{"id":100109,"date":"2026-02-15T20:17:02","date_gmt":"2026-02-15T20:17:02","guid":{"rendered":"https:\/\/vibromera.eu\/?post_type=calculator&#038;p=100109"},"modified":"2026-07-12T08:12:58","modified_gmt":"2026-07-12T08:12:58","slug":"gdt-tolerance-calculator","status":"publish","type":"calculator","link":"https:\/\/vibromera.eu\/fa\/calculators\/gdt-tolerance-calculator\/","title":{"rendered":"\u0628\u0631\u0631\u0633\u06cc \u0647\u0646\u062f\u0633\u0647 \u0627\u0646\u062d\u0631\u0627\u0641 \u0645\u062e\u062a\u0635\u0627\u062a \u062f\u0648 \u0628\u0639\u062f\u06cc"},"content":{"rendered":"\r\n<script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"WebApplication\",\"name\":\"2D Coordinate-Deviation Geometry Check\",\"description\":\"Calculate signed coordinate offsets,radial offset,twice-radial diametral geometry and direction angle from two-dimensional basic and measured coordinates or direct offsets.\",\"url\":\"https:\/\/vibromera.eu\/calculators\/gdt-tolerance-calculator\/\",\"applicationCategory\":\"Engineering Calculator\",\"operatingSystem\":\"Any (Web Browser)\",\"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\":\"FAQPage\",\"mainEntity\":[{\"@type\":\"Question\",\"name\":\"Does twice the radial coordinate offset prove GD&T position conformance?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"No. It is only Euclidean coordinate geometry. Conformance requires the complete drawing indication,correct datum establishment,feature extraction,tolerance-zone definition,material requirements and the governing licensed standard.\"}},{\"@type\":\"Question\",\"name\":\"Can this tool generate a feature control frame?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"No. It intentionally does not generate or interpret ISO or ASME callouts because their syntax,modifiers and datum rules require the exact governing standard and design context.\"}}]}<\/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\":\"2D coordinate-deviation geometry 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.vc-faq-chevron{transform:rotate(180deg)}.vc-faq-a{max-height:0;overflow:hidden;transition:max-height 0.35s}.vc-faq-item.vc-open .vc-faq-a{max-height:1200px}.vc-faq-a-inner{padding:14px 16px;border-top:1px solid var(--vc-border-light);font-size:14px;color:var(--vc-ink-secondary)}.vc-faq-a-inner p{margin:0 0 8px}.vc-faq-a-inner p:last-child{margin-bottom:0}.vc-faq-a-inner ul{margin:4px 0 8px 16px;padding:0}.vc-faq-a-inner li{margin-bottom:3px}\r\n.vc-related{display:flex;flex-wrap:wrap;gap:10px;margin-top:16px}.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 0.15s}.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}.vc-promo-text{flex:1;font-size:14px;color:var(--vc-ink-secondary)}.vc-promo-text strong{color:var(--vc-ink)}.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 0.15s}.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)}.vc-footer a{color:var(--vc-accent);text-decoration:none}.vc-footer a:hover{text-decoration:underline}.vc-footer-links{margin-top:8px;font-size:12px}.vc-footer-links a{margin:0 8px}\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\r\n.vc-form-grid-coord{display:grid;grid-template-columns:repeat(2,minmax(0,1fr));gap:18px}.vc-hidden{display:none!important}.vc-result-note{margin:0;color:var(--vc-ink-secondary);font-size:13px}@media(max-width:600px){.vc-form-grid-coord{grid-template-columns:1fr}}\r\n<\/style>\r\n<div class=\"vc-calculator\" id=\"vc-coordinate-geometry\"><header class=\"vc-header\"><p class=\"vc-header-eyebrow\">Euclidean coordinate arithmetic \u2014 not GD&amp;T acceptance<\/p><h1 class=\"vc-header-title\">2D Coordinate-Deviation Geometry Check<\/h1><p class=\"vc-header-subtitle\">Calculate signed X\/Y offsets,radial offset,twice-radial diametral geometry and direction from documented two-dimensional coordinates. The result does not generate or interpret a feature-control frame.<\/p><div class=\"vc-badges\"><span class=\"vc-badge\">r=hypot(\u0394x,\u0394y)<\/span><span class=\"vc-badge\">D=2r<\/span><span class=\"vc-badge\">No ISO\/ASME conformance decision<\/span><\/div><\/header>\r\n<div class=\"vc-card\"><form class=\"vc-form\" id=\"vc-form\" autocomplete=\"off\"><div class=\"vc-form-grid-coord\">\r\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-mode\">Input basis<\/label><select class=\"vc-select\" id=\"vc-mode\"><option value=\"\">Select\u2026<\/option><option value=\"coordinates\">Basic and measured coordinates<\/option><option value=\"offsets\">Direct coordinate offsets \u0394x,\u0394y<\/option><\/select><\/div>\r\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-unit\">Coordinate unit<\/label><select class=\"vc-select\" id=\"vc-unit\"><option value=\"\">Select\u2026<\/option><option value=\"mm\">mm<\/option><option value=\"um\">\u00b5m<\/option><option value=\"in\">in<\/option><\/select><\/div>\r\n<div class=\"vc-field vc-hidden\" id=\"vc-x0-wrap\"><label class=\"vc-label\" for=\"vc-x0\">Basic X<\/label><input class=\"vc-input\" id=\"vc-x0\" type=\"text\" inputmode=\"decimal\" placeholder=\"e.g. 10\"><\/div>\r\n<div class=\"vc-field vc-hidden\" id=\"vc-y0-wrap\"><label class=\"vc-label\" for=\"vc-y0\">Basic Y<\/label><input class=\"vc-input\" id=\"vc-y0\" type=\"text\" inputmode=\"decimal\" placeholder=\"e.g. 20\"><\/div>\r\n<div class=\"vc-field vc-hidden\" id=\"vc-x-wrap\"><label class=\"vc-label\" for=\"vc-x\">Measured X<\/label><input class=\"vc-input\" id=\"vc-x\" type=\"text\" inputmode=\"decimal\" placeholder=\"e.g. 10.03\"><\/div>\r\n<div class=\"vc-field vc-hidden\" id=\"vc-y-wrap\"><label class=\"vc-label\" for=\"vc-y\">Measured Y<\/label><input class=\"vc-input\" id=\"vc-y\" type=\"text\" inputmode=\"decimal\" placeholder=\"e.g. 19.96\"><\/div>\r\n<div class=\"vc-field vc-hidden\" id=\"vc-dx-wrap\"><label class=\"vc-label\" for=\"vc-dx\">Signed offset \u0394x<\/label><input class=\"vc-input\" id=\"vc-dx\" type=\"text\" inputmode=\"decimal\" placeholder=\"e.g. 0.03\"><\/div>\r\n<div class=\"vc-field vc-hidden\" id=\"vc-dy-wrap\"><label class=\"vc-label\" for=\"vc-dy\">Signed offset \u0394y<\/label><input class=\"vc-input\" id=\"vc-dy\" type=\"text\" inputmode=\"decimal\" placeholder=\"e.g. -0.04\"><\/div>\r\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-source\">Coordinate\/frame provenance<\/label><input class=\"vc-input\" id=\"vc-source\" type=\"text\" placeholder=\"e.g. CMM export in resolved drawing frame,rev 2\"><\/div>\r\n<\/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>Required interpretation boundary:<\/strong> coordinates must already be expressed in the correct documented frame and use the same unit. This tool does not establish or simulate datums,extract a feature,apply MMR\/LMR,projected\/composite\/profile requirements,uncertainty or any drawing default. D=2r is labelled a diametral geometry result only; it is not automatically a tolerance-zone result.<\/p><\/div><\/form>\r\n<div class=\"vc-results\" id=\"vc-results\" aria-live=\"polite\"><div class=\"vc-results-head\"><h2 class=\"vc-results-title\">2D geometry result<\/h2><button type=\"button\" class=\"vc-copy-btn\" id=\"vc-copy-btn\">Copy<\/button><\/div><div class=\"vc-result-grid\">\r\n<div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Signed \u0394x<\/div><div class=\"vc-rcard-value\" id=\"vc-r-dx\">\u2014<\/div><\/div><div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Signed \u0394y<\/div><div class=\"vc-rcard-value\" id=\"vc-r-dy\">\u2014<\/div><\/div><div class=\"vc-rcard vc-rcard-primary\"><div class=\"vc-rcard-label\">Radial coordinate offset r<\/div><div class=\"vc-rcard-value\" id=\"vc-r-r\">\u2014<\/div><\/div><div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Diametral geometry D=2r<\/div><div class=\"vc-rcard-value\" id=\"vc-r-d\">\u2014<\/div><\/div><div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Direction from +X,CCW<\/div><div class=\"vc-rcard-value\" id=\"vc-r-angle\">\u2014<\/div><\/div><div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Radial offset normalized<\/div><div class=\"vc-rcard-value\" id=\"vc-r-rmm\">\u2014<\/div><\/div><div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Diametral geometry normalized<\/div><div class=\"vc-rcard-value\" id=\"vc-r-dmm\">\u2014<\/div><\/div>\r\n<\/div><p class=\"vc-result-note\" id=\"vc-r-note\"><\/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\">Geometry,standards and applicability<\/span><\/span><\/button><div class=\"vc-section-body\"><div class=\"vc-section-inner vc-theory\">\r\n<h3>Implemented arithmetic<\/h3><div class=\"vc-formula-box\">\u0394x=x<sub>measured<\/sub>\u2212x<sub>basic<\/sub><br>\u0394y=y<sub>measured<\/sub>\u2212y<sub>basic<\/sub><br>r=\u221a(\u0394x\u00b2+\u0394y\u00b2)=hypot(\u0394x,\u0394y)<br>D=2r<br>\u03b8=atan2(\u0394y,\u0394x),normalized to0\u00b0\u2264\u03b8&lt;360\u00b0<\/div><p><a href=\"https:\/\/openstax.org\/books\/university-physics-volume-1\/pages\/2-2-coordinate-systems-and-components-of-a-vector\" target=\"_blank\" rel=\"noopener\">OpenStax University Physics,Volume1 \u00a72.2<\/a> gives vector magnitude \u221a(x\u00b2+y\u00b2) and the direction-angle relationship. Unit conversions are exact:1in=25.4mm and1\u00b5m=0.001mm. D is simply twice the Euclidean radius; no standards-based meaning is inferred.<\/p>\r\n<h3>ISO GPS scope checked<\/h3><p><a href=\"https:\/\/www.iso.org\/standard\/66777.html\" target=\"_blank\" rel=\"noopener\">ISO1101:2017,edition4,current\/confirmed2022<\/a> defines the symbol language and interpretation rules for geometrical specification. <a href=\"https:\/\/www.iso.org\/standard\/87855.html\" target=\"_blank\" rel=\"noopener\">ISO5459:2024,edition3<\/a> covers datums and datum systems and explicitly excludes verification operators. <a href=\"https:\/\/www.iso.org\/standard\/74592.html\" target=\"_blank\" rel=\"noopener\">ISO2692:2021,edition4<\/a> defines MMR\/LMR\/RPR and limits their application to specified linear features of size;it is under systematic review in2026.<\/p>\r\n<h3>Do not mix standards<\/h3><p><a href=\"https:\/\/www.asme.org\/codes-standards\/find-codes-standards\/dimensioning-and-tolerancing\/2018\" target=\"_blank\" rel=\"noopener\">ASME Y14.5-2018(R2024)<\/a> separately establishes ASME symbols,rules,definitions,requirements and defaults. ISO GPS and ASME callouts are not interchangeable. Their full texts are licensed;the former generic FCF generator,symbol table,modifier choices and inspection prescriptions were removed rather than reconstructed by guesswork.<\/p>\r\n<h3>No conformance decision<\/h3><p>A valid geometrical conformance assessment can require datum establishment,feature association,zone modifiers,material requirements,filters,measurement strategy and uncertainty. Compare this arithmetic with a drawing only after those operations are defined and executed under the exact governing edition and contract.<\/p>\r\n<\/div><\/div><\/div><footer class=\"vc-footer\"><p>\u00a92024\u20132026 <a href=\"https:\/\/vibromera.eu\/\">Vibromera<\/a><\/p><p>Euclidean coordinate arithmetic only,not a GD&amp;T callout generator or conformance calculation. Scientific review:July2026.<\/p><\/footer><\/div>\r\n<script>(function(){'use strict';function $(id){return document.getElementById(id)}var ids=['vc-r-dx','vc-r-dy','vc-r-r','vc-r-d','vc-r-angle','vc-r-rmm','vc-r-dmm'];function num(raw){var s=String(raw).trim().replace(',','.');return \/^[+-]?(?:\\d+(?:\\.\\d*)?|\\.\\d+)(?:[eE][+-]?\\d+)?$\/.test(s)?Number(s):NaN}function decParts(raw){var s=String(raw).trim().replace(',','.'),m=s.match(\/^([+-]?)(\\d*)(?:\\.(\\d*))?(?:[eE]([+-]?\\d+))?$\/),frac=m[3]||'',digits=(m[2]||'')+frac,n=BigInt((m[1]==='-'?'-':'')+(digits||'0')),scale=frac.length-Number(m[4]||0);return{n:n,scale:scale}}function decSub(a,b){var A=decParts(a),B=decParts(b),s=Math.max(A.scale,B.scale),an=A.n*10n**BigInt(s-A.scale),bn=B.n*10n**BigInt(s-B.scale);return Number(an-bn)*Math.pow(10,-s)}function fmt(x){return Number(x.toPrecision(12)).toString()}function clear(){ids.forEach(function(id){$(id).textContent='\u2014'});$('vc-r-note').textContent='';$('vc-results').classList.remove('vc-visible')}function fields(){var c=$('vc-mode').value==='coordinates',o=$('vc-mode').value==='offsets';['vc-x0-wrap','vc-y0-wrap','vc-x-wrap','vc-y-wrap'].forEach(function(id){$(id).classList.toggle('vc-hidden',!c)});['vc-dx-wrap','vc-dy-wrap'].forEach(function(id){$(id).classList.toggle('vc-hidden',!o)})}function setUrl(){var u=new URL(location),mode=$('vc-mode').value,map={mode:'vc-mode',unit:'vc-unit',x0:'vc-x0',y0:'vc-y0',x:'vc-x',y:'vc-y',dx:'vc-dx',dy:'vc-dy',source:'vc-source'};Object.keys(map).forEach(function(k){var relevant=!['x0','y0','x','y'].includes(k)||mode==='coordinates';relevant=relevant&&(!['dx','dy'].includes(k)||mode==='offsets');var v=relevant?$(map[k]).value.trim():'';if(v)u.searchParams.set(k,v);else u.searchParams.delete(k)});history.replaceState(null,'',u.toString())}function fail(m){clear();$('vc-error').textContent=m}function calc(){fields();setUrl();var mode=$('vc-mode').value,unit=$('vc-unit').value,source=$('vc-source').value.trim(),rawAll=['vc-x0','vc-y0','vc-x','vc-y','vc-dx','vc-dy'].map(function(id){return $(id).value.trim()});if(!mode&&!unit&&!source&&rawAll.every(function(x){return !x})){clear();$('vc-error').textContent='';return}if(!mode||!unit||!source){fail('Select an input basis and unit,and enter coordinate\/frame provenance.');return}var dx,dy,required;if(mode==='coordinates'){required=rawAll.slice(0,4);if(required.some(function(x){return !x})){fail('Enter all four basic and measured coordinates.');return}var x0=num(required[0]),y0=num(required[1]),x=num(required[2]),y=num(required[3]);if(![x0,y0,x,y].every(Number.isFinite)){fail('Every coordinate must be a strict finite number.');return}dx=decSub(required[2],required[0]);dy=decSub(required[3],required[1])}else{required=rawAll.slice(4,6);if(required.some(function(x){return !x})){fail('Enter both signed coordinate offsets.');return}dx=num(required[0]);dy=num(required[1]);if(![dx,dy].every(Number.isFinite)){fail('Both offsets must be strict finite numbers.');return}}var factor=unit==='um'?.001:unit==='in'?25.4:1,label=unit==='um'?'\u00b5m':unit;if(!Number.isFinite(dx)||!Number.isFinite(dy)||Math.abs(dx*factor)>1e100||Math.abs(dy*factor)>1e100){fail('Normalized offsets must have absolute value no greater than10\u00b9\u2070\u2070mm.');return}var r=Math.hypot(dx,dy),D=2*r,rmm=r*factor,Dmm=D*factor;if(![r,D,rmm,Dmm].every(Number.isFinite)){fail('The geometry result exceeds the finite numerical range.');return}var angle=r===0?null:(Math.atan2(dy,dx)*180\/Math.PI+360)%360;$('vc-error').textContent='';$('vc-r-dx').textContent=fmt(dx)+' '+label;$('vc-r-dy').textContent=fmt(dy)+' '+label;$('vc-r-r').textContent=fmt(r)+' '+label;$('vc-r-d').textContent=fmt(D)+' '+label;$('vc-r-angle').textContent=angle===null?'Undefined at zero offset':fmt(angle)+'\u00b0';$('vc-r-rmm').textContent=fmt(rmm)+' mm';$('vc-r-dmm').textContent=fmt(Dmm)+' mm';$('vc-r-note').textContent='Provenance:'+source+' | Input basis:'+mode+' | Euclidean arithmetic only;no tolerance or conformance result.';$('vc-results').classList.add('vc-visible')}$('vc-form').addEventListener('input',calc);$('vc-form').addEventListener('change',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 q=new URLSearchParams(location.search),map={mode:'vc-mode',unit:'vc-unit',x0:'vc-x0',y0:'vc-y0',x:'vc-x',y:'vc-y',dx:'vc-dx',dy:'vc-dy',source:'vc-source'};Object.keys(map).forEach(function(k){if(q.has(k))$(map[k]).value=q.get(k)});calc()})();<\/script>\n\n","protected":false},"excerpt":{"rendered":"<p>Calculate signed coordinate offsets,radial offset,twice-radial diametral geometry and direction from documented 2D coordinates. Not a GD&#038;T conformance result.<\/p>","protected":false},"featured_media":0,"template":"","meta":{"ai_generated_summary":"","footnotes":""},"categories":[],"tags":[],"class_list":["post-100109","calculator","type-calculator","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/vibromera.eu\/fa\/wp-json\/wp\/v2\/calculator\/100109","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":3,"href":"https:\/\/vibromera.eu\/fa\/wp-json\/wp\/v2\/calculator\/100109\/revisions"}],"predecessor-version":[{"id":102417,"href":"https:\/\/vibromera.eu\/fa\/wp-json\/wp\/v2\/calculator\/100109\/revisions\/102417"}],"wp:attachment":[{"href":"https:\/\/vibromera.eu\/fa\/wp-json\/wp\/v2\/media?parent=100109"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/vibromera.eu\/fa\/wp-json\/wp\/v2\/categories?post=100109"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/vibromera.eu\/fa\/wp-json\/wp\/v2\/tags?post=100109"}],"curies":[{"name":"\u0648\u0631\u062f\u067e\u0631\u0633","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}