{"id":100189,"date":"2026-02-15T20:25:50","date_gmt":"2026-02-15T20:25:50","guid":{"rendered":"https:\/\/vibromera.eu\/?post_type=calculator&#038;p=100189"},"modified":"2026-07-13T03:17:38","modified_gmt":"2026-07-13T03:17:38","slug":"pneumatic-cylinder-calculator","status":"publish","type":"calculator","link":"https:\/\/vibromera.eu\/fi\/calculators\/pneumatic-cylinder-calculator\/","title":{"rendered":"Documented Pneumatic-Cylinder Pressure-Force Arithmetic"},"content":{"rendered":"\n<script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"WebApplication\",\"name\":\"Documented Pneumatic-Cylinder Pressure-Force Arithmetic\",\"description\":\"Calculates ideal pressure force from measured cap\/rod chamber gauge pressures and piston geometry, plus optional kinematic speed from actual local chamber flow. It does not predict available force or speed.\",\"url\":\"https:\/\/vibromera.eu\/calculators\/pneumatic-cylinder-calculator\/\",\"applicationCategory\":\"EngineeringApplication\",\"operatingSystem\":\"Any (Web Browser)\",\"offers\":{\"@type\":\"Offer\",\"price\":\"0\",\"priceCurrency\":\"EUR\"},\"creator\":{\"@type\":\"Organization\",\"name\":\"Vibromera\",\"url\":\"https:\/\/vibromera.eu\/\"},\"datePublished\":\"2024-01-01\",\"dateModified\":\"2026-07-13\",\"inLanguage\":\"en\",\"isAccessibleForFree\":true,\"featureList\":[\"Cap and annular areas\",\"Two-chamber pressure force\",\"Selected-direction signed force\",\"Actual local-flow kinematic rate\",\"No friction or safety-factor guess\"],\"keywords\":\"pneumatic cylinder pressure force,back pressure,annular area,actual chamber flow\"}<\/script>\n<script type=\"application\/ld+json\">{\"@context\":\"https:\/\/schema.org\",\"@type\":\"FAQPage\",\"mainEntity\":[{\"@type\":\"Question\",\"name\":\"Is the calculated force the available cylinder force?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"No. It is ideal net pressure force before seal friction, side load, acceleration, gravity and other loads.\"}},{\"@type\":\"Question\",\"name\":\"Can I enter normal litres per minute or SCFM?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"No. Q\/A needs actual volumetric flow at the powered chamber state and operating point, not standardized free-air flow.\"}},{\"@type\":\"Question\",\"name\":\"Does ISO 15552 define this calculator formula?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"No. ISO 15552:2018 establishes interchangeability dimensions for a specified cylinder family; the pressure-area and continuity equations are general engineering relations.\"}},{\"@type\":\"Question\",\"name\":\"Why are both chamber pressures required?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Exhaust-side or opposing chamber pressure acts on the opposite effective area and changes net pressure force.\"}}]}<\/script>\n<style>:root{--s:#fff;--sa:#f8f6f2;--i:#1a1a1a;--is:#5a5650;--im:#8a857e;--a:#3e6483;--al:#edf4f8;--b:#d9d4cc;--bl:#e8e4dd;--y:#8a6500;--yl:#fef9e8;--r:#a12b2b;--f:'DM Sans',sans-serif;--m:'JetBrains Mono',monospace;--d:'Fraunces',serif}.vc-calculator{font-family:var(--f);font-size:15px;line-height:1.65;color:var(--i);max-width:960px;margin:auto;padding:20px 16px 40px}.vc-calculator *{box-sizing:border-box}.vc-header{text-align:center;padding:48px 20px 40px;border-bottom:3px solid var(--a)}.vc-header-eyebrow{font:500 11px var(--m);letter-spacing:.15em;text-transform:uppercase;color:var(--a)}.vc-header-title{font:800 clamp(24px,4vw,36px)\/1.15 var(--d);margin:10px 0 14px}.vc-header-subtitle{max-width:760px;margin:auto;color:var(--is)}.vc-badges{display:flex;gap:8px;justify-content:center;flex-wrap:wrap;margin-top:18px}.vc-badge{font:500 11px var(--m);padding:4px 10px;border:1px solid var(--b);border-radius:4px}.vc-card,.vc-section{background:var(--s);border:1px solid var(--b);border-radius:12px;overflow:hidden;margin-top:28px}.vc-form{padding:24px}.vc-grid{display:grid;grid-template-columns:1fr 1fr;gap:18px}.vc-field{display:flex;flex-direction:column}.vc-full{grid-column:1\/-1}.vc-label{font-size:12px;font-weight:600;letter-spacing:.04em;text-transform:uppercase;color:var(--is);margin-bottom:6px}.vc-hint{font-weight:400;text-transform:none;letter-spacing:0;color:var(--im)}.vc-input,.vc-select{width:100%;padding:10px 12px;border:1.5px solid var(--b);border-radius:6px;font:14px var(--f);background:var(--s)}.vc-pair{display:grid;grid-template-columns:2fr 1fr;gap:8px}.vc-check{display:flex;gap:10px;padding:12px;border:1px solid var(--bl);border-radius:6px;background:var(--sa);font-size:13px;color:var(--is)}.vc-check input{margin-top:4px}.vc-validation{min-height:22px;color:var(--r);font-size:13px;margin-top:10px}.vc-results{border-top:1px solid var(--bl);background:var(--sa);padding:0;max-height:0;overflow:hidden}.vc-results.vc-visible{max-height:1400px;padding:24px}.vc-result-grid{display:grid;grid-template-columns:repeat(2,1fr);gap:12px}.vc-rcard{background:var(--s);border:1px solid var(--bl);border-radius:8px;padding:16px}.vc-primary{grid-column:1\/-1;border:2px solid var(--a);background:var(--al)}.vc-rcard-label{font:500 10px var(--m);letter-spacing:.1em;text-transform:uppercase;color:var(--im)}.vc-rcard-value{font:600 18px var(--m);overflow-wrap:anywhere}.vc-primary .vc-rcard-value{font-size:23px;color:var(--a)}.vc-status{grid-column:1\/-1;padding:12px;background:var(--yl);border-left:3px solid var(--y);font-size:13px;color:var(--is)}.vc-section-toggle{width:100%;display:flex;justify-content:space-between;padding:18px 24px;border:0;background:transparent;cursor:pointer;text-align:left}.vc-section-title{font:700 18px var(--d)}.vc-section-body{max-height:0;overflow:hidden}.vc-section.vc-open .vc-section-body{max-height:15000px}.vc-section-inner{padding:0 24px 24px;border-top:1px solid var(--bl)}.vc-theory h3{font:700 17px var(--d);margin:24px 0 8px}.vc-theory p,.vc-theory li{font-size:14px;color:var(--is)}.vc-formula{padding:14px;border:2px solid var(--b);border-radius:6px;background:var(--sa);text-align:center;font:500 14px var(--m);margin:12px 0}.vc-warning{padding:14px;background:var(--yl);border-left:3px solid var(--y);color:var(--is)}.vc-faq-item{border:1px solid var(--bl);margin-top:8px}.vc-faq-q{width:100%;padding:14px;border:0;background:var(--sa);text-align:left;font-weight:600}.vc-faq-a{display:none;padding:14px;color:var(--is)}.vc-faq-item.vc-open .vc-faq-a{display:block}.vc-footer{text-align:center;padding:30px;color:var(--im);font-size:13px}@media(max-width:600px){.vc-grid,.vc-result-grid{grid-template-columns:1fr}.vc-full,.vc-primary,.vc-status{grid-column:1}.vc-pair{grid-template-columns:1fr}}<\/style>\n<div class=\"vc-calculator\"><header class=\"vc-header\"><p class=\"vc-header-eyebrow\">Pressure-area and actual-flow arithmetic \u2014 not cylinder sizing<\/p><h1 class=\"vc-header-title\">Documented Pneumatic-Cylinder Pressure-Force Arithmetic<\/h1><p class=\"vc-header-subtitle\">Compute ideal two-chamber pressure force from controlled piston geometry and measured cap\/rod chamber gauge pressures. Optionally compute a geometric rate from actual local powered-chamber volumetric flow. No friction, safety factor, valve capacity or available-force\/speed prediction is invented.<\/p><div class=\"vc-badges\"><span class=\"vc-badge\">Two chamber pressures<\/span><span class=\"vc-badge\">Signed net force<\/span><span class=\"vc-badge\">Actual flow only<\/span><span class=\"vc-badge\">No ISO formula claim<\/span><\/div><\/header>\n<div class=\"vc-card\"><form class=\"vc-form\" id=\"vc-form\" autocomplete=\"off\" novalidate><div class=\"vc-grid\">\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-mode\">Assessed motion direction<\/label><select class=\"vc-select\" id=\"vc-mode\"><option value=\"extend\">Extension<\/option><option value=\"retract\">Retraction<\/option><\/select><\/div>\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-bore\">Controlled piston\/bore diameter<\/label><div class=\"vc-pair\"><input class=\"vc-input\" id=\"vc-bore\" inputmode=\"decimal\"><select class=\"vc-select\" id=\"vc-length-unit\"><option value=\"mm\">mm<\/option><option value=\"in\">in<\/option><\/select><\/div><\/div>\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-rod\">Controlled rod diameter<\/label><input class=\"vc-input\" id=\"vc-rod\" inputmode=\"decimal\"><\/div>\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-cap-pressure\">Cap-chamber gauge pressure<\/label><div class=\"vc-pair\"><input class=\"vc-input\" id=\"vc-cap-pressure\" inputmode=\"decimal\"><select class=\"vc-select\" id=\"vc-pressure-unit\"><option value=\"bar\">bar<\/option><option value=\"psi\">psi<\/option><\/select><\/div><\/div>\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-rod-pressure\">Rod-chamber gauge pressure<\/label><input class=\"vc-input\" id=\"vc-rod-pressure\" inputmode=\"decimal\"><\/div>\n<div class=\"vc-field\"><label class=\"vc-label\" for=\"vc-flow\">Actual powered-chamber flow Q <span class=\"vc-hint\">optional<\/span><\/label><div class=\"vc-pair\"><input class=\"vc-input\" id=\"vc-flow\" inputmode=\"decimal\"><select class=\"vc-select\" id=\"vc-flow-unit\"><option value=\"lmin\">actual L\/min<\/option><option value=\"cfm\">actual ft\u00b3\/min<\/option><\/select><\/div><\/div>\n<div class=\"vc-field vc-full\"><label class=\"vc-label\" for=\"vc-source\">Controlled operating-point source<\/label><input class=\"vc-input\" id=\"vc-source\" type=\"text\" placeholder=\"cylinder\/component ID; measured bore\/rod; cap and rod port pressures; motion; flow location\/state\/basis; timestamp; instruments\/revisions\"><\/div>\n<div class=\"vc-field vc-full\"><label class=\"vc-check\" for=\"vc-gate\"><input id=\"vc-gate\" type=\"checkbox\"><span>Both gauge pressures use the same reference and are measured\/defined at the cylinder chambers for one operating point. Geometry is actual controlled piston and rod geometry. If Q is entered, it is actual volumetric inflow at the powered chamber state (not normal L\/min, NL\/min, ANR, SCFM or compressor free-air delivery). Leakage, gas storage\/compressibility, valve\/line transients, cushioning and deformation are excluded from Q\/A.<\/span><\/label><\/div>\n<\/div><div class=\"vc-validation\" id=\"vc-validation\" role=\"status\" aria-live=\"polite\"><\/div><\/form>\n<div class=\"vc-results\" id=\"vc-results\"><div class=\"vc-result-grid\"><div class=\"vc-rcard vc-primary\"><div class=\"vc-rcard-label\">Ideal pressure force in selected direction<\/div><div class=\"vc-rcard-value\" id=\"vc-r-force\">\u2014<\/div><\/div><div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Signed extension-axis pressure force<\/div><div class=\"vc-rcard-value\" id=\"vc-r-signed\">\u2014<\/div><\/div><div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Cap area Ab<\/div><div class=\"vc-rcard-value\" id=\"vc-r-cap-area\">\u2014<\/div><\/div><div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Rod-side annular area Aa<\/div><div class=\"vc-rcard-value\" id=\"vc-r-ann-area\">\u2014<\/div><\/div><div class=\"vc-rcard\"><div class=\"vc-rcard-label\">Q\/A geometric rate<\/div><div class=\"vc-rcard-value\" id=\"vc-r-speed\">\u2014<\/div><\/div><div class=\"vc-status\" id=\"vc-r-note\">Ideal arithmetic only.<\/div><\/div><\/div><\/div>\n<div class=\"vc-section vc-open\"><button class=\"vc-section-toggle\" type=\"button\" aria-expanded=\"true\"><span class=\"vc-section-title\">Equations and applicability<\/span><span>\u2304<\/span><\/button><div class=\"vc-section-body\"><div class=\"vc-section-inner vc-theory\"><div class=\"vc-formula\">Ab=\u03c0D\u00b2\/4;&nbsp; Aa=\u03c0(D\u00b2\u2212d\u00b2)\/4<br>Fext-axis=pc\u00b7Ab\u2212pr\u00b7Aa;&nbsp; Fselected=Fext-axis (extend) or \u2212Fext-axis (retract)<br>vgeom=Qactual\/Apowered<\/div><p>D is controlled piston\/bore diameter; d is rod diameter; pc and pr are cap- and rod-chamber gauge pressures referenced to the same ambient; positive Fext-axis acts toward extension. For Q\/A, Apowered is Ab during extension or Aa during retraction.<\/p><p>These relations are general force balance and geometric continuity. They are not formulas specified by ISO 15552.<\/p><div class=\"vc-warning\"><strong>Theoretical only.<\/strong> Available force also depends on seal\/bearing friction, breakaway, side load, acceleration, gravity, external load, cushioning, pressure dynamics and component condition. Actual speed also depends on compressibility\/storage, leakage, valve\/line conductance, upstream\/downstream pressure, temperature, load and control method.<\/div><h3>Critical flow basis<\/h3><p>Normal\/standard\/free-air flow is referenced to a stated standard condition and cannot be divided directly by chamber area. Convert it to actual chamber volumetric flow using a documented gas-state model and the same operating point before using this worksheet. The old imperial conversion was also nearly 1,000 times too small: one exact international cubic foot per minute is 471,947.4432 mm\u00b3\/s, not 473.176 mm\u00b3\/s.<\/p><h3>ISO 15552 scope<\/h3><p><strong>ISO 15552:2018<\/strong>, edition 2, published and confirmed 2025, establishes metric basic, mounting and accessory dimensions for interchangeability of detachable-mounting pneumatic cylinders, single or double rod, with\/without magnetic-sensor provision, rated up to 1,000 kPa (10 bar), with bores from 32 to 320 mm. It does not establish universal friction percentages, safety factors, rod sizes, available force or speed for an arbitrary cylinder.<\/p><div class=\"vc-warning\"><strong>NEEDS_LICENSED_SOURCE:<\/strong> exact selected-cylinder dimensions\/ratings, friction\/breakaway data, cushioning\/load limits, valve and tubing flow characteristics, standardized-flow reference conditions and sizing\/acceptance rules. Use the current manufacturer datasheet and complete applicable standards.<\/div><h3>Sources<\/h3><p><a href=\"https:\/\/www.iso.org\/standard\/66921.html\" target=\"_blank\" rel=\"noopener\">ISO 15552:2018 official record<\/a>; <a href=\"https:\/\/labvolt.festo.com\/downloads\/89791_F0.pdf\" target=\"_blank\" rel=\"noopener\">Festo\/Lab-Volt pneumatic actuator training<\/a>; <a href=\"https:\/\/www.smcworld.com\/products\/select_guide\/en-sg\/actuator\/aircylinder_data.html\" target=\"_blank\" rel=\"noopener\">SMC air-cylinder characteristics<\/a>; <a href=\"https:\/\/www.nist.gov\/pml\/special-publication-811\/nist-guide-si-appendix-b-conversion-factors\" target=\"_blank\" rel=\"noopener\">NIST exact unit conversions<\/a>.<\/p><\/div><\/div><\/div>\n<div class=\"vc-section\"><button class=\"vc-section-toggle\" type=\"button\" aria-expanded=\"false\"><span class=\"vc-section-title\">Frequently asked questions<\/span><span>\u2304<\/span><\/button><div class=\"vc-section-body\"><div class=\"vc-section-inner\"><div id=\"vc-faq-list\"><\/div><\/div><\/div><\/div><footer class=\"vc-footer\">\u00a9 2024\u20132026 Vibromera \u2014 reviewed 13 July 2026<\/footer><\/div>\n<script>(function(){'use strict';function $(id){return document.getElementById(id)}function read(raw,zero){var t=String(raw||'').trim();if(!t||(t.includes(',')&&t.includes('.')))return null;t=t.replace(',','.');if(!\/^(?:\\d+(?:\\.\\d*)?|\\.\\d+)$\/.test(t))return null;var v=Number(t);return Number.isFinite(v)&&(zero?v>=0:v>0)?v:null}function fmt(v){if(Math.abs(v)>=1e9||(Math.abs(v)>0&&Math.abs(v)<1e-7))return v.toExponential(8);return Number(v.toPrecision(12)).toString()}function hide(m){$('vc-results').classList.remove('vc-visible');$('vc-validation').textContent=m||''}function calc(){var source=$('vc-source').value.trim();if(!source)return hide('Enter the controlled operating-point source.');if(!$('vc-gate').checked)return hide('Confirm the pressure references,geometry and actual-flow basis.');var D=read($('vc-bore').value,false),d=read($('vc-rod').value,true),pc=read($('vc-cap-pressure').value,true),pr=read($('vc-rod-pressure').value,true);if(D===null||d===null||pc===null||pr===null)return hide('Enter complete positive bore and non-negative rod\/chamber-pressure values.');if(d>=D)return hide('Rod diameter must be smaller than bore diameter.');var rawQ=String($('vc-flow').value||'').trim(),Q=null;if(rawQ){Q=read(rawQ,true);if(Q===null)return hide('Optional actual flow must be a complete non-negative number.')}var IN=.0254,PSI=6894.757293168,LBF=4.4482216152605;if($('vc-length-unit').value==='in'){D*=IN;d*=IN}else{D*=.001;d*=.001}if($('vc-pressure-unit').value==='psi'){pc*=PSI;pr*=PSI}else{pc*=1e5;pr*=1e5}var Ab=Math.PI*D*D\/4,Aa=Math.PI*(D*D-d*d)\/4,Faxis=pc*Ab-pr*Aa,mode=$('vc-mode').value,Fsel=mode==='extend'?Faxis:-Faxis,speed=null;if(Q!==null){Q*=$('vc-flow-unit').value==='cfm'?.028316846592\/60:.001\/60;speed=Q\/(mode==='extend'?Ab:Aa)}if(![Ab,Aa,Faxis,Fsel].every(Number.isFinite)||(speed!==null&&!Number.isFinite(speed)))return hide('Arithmetic did not produce finite results.');function force(v){return fmt(v)+' N | '+fmt(v\/LBF)+' lbf'}function area(v){return fmt(v*1e6)+' mm\u00b2 | '+fmt(v\/(IN*IN))+' in\u00b2'}$('vc-r-force').textContent=force(Fsel);$('vc-r-signed').textContent=force(Faxis);$('vc-r-cap-area').textContent=area(Ab);$('vc-r-ann-area').textContent=area(Aa);$('vc-r-speed').textContent=speed===null?'Not entered':fmt(speed)+' m\/s | '+fmt(speed*1000)+' mm\/s | '+fmt(speed\/IN)+' in\/s';$('vc-r-note').textContent='Ideal two-chamber pressure force and geometric actual-flow rate only.No available-force,friction,safety-factor,load,acceleration,valve sizing,cushioning or actual-speed verdict.';$('vc-validation').textContent='';$('vc-results').classList.add('vc-visible')}$('vc-form').addEventListener('input',calc);$('vc-form').addEventListener('change',calc);document.querySelectorAll('.vc-section-toggle').forEach(function(b){b.addEventListener('click',function(){var s=this.closest('.vc-section');s.classList.toggle('vc-open');this.setAttribute('aria-expanded',String(s.classList.contains('vc-open')))})});var faq=[['Why can selected-direction force be negative?','It means the ideal chamber-pressure force acts opposite the selected direction at that operating point.It is not an error or a safety verdict.'],['Where do friction losses go?','They are not guessed.Use controlled manufacturer\/test data for the exact cylinder,pressure,lubrication,speed,temperature,side load and condition.'],['Can I size a valve from this speed result?','No.Valve\/tubing conductance,compressible flow,choking,pressure transients and load motion require a separate dynamic pneumatic model.'],['Does the ISO bore range make my cylinder compliant?','No.The official scope describes a family;conformity requires the complete standard and exact component documentation.']];var l=$('vc-faq-list');faq.forEach(function(x){var w=document.createElement('div');w.className='vc-faq-item';var b=document.createElement('button');b.type='button';b.className='vc-faq-q';b.textContent=x[0];var a=document.createElement('div');a.className='vc-faq-a';a.textContent=x[1];w.appendChild(b);w.appendChild(a);l.appendChild(w)});l.addEventListener('click',function(e){var b=e.target.closest('.vc-faq-q');if(b)b.closest('.vc-faq-item').classList.toggle('vc-open')});hide('')})();<\/script>\n","protected":false},"excerpt":{"rendered":"<p>Ideal two-chamber pneumatic pressure-force and optional actual local-flow geometric-rate arithmetic without friction,safety-factor,valve-sizing or actual-speed 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