-width:720px}}<\/style>\n<div class=\"th-wrap\"><header class=\"th-hero\"><div class=\"th-kicker\">Documented d and P \u00b7 basic-profile model \u00b7 separate stress screen<\/div><h1>Metric 60\u00b0 Thread Geometry &amp; Stress-Area Worksheet<\/h1><p class=\"th-lead\">Evaluate an explicitly defined symmetric 60\u00b0 metric-thread model from nominal diameter <em>d<\/em> and pitch <em>P<\/em>. The worksheet does not choose an ISO diameter\u2013pitch combination,derive manufacturing limits or certify a tolerance class.<\/p><div class=\"th-badges\"><span class=\"th-badge\">Starts blank<\/span><span class=\"th-badge\">Decimal point or comma<\/span><span class=\"th-badge\">Basic values\u2014not limits<\/span><span class=\"th-badge\">No automatic strength decision<\/span><\/div><\/header>\n<main class=\"th-main\"><section class=\"th-panel\"><h2>Enter the controlled thread definition<\/h2><p class=\"th-note\">Copy <em>d<\/em> and <em>P<\/em> from the applicable drawing,product standard or licensed thread standard. Both inputs are millimetres. A designation alone is not evidence of tolerance limits.<\/p><form id=\"th-form\" novalidate><div class=\"th-grid\"><div class=\"th-field\"><label class=\"th-label\" for=\"th-d\">Nominal diameter d (mm)<\/label><input class=\"th-input\" id=\"th-d\" inputmode=\"decimal\" autocomplete=\"off\"><span class=\"th-help\">Positive nominal major diameter used by the model.<\/span><\/div><div class=\"th-field\"><label class=\"th-label\" for=\"th-p\">Pitch P (mm)<\/label><input class=\"th-input\" id=\"th-p\" inputmode=\"decimal\" autocomplete=\"off\"><span class=\"th-help\">Axial distance between adjacent thread forms.<\/span><\/div><div class=\"th-field th-wide\"><label class=\"th-label\" for=\"th-source\">Designation,drawing and source record<\/label><textarea class=\"th-textarea\" id=\"th-source\" maxlength=\"1800\" placeholder=\"Thread designation;drawing\/product-standard revision;source of the d\/P combination;intended tolerance class and governing edition if applicable\"><\/textarea><\/div><\/div><p class=\"th-error\" id=\"th-error\" role=\"alert\"><\/p><\/form>\n<section class=\"th-results\" id=\"th-results\" hidden data-json=\"\"><div class=\"th-rhead\"><div class=\"th-rtitle\">Defined-model results<\/div><div class=\"th-rsub\" id=\"th-summary\">\u2014<\/div><\/div><div class=\"th-rgrid\"><article class=\"th-card\"><h3>Fundamental triangle H<\/h3><div class=\"th-val\" id=\"th-r-h\">\u2014<\/div><div class=\"th-unit\">geometric construction height\u2014not actual thread depth<\/div><\/article><article class=\"th-card\"><h3>Basic pitch diameter d\u2082=D\u2082<\/h3><div class=\"th-val\" id=\"th-r-d2\">\u2014<\/div><div class=\"th-unit\">basic value\u2014not a permissible limit<\/div><\/article><article class=\"th-card\"><h3>Basic-profile minor line d\u2081=D\u2081<\/h3><div class=\"th-val\" id=\"th-r-d1\">\u2014<\/div><div class=\"th-unit\">model value\u2014not an actual root limit<\/div><\/article><article class=\"th-card\"><h3>Stress-model diameter d\u209b<\/h3><div class=\"th-val\" id=\"th-r-ds\">\u2014<\/div><div class=\"th-unit\">d\u209b=d\u2081\u2212H\/6;not labelled an actual minor diameter<\/div><\/article><article class=\"th-card\"><h3>Nominal stress-area screen A\u209b*<\/h3><div class=\"th-val\" id=\"th-r-as\">\u2014<\/div><div class=\"th-unit\">arithmetic screen\u2014not load capacity<\/div><\/article><article class=\"th-card\"><h3>Circle area at d\u209b,A\u2083*<\/h3><div class=\"th-val\" id=\"th-r-a3\">\u2014<\/div><div class=\"th-unit\">geometric comparison\u2014not a net measured area<\/div><\/article><\/div><\/section>\n<div class=\"th-alert\"><strong>Decision boundary:<\/strong> basic dimensions are zero-deviation reference geometry,not tolerance limits. Actual external and internal major,pitch and minor diameters depend on tolerance class,coating,root\/crest design and the current applicable product and gauging standards. Do not use these outputs as machining limits,go\/no-go gauge sizes,thread-stripping capacity,proof load,fatigue capacity or an assembly recommendation.<\/div><\/section><\/main>\n<section class=\"th-section\"><h2>Exact model used by the code<\/h2><div class=\"th-table-wrap\"><table class=\"th-table\"><thead><tr><th>Output<\/th><th>Equation<\/th><th>Meaning and boundary<\/th><\/tr><\/thead><tbody><tr><td>fundamental triangle<\/td><td class=\"th-code\">H=\u221a3\u00b7P\/2<\/td><td>Height of the complete 60\u00b0 fundamental triangle;not actual thread height.<\/td><\/tr><tr><td>basic pitch diameter<\/td><td class=\"th-code\">d\u2082=D\u2082=d\u22123H\/4<\/td><td>Basic-profile reference value with no allowance or tolerance.<\/td><\/tr><tr><td>basic-profile minor line<\/td><td class=\"th-code\">d\u2081=D\u2081=d\u22125H\/4<\/td><td>Reference profile line only;external and internal design\/limit profiles differ.<\/td><\/tr><tr><td>stress-model diameter<\/td><td class=\"th-code\">d\u209b=d\u2081\u2212H\/6=d\u221217H\/12<\/td><td>A separately named calculation diameter;the former page misleadingly labelled this as the bolt&#8217;s actual minor diameter d\u2083.<\/td><\/tr><tr><td>nominal stress-area screen<\/td><td class=\"th-code\">A\u209b*=\u03c0[(d\u2082+d\u209b)\/2]\u00b2\/4<\/td><td>Common nominal fastener stress-area arithmetic;not a strength,proof-load,strip or fatigue result.<\/td><\/tr><tr><td>circle at stress diameter<\/td><td class=\"th-code\">A\u2083*=\u03c0d\u209b\u00b2\/4<\/td><td>Geometric circle only;not a tolerance-minimum net section.<\/td><\/tr><\/tbody><\/table><\/div><p>All variables are in millimetres and areas are in mm\u00b2. The code evaluates the equations directly with <span class=\"th-code\">Math.sqrt(3)<\/span> and <span class=\"th-code\">Math.PI<\/span>;it does not use rounded decimal coefficients internally.<\/p><\/section>\n<section class=\"th-section\"><h2>Standard scope and source status<\/h2><p><a href=\"https:\/\/www.iso.org\/standard\/4165.html\" target=\"_blank\" rel=\"noopener\">ISO261:1998<\/a>,Edition2,remains published and was confirmed in2024. Its general plan defines ISO general-purpose metric thread combinations;the public card states that basic dimensions are in ISO724 and tolerances are in ISO965-1.<\/p><p><a href=\"https:\/\/www.iso.org\/standard\/85104.html\" target=\"_blank\" rel=\"noopener\">ISO724:2023<\/a>,Edition3,is the current published basic-dimensions standard. It applies to metric fastening screw threads and refers to design profiles in <a href=\"https:\/\/www.iso.org\/standard\/85107.html\" target=\"_blank\" rel=\"noopener\">ISO68-1:2023<\/a>,Edition2. The former page did not identify these current editions and presented formula outputs as if they were usable tolerance dimensions.<\/p><p>Manufacturing limits require an applicable tolerance class and current licensed data. <a href=\"https:\/\/www.iso.org\/standard\/87889.html\" target=\"_blank\" rel=\"noopener\">ISO965-1:2026<\/a>,Edition5,now supplies tolerance-system principles;selected published limit tables are covered by <a href=\"https:\/\/www.iso.org\/standard\/86908.html\" target=\"_blank\" rel=\"noopener\">ISO965-6:2025<\/a>. This worksheet intentionally does not reproduce their closed tables. Exact table rows,clauses and permissible diameter\u2013pitch combinations remain <strong>NEEDS_LICENSED_SOURCE<\/strong>.<\/p><p><a href=\"https:\/\/www.iso.org\/standard\/60610.html\" target=\"_blank\" rel=\"noopener\">ISO898-1:2013<\/a>,Edition5 with Cor1:2013,was confirmed in2025 and is marked to be revised. Its public scope is restricted to specified carbon\/alloy-steel bolts,screws and studs,thread ranges,temperature and tolerance standards. The public card does not expose the exact stress-area clause;therefore this page labels the calculation non-normative and does not claim ISO898-1 conformity. As a published numerical cross-check,a fastener manufacturer&#8217;s coarse-thread table reports M12 nominal stress area84.3mm\u00b2,matching this worksheet after rounding.<\/p><\/section>\n<section class=\"th-section\"><h2>What was corrected<\/h2><p>The former tool called H \u201cthread height\u201d,called the stress-calculation diameter d\u2083 the bolt minor diameter,and displayed basic values as \u201call key dimensions\u201d without any tolerance class. It also supplied a partial hard-coded diameter\/pitch list under a \u201cfull reference table\u201d label and silently defaulted to M12.<\/p><p>The replacement starts blank,requires the controlled d\/P source,removes presets,the incomplete ISO table,URL state and local history,and rejects partial or nonphysical values. It separates basic-profile geometry from stress-area arithmetic and removes claims that fine pitch universally resists vibration loosening or guarantees greater load capacity.<\/p><\/section>\n<section class=\"th-section\"><h2>Use and interpretation<\/h2><ul><li>Verify the exact diameter\u2013pitch combination and designation in the governing drawing or licensed standard.<\/li><li>For manufacture or inspection,use the specified tolerance class and current limit\/gauging standards\u2014not the basic values shown here.<\/li><li>For bolt strength,use the applicable product\/material standard,actual stress-area table,property class,temperature and failure mode. Larger nominal area alone does not establish joint capacity.<\/li><li>For vibration,self-loosening and preload,assess the complete joint,clamp length,preload,friction,transverse motion and locking method;pitch alone is not a universal pass\/fail criterion.<\/li><\/ul><\/section>\n<footer class=\"th-footer\">\u00a92024\u20132026 <a href=\"https:\/\/vibromera.eu\/\">Vibromera<\/a> \u00b7 Scientific review July2026<\/footer><\/div>\n<script>(function(){'use strict';function $(id){return document.getElementById(id)}function num(s){s=String(s).trim();if(!s||s.includes('.')&&s.includes(',')||!\/^[+-]?(?:\\d+(?:[.,]\\d*)?|[.,]\\d+)(?:[eE][+-]?\\d+)?$\/.test(s))return NaN;var n=Number(s.replace(',','.'));return Number.isFinite(n)&&Math.abs(n)<=1e100?n:NaN}function fmt(n){if(n===0)return'0';var a=Math.abs(n);return a>=1e12||a<1e-8?n.toExponential(9):Number(n.toPrecision(12)).toLocaleString('en-US',{maximumFractionDigits:20})}function clear(){['th-r-h','th-r-d2','th-r-d1','th-r-ds','th-r-as','th-r-a3','th-summary'].forEach(function(id){$(id).textContent='\u2014'});$('th-results').hidden=true;$('th-results').dataset.json=''}function fail(m){clear();$('th-error').textContent=m}function calc(){var dr=$('th-d').value,pr=$('th-p').value,source=$('th-source').value.trim(),started=dr.trim()||pr.trim()||source;if(!started){$('th-error').textContent='';clear();return}if(!source){fail('Document the designation,drawing and source of the nominal diameter and pitch.');return}var d=num(dr),p=num(pr);if(!Number.isFinite(d)||!Number.isFinite(p)){fail('Enter d and P as complete finite numbers;use either decimal point or decimal comma,not both.');return}if(!(d>0&&p>0)){fail('Nominal diameter d and pitch P must both be positive.');return}var H=Math.sqrt(3)*p\/2,d2=d-3*H\/4,d1=d-5*H\/4,ds=d1-H\/6,as=Math.PI*Math.pow((d2+ds)\/2,2)\/4,a3=Math.PI*ds*ds\/4;if(![H,d2,d1,ds,as,a3].every(Number.isFinite)||!(d2>0&&d1>0&&ds>0&&as>0&&a3>0)){fail('The selected d\/P pair does not form positive model diameters or exceeds the supported numerical range.');return}$('th-error').textContent='';$('th-r-h').textContent=fmt(H)+' mm';$('th-r-d2').textContent=fmt(d2)+' mm';$('th-r-d1').textContent=fmt(d1)+' mm';$('th-r-ds').textContent=fmt(ds)+' mm';$('th-r-as').textContent=fmt(as)+' mm\u00b2';$('th-r-a3').textContent=fmt(a3)+' mm\u00b2';$('th-summary').textContent='d='+fmt(d)+' mm;P='+fmt(p)+' mm;basic-profile model plus separate non-normative stress screen.';$('th-results').dataset.json=JSON.stringify({nominal_diameter_mm:d,pitch_mm:p,fundamental_triangle_mm:H,basic_pitch_diameter_mm:d2,basic_profile_minor_line_mm:d1,stress_model_diameter_mm:ds,nominal_stress_area_screen_mm2:as,stress_model_circle_area_mm2:a3});$('th-results').hidden=false}$('th-form').addEventListener('input',calc);$('th-form').addEventListener('change',calc);calc()})();<\/script>\n","protected":false},"excerpt":{"rendered":"<p>\u0645\u062d\u0627\u0633\u0628\u0647\u200c\u06af\u0631 \u0622\u0646\u0644\u0627\u06cc\u0646 \u0631\u0627\u06cc\u06af\u0627\u0646 \u0628\u0631\u0627\u06cc \u0627\u0628\u0639\u0627\u062f \u0631\u0632\u0648\u0647 \u0645\u062a\u0631\u06cc\u06a9 \u0637\u0628\u0642 \u0627\u0633\u062a\u0627\u0646\u062f\u0627\u0631\u062f\u0647\u0627\u06cc ISO 261 \u0648 ISO 724. \u0642\u0637\u0631 \u06af\u0627\u0645\u060c \u0642\u0637\u0631 \u062c\u0632\u0626\u06cc\u060c \u0645\u0633\u0627\u062d\u062a \u062a\u0646\u0634\u060c \u0645\u0633\u0627\u062d\u062a \u0647\u0633\u062a\u0647 \u0631\u0627 \u0628\u0631\u0627\u06cc \u0631\u0632\u0648\u0647\u200c\u0647\u0627\u06cc \u06af\u0627\u0645 \u062f\u0631\u0634\u062a \u0648 \u06af\u0627\u0645 \u0631\u06cc\u0632 M3-M48 \u0628\u062f\u0633\u062a \u0622\u0648\u0631\u06cc\u062f.<\/p>","protected":false},"featured_media":0,"template":"","meta":{"ai_generated_summary":"","footnotes":""},"categories":[],"tags":[],"class_list":["post-100154","calculator","type-calculator","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/vibromera.eu\/fa\/wp-json\/wp\/v2\/calculator\/100154","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":2,"href":"https:\/\/vibromera.eu\/fa\/wp-json\/wp\/v2\/calculator\/100154\/revisions"}],"predecessor-version":[{"id":102490,"href":"https:\/\/vibromera.eu\/fa\/wp-json\/wp\/v2\/calculator\/100154\/revisions\/102490"}],"wp:attachment":[{"href":"https:\/\/vibromera.eu\/fa\/wp-json\/wp\/v2\/media?parent=100154"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/vibromera.eu\/fa\/wp-json\/wp\/v2\/categories?post=100154"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/vibromera.eu\/fa\/wp-json\/wp\/v2\/tags?post=100154"}],"curies":[{"name":"\u0648\u0631\u062f\u067e\u0631\u0633","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}