{"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":"2026-04-05T15:36:33","modified_gmt":"2026-04-05T15:36:33","slug":"pneumatic-cylinder-calculator","status":"publish","type":"calculator","link":"https:\/\/vibromera.eu\/nb\/calculators\/pneumatic-cylinder-calculator\/","title":{"rendered":"Kalkulator for kraft og hastighet for pneumatiske sylindere | Vibromera"},"content":{"rendered":"\n<script type=\"application\/ld+json\">\n{\"@context\":\"https:\/\/schema.org\",\"@type\":\"WebApplication\",\"name\":\"Pneumatic Cylinder Force & Speed Calculator\",\"alternateName\":[\"Air Cylinder Calculator\",\"Piston Force Calculator\",\"Pneumatic Actuator Calculator\"],\"description\":\"Free online engineering calculator for pneumatic cylinder force (F=P\u00d7A) and piston speed. Supports extend and retract calculations with rod diameter correction.\",\"url\":\"https:\/\/vibromera.eu\/calculators\/pneumatic-cylinder-calculator\/\",\"applicationCategory\":\"Engineering Calculator\",\"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\":\"2025-06-15\",\"inLanguage\":\"en\",\"isAccessibleForFree\":true,\"featureList\":[\"Extend and retract force\",\"Piston speed from flow rate\",\"Metric and Imperial units\",\"Auto-calculation on input change\",\"Preset quick-select\"],\"keywords\":\"pneumatic cylinder, force calculation, piston speed, bore diameter, rod diameter\"}\n<\/script>\n\n<script type=\"application\/ld+json\">\n{\"@context\":\"https:\/\/schema.org\",\"@type\":\"FAQPage\",\"mainEntity\":[\n{\"@type\":\"Question\",\"name\":\"How do I calculate pneumatic cylinder force?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Pneumatic cylinder extend force is F = P \u00d7 A, where P is the supply pressure and A is the full bore area (\u03c0\/4 \u00d7 D\u00b2). Retract force uses the annular area: A = \u03c0\/4 \u00d7 (D\u00b2 \u2212 d\u00b2), where d is the rod diameter.\"}},\n{\"@type\":\"Question\",\"name\":\"What is the difference between extend and retract force?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Extend force uses the full piston bore area, so it is always higher. Retract force uses the annular area (bore area minus rod area), giving a lower force output.\"}},\n{\"@type\":\"Question\",\"name\":\"How do I calculate pneumatic cylinder speed?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Piston speed v = Q \/ A, where Q is the volume flow rate and A is the effective piston area. For extension, A is the full bore area; for retraction, A is the annular area.\"}},\n{\"@type\":\"Question\",\"name\":\"What bore size do I need for a given force?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Rearrange F = P \u00d7 A to find A = F \/ P, then D = \u221a(4A\/\u03c0). Always size up to the next standard bore diameter and include a safety factor of 25\u201350% for friction and dynamic loads.\"}},\n{\"@type\":\"Question\",\"name\":\"Does friction affect pneumatic cylinder force?\",\"acceptedAnswer\":{\"@type\":\"Answer\",\"text\":\"Yes. Seal friction typically reduces the theoretical force by 5\u201320% depending on seal type, lubrication, and speed. 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}\n.vc-related { display:flex; flex-wrap:wrap; gap:10px; margin-top:16px; }\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 0.15s; }\n.vc-related-link:hover { border-color:var(--vc-accent); color:var(--vc-accent); background:var(--vc-accent-light); }\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; }\n.vc-promo-text { flex:1; font-size:14px; color:var(--vc-ink-secondary); }\n.vc-promo-text strong { color:var(--vc-ink); }\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; 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Enter bore, rod diameter, and supply pressure.<\/p>\n    <div class=\"vc-badges\">\n        <span class=\"vc-badge\">F = P \u00d7 A<\/span>\n        <span class=\"vc-badge\">v = Q \/ A<\/span>\n        <span class=\"vc-badge\">Extend &amp; Retract<\/span>\n    <\/div>\n<\/header>\n\n<div class=\"vc-card\">\n    <div class=\"vc-unit-bar\">\n        <button type=\"button\" class=\"vc-unit-btn vc-active\" data-system=\"metric\">Metric (mm, bar, N)<\/button>\n        <button type=\"button\" class=\"vc-unit-btn\" data-system=\"imperial\">Imperial (in, psi, lbf)<\/button>\n    <\/div>\n\n    <form class=\"vc-form\" id=\"vc-form\" autocomplete=\"off\">\n        <div class=\"vc-form-grid\">\n            <div class=\"vc-field\">\n                <label class=\"vc-label\" for=\"vc-bore\">Bore Diameter <span class=\"vc-label-hint\" id=\"vc-bore-hint\">(mm)<\/span><\/label>\n                <input class=\"vc-input\" type=\"number\" id=\"vc-bore\" inputmode=\"decimal\" step=\"any\" min=\"0.1\" placeholder=\"e.g. 63\" value=\"63\">\n            <\/div>\n            <div class=\"vc-field\">\n                <label class=\"vc-label\" for=\"vc-rod\">Rod Diameter <span class=\"vc-label-hint\" id=\"vc-rod-hint\">(mm)<\/span><\/label>\n                <input class=\"vc-input\" type=\"number\" id=\"vc-rod\" inputmode=\"decimal\" step=\"any\" min=\"0\" placeholder=\"e.g. 20\" value=\"20\">\n            <\/div>\n            <div class=\"vc-field\">\n                <label class=\"vc-label\" for=\"vc-pressure\">Supply Pressure <span class=\"vc-label-hint\" id=\"vc-pressure-hint\">(bar)<\/span><\/label>\n                <input class=\"vc-input\" type=\"number\" id=\"vc-pressure\" inputmode=\"decimal\" step=\"any\" min=\"0\" placeholder=\"e.g. 6\" value=\"6\">\n            <\/div>\n            <div class=\"vc-field\">\n                <label class=\"vc-label\" for=\"vc-flow\">Air Flow Rate <span class=\"vc-label-hint\" id=\"vc-flow-hint\">(L\/min, optional)<\/span><\/label>\n                <input class=\"vc-input\" type=\"number\" id=\"vc-flow\" inputmode=\"decimal\" step=\"any\" min=\"0\" placeholder=\"e.g. 200\" value=\"200\">\n            <\/div>\n        <\/div>\n\n        <div class=\"vc-presets\">\n            <div class=\"vc-presets-label\">Quick presets<\/div>\n            <button type=\"button\" class=\"vc-preset-btn\" data-b=\"32\" data-r=\"12\" data-p=\"6\" data-q=\"80\">32\/12 mm, 6 bar<\/button>\n            <button type=\"button\" class=\"vc-preset-btn\" data-b=\"63\" data-r=\"20\" data-p=\"6\" data-q=\"200\">63\/20 mm, 6 bar<\/button>\n            <button type=\"button\" class=\"vc-preset-btn\" data-b=\"100\" data-r=\"25\" data-p=\"6\" data-q=\"500\">100\/25 mm, 6 bar<\/button>\n            <button type=\"button\" class=\"vc-preset-btn\" data-b=\"125\" data-r=\"32\" data-p=\"8\" data-q=\"700\">125\/32 mm, 8 bar<\/button>\n        <\/div>\n    <\/form>\n\n    <div class=\"vc-results\" id=\"vc-results\">\n        <div class=\"vc-results-head\">\n            <h2 class=\"vc-results-title\">Results<\/h2>\n            <button type=\"button\" class=\"vc-copy-btn\" id=\"vc-copy-btn\">\n                <svg width=\"14\" height=\"14\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><rect x=\"9\" y=\"9\" width=\"13\" height=\"13\" rx=\"2\"\/><path d=\"M5 15H4a2 2 0 01-2-2V4a2 2 0 012-2h9a2 2 0 012 2v1\"\/><\/svg>\n                Copy\n            <\/button>\n        <\/div>\n        <div class=\"vc-result-grid\">\n            <div class=\"vc-rcard vc-rcard-primary\">\n                <div class=\"vc-rcard-label\">Extend Force (Push)<\/div>\n                <div class=\"vc-rcard-value\" id=\"vc-r-fext\">\u2014<\/div>\n            <\/div>\n            <div class=\"vc-rcard\">\n                <div class=\"vc-rcard-label\">Retract Force (Pull)<\/div>\n                <div class=\"vc-rcard-value\" id=\"vc-r-fret\">\u2014<\/div>\n            <\/div>\n            <div class=\"vc-rcard\">\n                <div class=\"vc-rcard-label\">Bore Area<\/div>\n                <div class=\"vc-rcard-value\" id=\"vc-r-abore\">\u2014<\/div>\n            <\/div>\n            <div class=\"vc-rcard\">\n                <div class=\"vc-rcard-label\">Annular Area<\/div>\n                <div class=\"vc-rcard-value\" id=\"vc-r-aann\">\u2014<\/div>\n            <\/div>\n            <div class=\"vc-rcard\">\n                <div class=\"vc-rcard-label\">Extend Speed<\/div>\n                <div class=\"vc-rcard-value\" id=\"vc-r-vext\">\u2014<\/div>\n            <\/div>\n            <div class=\"vc-rcard\">\n                <div class=\"vc-rcard-label\">Retract Speed<\/div>\n                <div class=\"vc-rcard-value\" id=\"vc-r-vret\">\u2014<\/div>\n            <\/div>\n        <\/div>\n    <\/div>\n<\/div>\n\n<!-- Theory -->\n<div class=\"vc-section vc-open\" id=\"vc-sec-theory\">\n    <button type=\"button\" class=\"vc-section-toggle\" aria-expanded=\"true\">\n        <span class=\"vc-section-toggle-text\">\n            <span class=\"vc-section-icon\">\ud83d\udcd8<\/span>\n            <span class=\"vc-section-title\">Theory &amp; Formulas<\/span>\n        <\/span>\n        <svg class=\"vc-section-chevron\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><path d=\"M6 9l6 6 6-6\"\/><\/svg>\n    <\/button>\n    <div class=\"vc-section-body\">\n        <div class=\"vc-section-inner vc-theory\">\n            <h3>Cylinder Extend Force<\/h3>\n            <p>When the piston extends, pressure acts on the full bore area:<\/p>\n            <div class=\"vc-formula-box\" id=\"vc-katex-1\"><\/div>\n            <h3>Cylinder Retract Force<\/h3>\n            <p>When retracting, the rod occupies part of the piston, reducing effective area:<\/p>\n            <div class=\"vc-formula-box\" id=\"vc-katex-2\"><\/div>\n            <h3>Piston Speed<\/h3>\n            <p>Speed depends on the air flow rate and effective piston area:<\/p>\n            <div class=\"vc-formula-box\" id=\"vc-katex-3\"><\/div>\n            <ul>\n                <li><strong>P<\/strong> \u2014 supply pressure<\/li>\n                <li><strong>D<\/strong> \u2014 bore diameter<\/li>\n                <li><strong>d<\/strong> \u2014 rod diameter<\/li>\n                <li><strong>Q<\/strong> \u2014 volume flow rate at working pressure<\/li>\n            <\/ul>\n\n            <h3>Standard Bore Sizes (ISO 15552)<\/h3>\n            <table class=\"vc-table\">\n                <thead><tr><th>Bore (mm)<\/th><th>Rod (mm)<\/th><th>Extend Area (cm\u00b2)<\/th><\/tr><\/thead>\n                <tbody>\n                    <tr><td>32<\/td><td>12<\/td><td>8.04<\/td><\/tr>\n                    <tr><td>40<\/td><td>16<\/td><td>12.57<\/td><\/tr>\n                    <tr><td>50<\/td><td>20<\/td><td>19.63<\/td><\/tr>\n                    <tr><td>63<\/td><td>20<\/td><td>31.17<\/td><\/tr>\n                    <tr><td>80<\/td><td>25<\/td><td>50.27<\/td><\/tr>\n                    <tr><td>100<\/td><td>25<\/td><td>78.54<\/td><\/tr>\n                    <tr><td>125<\/td><td>32<\/td><td>122.72<\/td><\/tr>\n                    <tr><td>160<\/td><td>40<\/td><td>201.06<\/td><\/tr>\n                    <tr><td>200<\/td><td>50<\/td><td>314.16<\/td><\/tr>\n                <\/tbody>\n            <\/table>\n\n            <div class=\"vc-example-box\">\n                <div class=\"vc-example-title\">Example \u2014 63 mm Cylinder at 6 bar<\/div>\n                <p><strong>Given:<\/strong> Bore = 63 mm, Rod = 20 mm, Pressure = 6 bar<\/p>\n                <p>A<sub>bore<\/sub> = \u03c0\/4 \u00d7 63\u00b2 = 3117 mm\u00b2 = 31.17 cm\u00b2<\/p>\n                <p>F<sub>extend<\/sub> = 6 \u00d7 10\u2075 \u00d7 3117 \u00d7 10\u207b\u2076 = <strong>1870 N (190.6 kgf)<\/strong><\/p>\n                <p>A<sub>annular<\/sub> = \u03c0\/4 \u00d7 (63\u00b2 \u2212 20\u00b2) = 2803 mm\u00b2<\/p>\n                <p>F<sub>retract<\/sub> = 6 \u00d7 10\u2075 \u00d7 2803 \u00d7 10\u207b\u2076 = <strong>1682 N (171.4 kgf)<\/strong><\/p>\n            <\/div>\n\n            <div class=\"vc-warning-box\">\n                <p style=\"margin:0;font-size:14px;color:var(--vc-ink-secondary);\"><strong>\u26a0\ufe0f Note:<\/strong> Actual force is reduced by 5\u201320% due to seal friction. Apply a safety factor when sizing cylinders for real applications.<\/p>\n            <\/div>\n        <\/div>\n    <\/div>\n<\/div>\n\n<!-- Related -->\n<div class=\"vc-section\" id=\"vc-sec-related\">\n    <button type=\"button\" class=\"vc-section-toggle\" aria-expanded=\"false\">\n        <span class=\"vc-section-toggle-text\">\n            <span class=\"vc-section-icon\">\ud83d\udd17<\/span>\n            <span class=\"vc-section-title\">Related Calculators<\/span>\n        <\/span>\n        <svg class=\"vc-section-chevron\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><path d=\"M6 9l6 6 6-6\"\/><\/svg>\n    <\/button>\n    <div class=\"vc-section-body\">\n        <div class=\"vc-section-inner\">\n            <div class=\"vc-related\">\n                <a class=\"vc-related-link\" href=\"\/calculators\/air-receiver-volume\/\">Air Receiver Volume<\/a>\n                <a class=\"vc-related-link\" href=\"\/calculators\/compressed-air-consumption\/\">Air Consumption<\/a>\n                <a class=\"vc-related-link\" href=\"\/calculators\/compressed-air-cost\/\">Air Cost Calculator<\/a>\n                <a class=\"vc-related-link\" href=\"\/calculators\/pneumatic-cylinder-response-time\/\">Cylinder Response Time<\/a>\n                <a class=\"vc-related-link\" href=\"\/calculators\/compressed-air-leak-cost\/\">Air Leak Cost<\/a>\n            <\/div>\n        <\/div>\n    <\/div>\n<\/div>\n\n<!-- FAQ -->\n<div class=\"vc-section\" id=\"vc-sec-faq\">\n    <button type=\"button\" class=\"vc-section-toggle\" aria-expanded=\"false\">\n        <span class=\"vc-section-toggle-text\">\n            <span class=\"vc-section-icon\">\u2753<\/span>\n            <span class=\"vc-section-title\">Frequently Asked Questions<\/span>\n        <\/span>\n        <svg class=\"vc-section-chevron\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><path d=\"M6 9l6 6 6-6\"\/><\/svg>\n    <\/button>\n    <div class=\"vc-section-body\">\n        <div class=\"vc-section-inner\">\n            <div class=\"vc-faq-list\" id=\"vc-faq-list\"><\/div>\n        <\/div>\n    <\/div>\n<\/div>\n\n<!-- Promo -->\n<div class=\"vc-promo\">\n    <div class=\"vc-promo-text\">\n        <strong>Vibromera \u2014 Portable Balancing &amp; Vibration Analysis<\/strong><br>\n        Professional field balancing instruments and software. Used in 50+ countries.\n    <\/div>\n    <a class=\"vc-promo-link\" href=\"https:\/\/vibromera.eu\/\" target=\"_blank\" rel=\"noopener\">Learn More<\/a>\n<\/div>\n\n<footer class=\"vc-footer\">\n    <p>\u00a9 2024\u20132025 <a href=\"https:\/\/vibromera.eu\/\">Vibromera<\/a> \u2014 Engineering Calculators<\/p>\n    <p style=\"font-size:12px;margin-top:4px;\">Pneumatic cylinder force and speed. Last updated: June 2025<\/p>\n    <div class=\"vc-footer-links\">\n        <a href=\"\/calculators\/engineering-calculators\/\">All Calculators<\/a>\n        <a href=\"https:\/\/vibromera.eu\/contacts\/\">Contact<\/a>\n    <\/div>\n<\/footer>\n\n<\/div>\n\n<script src=\"https:\/\/cdn.jsdelivr.net\/npm\/katex@0.16.11\/dist\/katex.min.js\"><\/script>\n<script>\n(function() {\n    'use strict';\n\n    var SLUG = 'pneumatic-cylinder-calculator';\n    var unitSystem = 'metric';\n\n    function $(id) { return document.getElementById(id); }\n    function fmt(n, d) { if(isNaN(n)||!isFinite(n)) return '\u2014'; var f=n.toFixed(d===undefined?2:d); return f.replace(\/(\\.\\d*?)0+$\/,'$1').replace(\/\\.$\/,''); }\n\n    function calculate() {\n        var bore = parseFloat($('vc-bore').value);\n        var rod = parseFloat($('vc-rod').value);\n        var pressure = parseFloat($('vc-pressure').value);\n        var flow = parseFloat($('vc-flow').value);\n\n        if (!bore || bore <= 0 || !pressure || pressure <= 0) {\n            $('vc-results').classList.remove('vc-visible');\n            return;\n        }\n        if (!rod || rod < 0) rod = 0;\n\n        var boreMM, rodMM, pressurePa;\n        if (unitSystem === 'imperial') {\n            boreMM = bore * 25.4;\n            rodMM = rod * 25.4;\n            pressurePa = pressure * 6894.76; \/\/ psi to Pa\n        } else {\n            boreMM = bore;\n            rodMM = rod;\n            pressurePa = pressure * 1e5; \/\/ bar to Pa\n        }\n\n        var aBore = Math.PI \/ 4 * Math.pow(boreMM, 2); \/\/ mm\u00b2\n        var aAnn = Math.PI \/ 4 * (Math.pow(boreMM, 2) - Math.pow(rodMM, 2)); \/\/ mm\u00b2\n\n        var fExt = pressurePa * aBore * 1e-6; \/\/ N\n        var fRet = pressurePa * aAnn * 1e-6; \/\/ N\n\n        if (unitSystem === 'imperial') {\n            $('vc-r-fext').innerHTML = fmt(fExt * 0.224809, 1) + ' <span class=\"vc-rcard-unit\">lbf<\/span>';\n            $('vc-r-fret').innerHTML = fmt(fRet * 0.224809, 1) + ' <span class=\"vc-rcard-unit\">lbf<\/span>';\n            $('vc-r-abore').innerHTML = fmt(aBore \/ 645.16, 3) + ' <span class=\"vc-rcard-unit\">in\u00b2<\/span>';\n            $('vc-r-aann').innerHTML = fmt(aAnn \/ 645.16, 3) + ' <span class=\"vc-rcard-unit\">in\u00b2<\/span>';\n        } else {\n            $('vc-r-fext').innerHTML = fmt(fExt, 1) + ' <span class=\"vc-rcard-unit\">N<\/span> <span class=\"vc-rcard-unit\">(' + fmt(fExt \/ 9.80665, 1) + ' kgf)<\/span>';\n            $('vc-r-fret').innerHTML = fmt(fRet, 1) + ' <span class=\"vc-rcard-unit\">N<\/span> <span class=\"vc-rcard-unit\">(' + fmt(fRet \/ 9.80665, 1) + ' kgf)<\/span>';\n            $('vc-r-abore').innerHTML = fmt(aBore, 1) + ' <span class=\"vc-rcard-unit\">mm\u00b2<\/span>';\n            $('vc-r-aann').innerHTML = fmt(aAnn, 1) + ' <span class=\"vc-rcard-unit\">mm\u00b2<\/span>';\n        }\n\n        \/\/ Speed\n        if (flow && flow > 0) {\n            var flowMM3s;\n            if (unitSystem === 'imperial') {\n                flowMM3s = flow * 473.176; \/\/ CFM approx to mm\u00b3\/s (simplified)\n            } else {\n                flowMM3s = flow * 1e6 \/ 60; \/\/ L\/min to mm\u00b3\/s\n            }\n            var vExt = flowMM3s \/ aBore; \/\/ mm\/s\n            var vRet = flowMM3s \/ aAnn; \/\/ mm\/s\n            if (unitSystem === 'imperial') {\n                $('vc-r-vext').innerHTML = fmt(vExt \/ 25.4, 2) + ' <span class=\"vc-rcard-unit\">in\/s<\/span>';\n                $('vc-r-vret').innerHTML = fmt(vRet \/ 25.4, 2) + ' <span class=\"vc-rcard-unit\">in\/s<\/span>';\n            } else {\n                $('vc-r-vext').innerHTML = fmt(vExt, 1) + ' <span class=\"vc-rcard-unit\">mm\/s<\/span>';\n                $('vc-r-vret').innerHTML = fmt(vRet, 1) + ' <span class=\"vc-rcard-unit\">mm\/s<\/span>';\n            }\n        } else {\n            $('vc-r-vext').innerHTML = '\u2014';\n            $('vc-r-vret').innerHTML = '\u2014';\n        }\n\n        $('vc-results').classList.add('vc-visible');\n\n        var u = new URL(window.location);\n        u.searchParams.set('bore', $('vc-bore').value);\n        u.searchParams.set('rod', $('vc-rod').value);\n        u.searchParams.set('pressure', $('vc-pressure').value);\n        u.searchParams.set('flow', $('vc-flow').value);\n        history.replaceState(null, '', u.toString());\n\n        saveHistory({ bore: bore, rod: rod, pressure: pressure, flow: flow,\n            _summary: 'D=' + bore + (unitSystem==='imperial'?' in':' mm') + ', P=' + pressure + (unitSystem==='imperial'?' psi':' bar') });\n    }\n\n    var unitBtns = document.querySelectorAll('.vc-unit-btn');\n    unitBtns.forEach(function(btn) {\n        btn.addEventListener('click', function() {\n            unitBtns.forEach(function(b) { b.classList.remove('vc-active'); });\n            this.classList.add('vc-active');\n            unitSystem = this.getAttribute('data-system');\n            $('vc-bore-hint').textContent = unitSystem === 'imperial' ? '(in)' : '(mm)';\n            $('vc-rod-hint').textContent = unitSystem === 'imperial' ? '(in)' : '(mm)';\n            $('vc-pressure-hint').textContent = unitSystem === 'imperial' ? '(psi)' : '(bar)';\n            $('vc-flow-hint').textContent = unitSystem === 'imperial' ? '(CFM, optional)' : '(L\/min, optional)';\n            try { localStorage.setItem('vc_units', unitSystem); } catch(e) {}\n            calculate();\n        });\n    });\n\n    document.querySelectorAll('.vc-preset-btn').forEach(function(btn) {\n        btn.addEventListener('click', function(e) {\n            e.preventDefault();\n            $('vc-bore').value = this.getAttribute('data-b');\n            $('vc-rod').value = this.getAttribute('data-r');\n            $('vc-pressure').value = this.getAttribute('data-p');\n            $('vc-flow').value = this.getAttribute('data-q');\n            calculate();\n        });\n    });\n\n    $('vc-form').addEventListener('input', calculate);\n    $('vc-form').addEventListener('change', calculate);\n\n    $('vc-copy-btn').addEventListener('click', function() {\n        var text = 'Pneumatic Cylinder Calculation\\n\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\\n' +\n            'Bore: ' + $('vc-bore').value + (unitSystem==='imperial'?' in':' mm') + '\\n' +\n            'Rod: ' + $('vc-rod').value + (unitSystem==='imperial'?' in':' mm') + '\\n' +\n            'Pressure: ' + $('vc-pressure').value + (unitSystem==='imperial'?' psi':' bar') + '\\n' +\n            'Extend Force: ' + $('vc-r-fext').textContent + '\\n' +\n            'Retract Force: ' + $('vc-r-fret').textContent + '\\n' +\n            'Extend Speed: ' + $('vc-r-vext').textContent + '\\n' +\n            'Retract Speed: ' + $('vc-r-vret').textContent + '\\n' +\n            '\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\u2501\\nvibromera.eu';\n        if (navigator.clipboard) {\n            navigator.clipboard.writeText(text).then(function() {\n                var btn = $('vc-copy-btn');\n                btn.classList.add('vc-copied');\n                btn.innerHTML = '<svg width=\"14\" height=\"14\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><polyline points=\"20 6 9 17 4 12\"\/><\/svg> Copied!';\n                setTimeout(function() { btn.classList.remove('vc-copied'); btn.innerHTML = '<svg width=\"14\" height=\"14\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><rect x=\"9\" y=\"9\" width=\"13\" height=\"13\" rx=\"2\"\/><path d=\"M5 15H4a2 2 0 01-2-2V4a2 2 0 012-2h9a2 2 0 012 2v1\"\/><\/svg> Copy'; }, 2000);\n            });\n        }\n    });\n\n    document.querySelectorAll('.vc-section-toggle').forEach(function(btn) {\n        btn.addEventListener('click', function() {\n            var section = this.closest('.vc-section');\n            var isOpen = section.classList.contains('vc-open');\n            section.classList.toggle('vc-open');\n            this.setAttribute('aria-expanded', !isOpen);\n        });\n    });\n\n    var faqData = [\n        { q: 'How do I calculate pneumatic cylinder force?', a: '<p>Pneumatic cylinder extend force is F = P \u00d7 A, where P is supply pressure and A is bore area (\u03c0\/4 \u00d7 D\u00b2). For retract force, use the annular area: A = \u03c0\/4 \u00d7 (D\u00b2 \u2212 d\u00b2), where d is the rod diameter.<\/p>' },\n        { q: 'What is the difference between extend and retract force?', a: '<p>Extend force uses the full bore area and is always higher. Retract force uses the annular area (bore minus rod cross-section), giving less force. Retract speed is faster for the same flow rate since the volume is smaller.<\/p>' },\n        { q: 'How do I calculate piston speed?', a: '<p>Piston speed v = Q \/ A. For extend: v = Q \/ A_bore. For retract: v = Q \/ A_annular. The retract stroke is faster than extend at the same flow rate because the annular area is smaller.<\/p>' },\n        { q: 'What safety factor should I use for pneumatic cylinders?', a: '<p>A safety factor of 1.5\u20132.0 is typical. Seal friction reduces theoretical force by 5\u201320%. Also consider dynamic loads, acceleration forces, and pressure drops in the supply line.<\/p>' },\n        { q: 'Does friction affect actual cylinder force?', a: '<p>Yes. Seal friction typically reduces theoretical force by 5\u201320% depending on seal type (O-ring, lip seal), lubrication, and operating speed. At low speed, breakaway friction is higher than running friction.<\/p>' }\n    ];\n    var faqList = $('vc-faq-list');\n    faqData.forEach(function(faq) {\n        faqList.innerHTML += '<div class=\"vc-faq-item\"><button type=\"button\" class=\"vc-faq-q\"><span>' + faq.q + '<\/span><svg class=\"vc-faq-chevron\" viewBox=\"0 0 24 24\" fill=\"none\" stroke=\"currentColor\" stroke-width=\"2\"><path d=\"M6 9l6 6 6-6\"\/><\/svg><\/button><div class=\"vc-faq-a\"><div class=\"vc-faq-a-inner\">' + faq.a + '<\/div><\/div><\/div>';\n    });\n    faqList.addEventListener('click', function(e) {\n        var btn = e.target.closest('.vc-faq-q');\n        if (!btn) return;\n        btn.closest('.vc-faq-item').classList.toggle('vc-open');\n    });\n\n    function saveHistory(entry) {\n        var key = 'vc_history_' + SLUG;\n        var arr = [];\n        try { arr = JSON.parse(localStorage.getItem(key)) || []; } catch(e) {}\n        entry._ts = new Date().toISOString();\n        arr.unshift(entry);\n        if (arr.length > 10) arr = arr.slice(0, 10);\n        try { localStorage.setItem(key, JSON.stringify(arr)); } catch(e) {}\n    }\n\n    function loadParams() {\n        var p = new URLSearchParams(window.location.search);\n        p.forEach(function(v, k) { var el = $(k) || $('vc-' + k); if (el) el.value = v; });\n    }\n\n    function renderFormulas() {\n        try {\n            katex.render('F_{extend} = P \\\\times \\\\frac{\\\\pi}{4} D^2', $('vc-katex-1'), { displayMode: true, throwOnError: false });\n            katex.render('F_{retract} = P \\\\times \\\\frac{\\\\pi}{4} (D^2 - d^2)', $('vc-katex-2'), { displayMode: true, throwOnError: false });\n            katex.render('v = \\\\frac{Q}{A}', $('vc-katex-3'), { displayMode: true, throwOnError: false });\n        } catch(e) {}\n    }\n\n    function init() {\n        try {\n            var saved = localStorage.getItem('vc_units');\n            if (saved === 'imperial') {\n                unitSystem = 'imperial';\n                unitBtns.forEach(function(b) { b.classList.toggle('vc-active', b.getAttribute('data-system') === 'imperial'); });\n                $('vc-bore-hint').textContent = '(in)';\n                $('vc-rod-hint').textContent = '(in)';\n                $('vc-pressure-hint').textContent = '(psi)';\n                $('vc-flow-hint').textContent = '(CFM, optional)';\n            }\n        } catch(e) {}\n        loadParams();\n        renderFormulas();\n        calculate();\n    }\n\n    if (document.readyState === 'loading') document.addEventListener('DOMContentLoaded', init);\n    else init();\n})();\n<\/script>\n","protected":false},"excerpt":{"rendered":"<p>Gratis online kalkulator for pneumatiske sylindere. Beregn forlengelses- og tilbaketrekningskraft (F=P\u00d7A), stempelhastighet fra str\u00f8mningshastighet. Angi boring, stangdiameter og trykk.<\/p>","protected":false},"featured_media":0,"template":"","meta":{"ai_generated_summary":"","footnotes":""},"categories":[],"tags":[],"class_list":["post-100189","calculator","type-calculator","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/vibromera.eu\/nb\/wp-json\/wp\/v2\/calculator\/100189","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/vibromera.eu\/nb\/wp-json\/wp\/v2\/calculator"}],"about":[{"href":"https:\/\/vibromera.eu\/nb\/wp-json\/wp\/v2\/types\/calculator"}],"version-history":[{"count":2,"href":"https:\/\/vibromera.eu\/nb\/wp-json\/wp\/v2\/calculator\/100189\/revisions"}],"predecessor-version":[{"id":100920,"href":"https:\/\/vibromera.eu\/nb\/wp-json\/wp\/v2\/calculator\/100189\/revisions\/100920"}],"wp:attachment":[{"href":"https:\/\/vibromera.eu\/nb\/wp-json\/wp\/v2\/media?parent=100189"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/vibromera.eu\/nb\/wp-json\/wp\/v2\/categories?post=100189"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/vibromera.eu\/nb\/wp-json\/wp\/v2\/tags?post=100189"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}