{"id":100095,"date":"2026-02-15T20:45:18","date_gmt":"2026-02-15T20:45:18","guid":{"rendered":"https:\/\/vibromera.eu\/?post_type=calculator&#038;p=100095"},"modified":"2026-07-12T05:17:00","modified_gmt":"2026-07-12T05:17:00","slug":"flange-bolt-calculator","status":"publish","type":"calculator","link":"https:\/\/vibromera.eu\/lv\/calculators\/flange-bolt-calculator\/","title":{"rendered":"Bolt Circle Geometry &#038; Coordinates | Chord and Hole Spacing"},"content":{"rendered":"\r\n<script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"WebApplication\",\"name\":\"Bolt Circle Geometry and Coordinates Calculator\",\"description\":\"Calculate equal angular pitch,adjacent chord and arc spacing,edge gap,and Cartesian coordinates for equally spaced holes on a bolt circle. No flange load or standards-table lookup.\",\"url\":\"https:\/\/vibromera.eu\/calculators\/flange-bolt-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 this calculator determine flange bolt load or preload?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"No. It calculates only planar geometry for equally spaced hole centres. Pressure rating,bolt load,preload,torque,gasket stress and leak tightness require the applicable joint standard and engineering inputs.\"}},{\"@type\":\"Question\",\"name\":\"How is adjacent bolt-hole centre spacing calculated?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"For bolt-circle diameter D and n equally spaced centres,the straight-line adjacent chord is D sin(pi\/n). The circular arc pitch is pi D\/n.\"}}]}<\/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\":\"Bolt circle geometry\",\"item\":\"https:\/\/vibromera.eu\/calculators\/flange-bolt-calculator\/\"}]}<\/script>\r\n<link rel=\"preconnect\" 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td:first-child{text-align:center}.vc-result-note{margin:0;color:var(--vc-ink-secondary);font-size:13px}@media(max-width:650px){.vc-form-grid-geom{grid-template-columns:1fr}.vc-field-source{grid-column:auto}}\r\r\r\n<\/style>\r\n<div class=\"vc-calculator\" id=\"vc-bolt-circle\"><header class=\"vc-header\"><p class=\"vc-header-eyebrow\">Planar geometry \u2014 no pressure\/load calculation<\/p><h1 class=\"vc-header-title\">Bolt Circle Geometry and Coordinates<\/h1><p class=\"vc-header-subtitle\">Calculate spacing and centre coordinates for equally spaced holes on a true bolt circle. Enter the dimensions and orientation from your drawing.<\/p><div class=\"vc-badges\"><span class=\"vc-badge\">Chord = D\u00b7sin(\u03c0\/n)<\/span><span class=\"vc-badge\">Pitch angle = 360\u00b0\/n<\/span><span class=\"vc-badge\">mm or in<\/span><\/div><\/header>\r\n<div class=\"vc-card\"><form class=\"vc-form\" id=\"vc-form\" autocomplete=\"off\"><div class=\"vc-form-grid-geom\">\r\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-unit\">Length unit<\/label><select class=\"vc-select\" id=\"vc-unit\"><option value=\"\">Select\u2026<\/option><option value=\"mm\">millimetres (mm)<\/option><option value=\"in\">inches (in)<\/option><\/select><\/div>\r\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-pcd\">Bolt-circle diameter, D<\/label><input class=\"vc-input\" id=\"vc-pcd\" type=\"text\" inputmode=\"decimal\" placeholder=\"e.g. 200\"><\/div>\r\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-n\">Number of equally spaced holes, n <span class=\"vc-label-hint\">(integer 2\u2013360)<\/span><\/label><input class=\"vc-input\" id=\"vc-n\" type=\"text\" inputmode=\"numeric\" placeholder=\"e.g. 8\"><\/div>\r\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-hole\">Hole diameter, d<sub>h<\/sub><\/label><input class=\"vc-input\" id=\"vc-hole\" type=\"text\" inputmode=\"decimal\" placeholder=\"e.g. 18\"><\/div>\r\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-angle\">First-hole angle, \u03b8<sub>0<\/sub> <span class=\"vc-label-hint\">(degrees from +x)<\/span><\/label><input class=\"vc-input\" id=\"vc-angle\" type=\"text\" inputmode=\"decimal\" placeholder=\"e.g. 0\"><\/div>\r\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-direction\">Numbering direction<\/label><select class=\"vc-select\" id=\"vc-direction\"><option value=\"\">Select\u2026<\/option><option value=\"ccw\">counter-clockwise (+\u03b8)<\/option><option value=\"cw\">clockwise (\u2212\u03b8)<\/option><\/select><\/div>\r\n<div class=\"vc-field vc-field-source\"><label class=\"vc-label\" for=\"vc-source\">Drawing\/configuration source <span class=\"vc-label-hint\">(required)<\/span><\/label><input class=\"vc-input\" id=\"vc-source\" type=\"text\" maxlength=\"500\" placeholder=\"e.g. flange drawing F-204 rev B\"><\/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>Scope:<\/strong> all centres are assumed equally spaced on one exact circle in one plane. This tool does not select a standard flange or calculate pressure rating,loads,preload,torque,bolt stress,flange stress,gasket seating,leak tightness,fatigue,thermal effects or tolerances.<\/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\">Geometric results<\/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 vc-rcard-primary\"><div class=\"vc-rcard-label\">Adjacent centre chord<\/div><div class=\"vc-rcard-value\" id=\"vc-r-chord\">\u2014<\/div><\/div>\r\n<div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Bolt-circle radius<\/div><div class=\"vc-rcard-value\" id=\"vc-r-radius\">\u2014<\/div><\/div>\r\n<div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Angular pitch<\/div><div class=\"vc-rcard-value\" id=\"vc-r-pitch\">\u2014<\/div><\/div>\r\n<div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Adjacent arc pitch<\/div><div class=\"vc-rcard-value\" id=\"vc-r-arc\">\u2014<\/div><\/div>\r\n<div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Adjacent edge-to-edge gap<\/div><div class=\"vc-rcard-value\" id=\"vc-r-gap\">\u2014<\/div><\/div>\r\n<div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Outer hole envelope diameter<\/div><div class=\"vc-rcard-value\" id=\"vc-r-outer\">\u2014<\/div><\/div>\r\n<div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Inner hole envelope diameter<\/div><div class=\"vc-rcard-value\" id=\"vc-r-inner\">\u2014<\/div><\/div>\r\n<div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Normalized first-hole angle<\/div><div class=\"vc-rcard-value\" id=\"vc-r-angle\">\u2014<\/div><\/div>\r\n<\/div><p class=\"vc-result-note\" id=\"vc-r-note\"><\/p><div class=\"vc-table-wrap\"><table class=\"vc-coordinate-table\"><thead><tr><th>Hole<\/th><th>Angle (\u00b0)<\/th><th id=\"vc-x-head\">x<\/th><th id=\"vc-y-head\">y<\/th><\/tr><\/thead><tbody id=\"vc-coordinates\"><\/tbody><\/table><\/div><\/div><\/div>\r\n\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\udcd0<\/span><span class=\"vc-section-title\">Derivation,units and limits<\/span><\/span><\/button><div class=\"vc-section-body\"><div class=\"vc-section-inner vc-theory\">\r\n<h3>Equally spaced circle geometry<\/h3><p>Let D be the bolt-circle diameter,R=D\/2,n the number of equally spaced centres,and \u03b8<sub>0<\/sub> the first-hole angle. The central angle between adjacent centres is \u0394\u03b8=360\u00b0\/n=2\u03c0\/n radians. Bisecting the isosceles triangle formed by two adjacent radii gives half-chord R\u00b7sin(\u03c0\/n),therefore the full chord is 2R\u00b7sin(\u03c0\/n)=D\u00b7sin(\u03c0\/n).<\/p>\r\n<div class=\"vc-formula-box\">R = D\/2 &nbsp; \u00b7 &nbsp; \u0394\u03b8 = 360\u00b0\/n<br>chord = D\u00b7sin(\u03c0\/n) &nbsp; \u00b7 &nbsp; arc pitch = \u03c0D\/n<\/div>\r\n<p>For hole k=1\u2026n,with index j=k\u22121,the angle is \u03b8<sub>j<\/sub>=\u03b8<sub>0<\/sub>+s\u00b7j\u00b7360\u00b0\/n,where s=+1 counter-clockwise or\u22121 clockwise. Coordinates relative to the bolt-circle centre are x<sub>j<\/sub>=R cos \u03b8<sub>j<\/sub>,y<sub>j<\/sub>=R sin \u03b8<sub>j<\/sub>. The adjacent clear gap is chord\u2212d<sub>h<\/sub>; a negative value means the entered circular holes geometrically overlap. Outer and inner radial envelopes are D+d<sub>h<\/sub> and D\u2212d<sub>h<\/sub>; they are geometry,not required flange diameters.<\/p>\r\n<h3>Units and numerical scope<\/h3><p>All length inputs and outputs use the selected unit consistently. The inch is exactly25.4mm according to NIST. Thus a physically identical pattern entered as254mm or10in produces outputs that differ by exactly25.4 in numerical scale. The computational bounds (positive lengths\u226410\u2079 selected units,n=2\u2026360,|\u03b8<sub>0<\/sub>|\u226410\u2079\u00b0) prevent non-finite or impractically large browser calculations; they are not standards limits.<\/p>\r\n<h3>Standards context \u2014 none is implemented here<\/h3><p><a href=\"https:\/\/www.asme.org\/codes-standards\/find-codes-standards\/pressure-boundary-bolted-flange-joint-assembly\" target=\"_blank\" rel=\"noopener\">ASME PCC-1\u20142022<\/a> is an assembly guideline for pressure-boundary bolted flange joints within its stated scope; it is not the source of the elementary circle formulas above. <a href=\"https:\/\/www.asme.org\/codes-standards\/find-codes-standards\/b16-5-pipe-flanges-flanged-fittings-nps-1-2-nps-24-metric-inch-standard\/2025\" target=\"_blank\" rel=\"noopener\">ASME B16.5\u20142025<\/a> covers specified pressure-temperature ratings,materials,dimensions,tolerances,marking and testing for its listed standard flanges; this page does not reproduce its tables.<\/p>\r\n<p><a href=\"https:\/\/knowledge.bsigroup.com\/products\/flanges-and-their-joints-design-rules-for-gasketed-circular-flange-connections-calculation-1\" target=\"_blank\" rel=\"noopener\">BS EN1591-1:2024<\/a> is the current calculation standard for structural integrity and leak tightness of gasketed circular flange joints using gasket parameters tied to EN13555:2021. Its joint model is not the former page\u2019s two-term load estimate and is not implemented here.<\/p>\r\n<div class=\"vc-warning-box\"><p style=\"margin:0\"><strong>Do not use these geometric outputs as bolt load or preload.<\/strong> The former calculator ignored its gasket-y input,omitted seating load and effective-gasket-geometry rules,and labelled a simplified estimate as PCC-1\/EN1591. Those load calculations were removed because the necessary licensed procedure and design inputs were absent.<\/p><\/div>\r\n<p>Sources: official ASME PCC-1\u20142022 and B16.5\u20142025 records;BSI current BS EN1591-1:2024 scope\/history;and <a href=\"https:\/\/www.nist.gov\/pml\/owm\/si-units-length\" target=\"_blank\" rel=\"noopener\">NIST length-unit definition<\/a>. Checked12July2026. No closed clause,table or coefficient is asserted.<\/p>\r\n<\/div><\/div><\/div>\r\n<footer class=\"vc-footer\"><p>\u00a92024\u20132026 <a href=\"https:\/\/vibromera.eu\/\">Vibromera<\/a><\/p><p>Reference planar geometry only;not a pressure-joint design,load calculation,standards lookup or conformity decision. Scientific review:July2026.<\/p><\/footer><\/div>\r\n<script>(function(){'use strict';function $(i){return document.getElementById(i)}var outs=['vc-r-chord','vc-r-radius','vc-r-pitch','vc-r-arc','vc-r-gap','vc-r-outer','vc-r-inner','vc-r-angle'];function pnum(s){s=s.trim().replace(',','.');return \/^[+-]?(?:\\d+(?:\\.\\d*)?|\\.\\d+)(?:[eE][+-]?\\d+)?$\/.test(s)?Number(s):NaN}function pint(s){var x=pnum(s);return Number.isSafeInteger(x)?x:NaN}function fmt(x){if(Object.is(x,-0))x=0;return Number(x.toPrecision(12)).toString()}function norm(a){return ((a%360)+360)%360}function clear(){outs.forEach(function(id){$(id).textContent='\u2014'});$('vc-coordinates').textContent='';$('vc-r-note').textContent='';$('vc-results').classList.remove('vc-visible')}function calc(){var ids=['vc-unit','vc-pcd','vc-n','vc-hole','vc-angle','vc-direction','vc-source'],raw=ids.map(function(id){return $(id).value.trim()}),any=raw.some(Boolean),u=new URL(location),keys=['unit','pcd','holes','hole_diameter','start_angle_deg','direction','source'];keys.forEach(function(k,i){if(raw[i])u.searchParams.set(k,raw[i]);else u.searchParams.delete(k)});history.replaceState(null,'',u.toString());if(!raw.every(Boolean)){clear();$('vc-error').textContent=any?'Complete all seven fields.':'';return}var D=pnum(raw[1]),n=pint(raw[2]),dh=pnum(raw[3]),a0=pnum(raw[4]);if(!Number.isFinite(D)||D<=0||D>1e9){clear();$('vc-error').textContent='Bolt-circle diameter must be a strict,finite number greater than0 and no more than10\u2079 selected units.';return}if(!Number.isSafeInteger(n)||n<2||n>360){clear();$('vc-error').textContent='Hole count must be a whole number from2 to360.';return}if(!Number.isFinite(dh)||dh<=0||dh>1e9||dh>D){clear();$('vc-error').textContent='Hole diameter must be a strict,finite number greater than0,no more than10\u2079 selected units,and no greater than the bolt-circle diameter.';return}if(!Number.isFinite(a0)||Math.abs(a0)>1e9){clear();$('vc-error').textContent='First-hole angle must be a strict,finite number from\u221210\u2079\u00b0 to+10\u2079\u00b0.';return}var R=D\/2,pitch=360\/n,arc=Math.PI*D\/n,chord=D*Math.sin(Math.PI\/n),gap=chord-dh;if(Math.abs(gap)<=1e-12*Math.max(1,D,dh))gap=0;var outer=D+dh,inner=D-dh,start=norm(a0),sgn=raw[5]==='ccw'?1:-1;if(![R,pitch,arc,chord,gap,outer,inner,start].every(Number.isFinite)){clear();$('vc-error').textContent='The result exceeds the finite numerical range.';return}$('vc-error').textContent='';$('vc-r-chord').textContent=fmt(chord)+' '+raw[0];$('vc-r-radius').textContent=fmt(R)+' '+raw[0];$('vc-r-pitch').textContent=fmt(pitch)+'\u00b0';$('vc-r-arc').textContent=fmt(arc)+' '+raw[0];$('vc-r-gap').textContent=fmt(gap)+' '+raw[0];$('vc-r-outer').textContent=fmt(outer)+' '+raw[0];$('vc-r-inner').textContent=fmt(inner)+' '+raw[0];$('vc-r-angle').textContent=fmt(start)+'\u00b0';$('vc-x-head').textContent='x ('+raw[0]+')';$('vc-y-head').textContent='y ('+raw[0]+')';var rows='';for(var j=0;j<n;j++){var aa=norm(start+sgn*j*pitch),rad=aa*Math.PI\/180,c=Math.cos(rad),s=Math.sin(rad);if(Math.abs(c)<1e-14)c=0;if(Math.abs(s)<1e-14)s=0;var x=R*c,y=R*s;rows+='<tr><td>'+(j+1)+'<\/td><td>'+fmt(aa)+'<\/td><td>'+fmt(x)+'<\/td><td>'+fmt(y)+'<\/td><\/tr>'}$('vc-coordinates').innerHTML=rows;$('vc-r-note').textContent='Source:'+raw[6]+' | '+(gap<0?'Warning:adjacent circular holes overlap by '+fmt(-gap)+' '+raw[0]+'.':gap===0?'Adjacent circular holes are exactly tangent in this ideal geometry.':'Adjacent ideal edge gap:'+fmt(gap)+' '+raw[0]+'.')+' No load,stress or suitability verdict is calculated.';$('vc-results').classList.add('vc-visible')}$('vc-form').addEventListener('input',calc);$('vc-form').addEventListener('change',calc);$('vc-copy-btn').addEventListener('click',function(){if(navigator.clipboard)navigator.clipboard.writeText($('vc-results').innerText)});document.querySelectorAll('.vc-section-toggle').forEach(function(b){b.addEventListener('click',function(){var s=this.closest('.vc-section');s.classList.toggle('vc-open');this.setAttribute('aria-expanded',s.classList.contains('vc-open'))})});var p=new URLSearchParams(location.search),keys=['unit','pcd','holes','hole_diameter','start_angle_deg','direction','source'],ids=['vc-unit','vc-pcd','vc-n','vc-hole','vc-angle','vc-direction','vc-source'];keys.forEach(function(k,i){if(p.has(k))$(ids[i]).value=p.get(k)});calc()})();<\/script>\r\n","protected":false},"excerpt":{"rendered":"<p>Calculate angular pitch,adjacent chord and arc spacing,edge gap,and Cartesian coordinates for equally spaced holes on a bolt circle. No pressure or bolt-load calculation.<\/p>","protected":false},"featured_media":0,"template":"","meta":{"ai_generated_summary":"","footnotes":""},"categories":[],"tags":[],"class_list":["post-100095","calculator","type-calculator","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/vibromera.eu\/lv\/wp-json\/wp\/v2\/calculator\/100095","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/vibromera.eu\/lv\/wp-json\/wp\/v2\/calculator"}],"about":[{"href":"https:\/\/vibromera.eu\/lv\/wp-json\/wp\/v2\/types\/calculator"}],"version-history":[{"count":5,"href":"https:\/\/vibromera.eu\/lv\/wp-json\/wp\/v2\/calculator\/100095\/revisions"}],"predecessor-version":[{"id":102400,"href":"https:\/\/vibromera.eu\/lv\/wp-json\/wp\/v2\/calculator\/100095\/revisions\/102400"}],"wp:attachment":[{"href":"https:\/\/vibromera.eu\/lv\/wp-json\/wp\/v2\/media?parent=100095"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/vibromera.eu\/lv\/wp-json\/wp\/v2\/categories?post=100095"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/vibromera.eu\/lv\/wp-json\/wp\/v2\/tags?post=100095"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}