{"id":66915,"date":"2026-10-13T10:13:19","date_gmt":"2026-10-13T07:13:19","guid":{"rendered":"https:\/\/wpcalc.com\/en\/?p=66915"},"modified":"2026-10-13T10:13:19","modified_gmt":"2026-10-13T07:13:19","slug":"mean-free-path-of-gas-molecules-calculator","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/chemistry\/mean-free-path-of-gas-molecules-calculator\/","title":{"rendered":"Mean Free Path of Gas Molecules Calculator"},"content":{"rendered":"<section class=\"not-prose calculator-box\" aria-labelledby=\"calculator-title\"><div class=\"flex items-baseline sm:items-center justify-between gap-2 sm:gap-3\"><div class=\"flex flex-col sm:flex-row sm:items-center gap-2\"><span class=\"icon icon-calculator text-primary-700! text-base! dark:text-primary-300!\" aria-hidden=\"true\"><\/span><h2 id=\"calculator-title\" class=\"text-lg font-display font-bold\">Find the Mean Free Path from Temperature, Pressure and Collision Diameter<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"66915\" data-favorite-title=\"Mean Free Path\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/chemistry\/mean-free-path-of-gas-molecules-calculator\/\" data-favorite-excerpt=\"Calculate the mean free path of gas molecules from temperature, pressure, and collision diameter. Enter the gas conditions in any common unit and get \u03bb in nm, \u00b5m, mm, or m.\" aria-label=\"Add to Favorites\" data-favorite-icon=\"icon icon-wind-2\">\n    <span class=\"icon icon-shape-star-empty\" aria-hidden=\"true\"><\/span>\n  <\/button>\n  <div class=\"calcdash-favorite__tip\" aria-hidden=\"true\">\n   <span class=\"favorite-tooltip\" id=\"favorite-tooltip\"><\/span>\n  <\/div>\n  <span class=\"sr-only\" role=\"status\" id=\"favorite-status\"><\/span>\n<\/div><\/div><form action=\"https:\/\/wpcalc.com\/en\/chemistry\/mean-free-path-of-gas-molecules-calculator\/\" method=\"POST\" class=\"calculator\" id=\"calculator-66915\" data-post=\"66915\"><fieldset class=\"fieldset-input is-2\"><legend class=\"sr-only\">Input Fields<\/legend><div class=\"field has-term\" id=\"input-1\"><label for=\"field-1\">Temperature (T)<\/label><div class=\"term\">T<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"number\" name=\"temperature_t\" id=\"field-1\" aria-describedby=\"calc-info-1\" placeholder=\"e.g. 25\" min=\"-270\" step=\"any\" value=\"25\"\/><div class=\"grid grid-cols-1\"><select id=\"field-2\" name=\"unit\" aria-label=\"Unit\"><option value=\"C\" selected>\u00b0C<\/option><option value=\"K\">K<\/option><option value=\"F\">\u00b0F<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><small id=\"calc-info-1\">Absolute temperature of the gas. Room temperature (25 \u00b0C \u2248 298 K) is a typical reference point.<\/small><\/div><div class=\"field has-term\" id=\"input-2\"><label for=\"field-3\">Pressure (p)<\/label><div class=\"term\">p<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"text\" name=\"pressure_p\" id=\"field-3\" aria-describedby=\"calc-info-3\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 1\" min=\"0\" value=\"1\"\/><div class=\"grid grid-cols-1\"><select id=\"field-4\" name=\"unit\" aria-label=\"Unit\"><option value=\"atm\" selected>atm<\/option><option value=\"kPa\">kPa<\/option><option value=\"Pa\">Pa<\/option><option value=\"bar\">bar<\/option><option value=\"mmHg\">mmHg (Torr)<\/option><option value=\"psi\">psi<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><small id=\"calc-info-3\">Absolute (not gauge) pressure of the gas. One atmosphere is the standard reference.<\/small><\/div><div class=\"field has-term\" id=\"input-3\"><label for=\"field-5\">Collision Diameter (d)<\/label><div class=\"term\">d<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><div class=\"field-group\"><input type=\"text\" name=\"collision_diameter_d\" id=\"field-5\" aria-describedby=\"calc-info-5\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 0.37\" min=\"0\" value=\"0.37\"\/><div class=\"grid grid-cols-1\"><select id=\"field-6\" name=\"unit\" aria-label=\"Unit\"><option value=\"nm\" selected>nm<\/option><option value=\"pm\">pm<\/option><option value=\"A\">\u00c5<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><small id=\"calc-info-5\">Effective molecular diameter assumed for a hard-sphere collision. N\u2082 \u2248 0.37 nm, O\u2082 \u2248 0.36 nm, Ar \u2248 0.34 nm, He \u2248 0.26 nm.<\/small><\/div><div class=\"field is-single\" id=\"input-4\"><label for=\"field-7\">Show Mean Free Path in<\/label><div class=\"grid grid-cols-1\"><select id=\"field-7\" name=\"show_mean_free_path_in\"><option value=\"nm\" selected>nanometers (nm)<\/option><option value=\"um\">micrometers (\u00b5m)<\/option><option value=\"mm\">millimeters (mm)<\/option><option value=\"m\">meters (m)<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Re-Calculate\" id=\"calculate-button\" data-post=\"66915\">Calculate<\/button><button type=\"reset\">Reset<\/button><\/div><div class=\"field is-checkbox hidden!\" id=\"field-auto-calc\"><input type=\"checkbox\" id=\"auto-calc\"><label for=\"auto-calc\">Calculate automatically<\/label><small>If enabled, the result will update automatically when you change any value.<\/small><\/div><div class=\"fieldset-result is-hidden\" aria-labelledby=\"result-title\" aria-live=\"polite\" role=\"region\"> <h3 class=\"result-title bg-gradient-to-r from-primary-50 to-gray-50 dark:from-primary-900 dark:to-gray-800\" id=\"result-title\"><span class=\"icon icon-s-pulse\" aria-hidden=\"true\"><\/span> Mean Free Path Results<\/h3><div class=\"result-box\"><div class=\"field-result\" id=\"output-1\"><span class=\"field-title\"><span>Mean Free Path (\u03bb)<\/span><span class=\"result-term\">\u03bb<\/span><\/span><span class=\"field-value\" id=\"result-1\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copy Result\" aria-label=\"Copy Result\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result is-column\" id=\"output-2\"><span class=\"field-title\"><span>In Other Units<\/span><\/span><span class=\"field-value\" id=\"result-2\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copy Result\" aria-label=\"Copy Result\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result is-column\" id=\"output-3\"><span class=\"field-title\"><span>Calculation Details<\/span><\/span><span class=\"field-value\" id=\"result-3\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copy Result\" aria-label=\"Copy Result\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><div class=\"field-result is-column\" id=\"output-4\"><span class=\"field-title\"><span>About the Mean Free Path<\/span><\/span><span class=\"field-value\" id=\"result-4\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copy Result\" aria-label=\"Copy Result\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><\/div><div class=\"result-actions\"><button type=\"button\" class=\"copy-link\"><svg viewBox=\"0 0 20 20\" fill=\"currentColor\" aria-hidden=\"true\"><path d=\"M12.232 4.232a2.5 2.5 0 0 1 3.536 3.536l-1.225 1.224a.75.75 0 0 0 1.061 1.06l1.224-1.224a4 4 0 0 0-5.656-5.656l-3 3a4 4 0 0 0 .225 5.865.75.75 0 0 0 .977-1.138 2.5 2.5 0 0 1-.142-3.667l3-3Z\"\/><path d=\"M11.603 7.963a.75.75 0 0 0-.977 1.138 2.5 2.5 0 0 1 .142 3.667l-3 3a2.5 2.5 0 0 1-3.536-3.536l1.225-1.224a.75.75 0 0 0-1.061-1.06l-1.224 1.224a4 4 0 1 0 5.656 5.656l3-3a4 4 0 0 0-.225-5.865Z\"\/><\/svg><span class=\"copy-link__text\">Copy link to this calculation<\/span><\/button><span class=\"sr-only\" role=\"status\" id=\"copy-link-status\"><\/span><\/div><\/div><a href=\"#respond\" class=\"hidden transition-opacity duration-300 opacity-0 w-50 text-sm justify-center items-center gap-2 px-4 py-2 rounded bg-gray-200 text-gray-700 hover:bg-gray-300\" id=\"leave-comment\"><span class=\"icon icon-comments\" aria-hidden=\"true\"><\/span>Leave a Comment<\/a><\/form><\/section><section id=\"calc-reactions\" class=\"not-prose hidden my-12 bg-gradient-to-r from-primary-50 to-gray-50 border border-indigo-100 rounded-xl px-6 py-4 shadow-sm\" data-post=\"66915\" aria-live=\"polite\" aria-labelledby=\"calc-reactions-title\"><p id=\"calc-reactions-title\" class=\"text-sm text-gray-500 text-center mb-2\">How did this result make you feel?<\/p><div role=\"group\" aria-labelledby=\"calc-reactions-title\" class=\"grid grid-cols-3 sm:flex sm:flex-row sm:justify-around gap-4 sm:items-center sm:flex-wrap\"><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"like\"><span class=\"reaction-count\" data-reaction-count=\"like\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude00 <\/span><span class=\"reaction-description font-medium\">Like <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"helpful\"><span class=\"reaction-count\" data-reaction-count=\"helpful\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\udca1 <\/span><span class=\"reaction-description font-medium\">Helpful <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"confused\"><span class=\"reaction-count\" data-reaction-count=\"confused\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude15 <\/span><span class=\"reaction-description font-medium\">Confused <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"disappointed\"><span class=\"reaction-count\" data-reaction-count=\"disappointed\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude1e <\/span><span class=\"reaction-description font-medium\">Disappointed <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"inaccurate\"><span class=\"reaction-count\" data-reaction-count=\"inaccurate\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\u274c <\/span><span class=\"reaction-description font-medium\">Inaccurate <\/span><\/button><\/div><div id=\"reaction-message\" class=\"hidden mt-8 rounded-md border border-primary-100 bg-white\/50 backdrop-blur-sm px-4 py-2 text-sm text-center shadow-sm\"><\/div><\/section><div class=\"calcdash-ad not-prose calcdash-ad--calc_result calcdash-ad--in-article\"><ins class=\"adsbygoogle\" style=\"display:block\" data-ad-client=\"ca-pub-1721569815777345\" data-ad-slot=\"6317458308\" data-ad-layout=\"in-article\" data-ad-format=\"fluid\"><\/ins><script>(adsbygoogle = window.adsbygoogle || []).push({});<\/script><\/div>\n<style id=\"wpcoderpro-inline-1\">.formula-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section class=\"formula-box\" aria-labelledby=\"formula-title\">\r\n\t<div id=\"formula-title\" class=\"not-prose font-display mb-4\"><span class=\"icon icon-formula\" aria-hidden=\"true\"><\/span><h2>Mean Free Path<\/h2><\/div>\r\n\t<figure class=\"not-prose formula\">\r\n\t\t<figcaption class=\"formula-title\">Formula<\/figcaption>\r\n\t\t<div class=\"text-base text-gray-800\" id=\"formula\">\n\\[ \\lambda = \\frac{k\\,T}{\\sqrt{2}\\,\\pi\\,d^{2}\\,p} = \\frac{1}{\\sqrt{2}\\,\\sigma\\,n} \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Where:<\/strong><\/p>\n<ul>\n<li>\\(\\lambda\\) \u2014 mean free path, the average distance a molecule travels between collisions (m)<\/li>\n<li>\\(k = 1.380649\\times10^{-23}\\) J\/K \u2014 the Boltzmann constant (exact SI value)<\/li>\n<li>\\(T\\) \u2014 absolute temperature of the gas (K)<\/li>\n<li>\\(d\\) \u2014 molecular collision diameter, hard-sphere model (m)<\/li>\n<li>\\(p\\) \u2014 absolute pressure of the gas (Pa)<\/li>\n<li>\\(\\sigma = \\pi d^{2}\\) \u2014 collision cross-section (m\u00b2)<\/li>\n<li>\\(n = p\/(kT)\\) \u2014 number density of molecules (m\u207b\u00b3)<\/li>\n<\/ul>\n<p>The formula comes from the kinetic theory of a dilute gas: a molecule sweeps out a collision volume \\(\\sigma\\) per unit distance traveled, and the \\(\\sqrt{2}\\) factor accounts for the relative motion of the colliding pairs.<\/p>\n<p>\r\n<\/section>\n<style id=\"wpcoderpro-inline-459\">.calculation-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section id=\"calculation\" class=\"calculation-box\" aria-labelledby=\"calculation-title\">\r\n\t<div id=\"calculation-title\" class=\"not-prose font-display\"><span class=\"icon icon-unordered-list\" aria-hidden=\"true\"><\/span><h2>Mean Free Path \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Example:<\/strong> nitrogen gas at room temperature and atmospheric pressure (25 \u00b0C, 1 atm), with a collision diameter of 0.37 nm \u2014 the default values of the calculator.<\/p>\n<p>\\[ T = 25 + 273.15 = 298.15\\ \\text{K}, \\quad p = 1\\ \\text{atm} = 101{,}325\\ \\text{Pa}, \\quad d = 0.37\\ \\text{nm} = 3.7\\times10^{-10}\\ \\text{m} \\]<\/p>\n<p>\\[ \\sigma = \\pi d^{2} = \\pi \\times (3.7\\times10^{-10})^{2} = 4.30\\times10^{-19}\\ \\text{m}^{2} \\]<\/p>\n<p>\\[ \\lambda = \\frac{1.380649\\times10^{-23} \\times 298.15}{\\sqrt{2} \\times \\pi \\times (3.7\\times10^{-10})^{2} \\times 101{,}325} = \\frac{4.116\\times10^{-21}}{6.162\\times10^{-14}} \\]<\/p>\n<p><strong>Result:<\/strong> \\(\\lambda \\approx 6.68\\times10^{-8}\\) m \u2248 <strong>66.8 nm<\/strong>. A nitrogen molecule at room conditions flies on average about 67 nanometers \u2014 roughly 180 molecular diameters \u2014 before hitting another molecule.<\/p>\n<p>\n\r\n<\/section>\n<h2>How to Use the Calculator<\/h2>\n<ol>\n<li>Enter the gas <strong>Temperature (T)<\/strong> and choose its unit (\u00b0C, K, or \u00b0F). Use absolute temperature scales correctly \u2014 25 \u00b0C is converted to 298.15 K automatically.<\/li>\n<li>Enter the <strong>Pressure (p)<\/strong> with its unit (atm, kPa, Pa, bar, mmHg\/Torr, or psi). Make sure this is the absolute pressure, not gauge pressure.<\/li>\n<li>Enter the <strong>Collision Diameter (d)<\/strong> of the molecules in nm, pm, or \u00c5. Typical values: N\u2082 \u2248 0.37 nm, O\u2082 \u2248 0.36 nm, Ar \u2248 0.34 nm, He \u2248 0.26 nm.<\/li>\n<li>Select the output unit under <strong>Show Mean Free Path in<\/strong> \u2014 nanometers suit near-atmospheric pressures, micrometers or meters suit vacuum conditions.<\/li>\n<li>Read the mean free path (\u03bb), its value in all common length units, and a step-by-step breakdown of the calculation.<\/li>\n<\/ol>\n<h2>What Is the Mean Free Path?<\/h2>\n<p>The mean free path \\(\\lambda\\) is the average distance a gas molecule travels between two successive collisions with other molecules. In air at sea level it is only about 70 nm \u2014 a molecule collides billions of times per second. In a high-vacuum chamber the same gas can have a mean free path of centimeters or meters, meaning molecules fly mostly unimpeded until they strike the chamber walls.<\/p>\n<p>The value is set by two competing effects. The number density \\(n = p\/(kT)\\) tells you how crowded the gas is: more molecules per cubic meter mean shorter flights. The collision cross-section \\(\\sigma = \\pi d^2\\) tells you how large a target each molecule presents. Combining them gives \\(\\lambda = 1\/(\\sqrt{2}\\,\\sigma\\,n)\\), which is equivalent to the pressure form used by this calculator.<\/p>\n<p>The result scales in intuitive ways: <strong>halving the pressure doubles \\(\\lambda\\)<\/strong>, raising the temperature at fixed pressure increases \\(\\lambda\\) proportionally, and <strong>doubling the molecular diameter cuts \\(\\lambda\\) fourfold<\/strong> because the cross-section grows with \\(d^2\\). This is why the mean free path is the key parameter in vacuum technology: it determines whether a gas flows as a continuum or in the free-molecular (Knudsen) regime.<\/p>\n<p>If you also want to know how fast the molecules move between those collisions, combine this result with the <a href=\"https:\/\/wpcalc.com\/en\/chemistry\/molecular-speed-of-a-gas-calculator\/\">Molecular Speed of a Gas calculator<\/a> \u2014 dividing the mean speed by the mean free path gives the collision frequency.<\/p>\n<h2>Interpreting the Result<\/h2>\n<p>The \"In Other Units\" block also reports the number density \\(n\\) and the mean spacing between molecules, \\(n^{-1\/3}\\). A useful sanity check: the mean free path should be much larger than both the molecular diameter and the molecular spacing (for air, roughly 180 spacings). If \\(\\lambda\\) becomes comparable to the size of your apparatus, you are in the molecular-flow regime, where concepts like viscosity and continuum pressure lose their usual meaning.<\/p>\n<p>Related gas properties you can compute with our other tools include the <a href=\"https:\/\/wpcalc.com\/en\/chemistry\/gas-density-calculator\/\">Gas Density calculator<\/a> and the <a href=\"https:\/\/wpcalc.com\/en\/chemistry\/avogadros-law-calculator\/\">Avogadro's Law calculator<\/a>, which links the number of molecules to volume at fixed temperature and pressure.<\/p>\n<h2>Assumptions and Limitations<\/h2>\n<ul>\n<li><strong>Hard-sphere model:<\/strong> molecules are treated as rigid spheres of a single diameter. Real molecules interact through soft, long-ranged potentials, so tabulated collision diameters are effective values usually fitted to viscosity data \u2014 expect results accurate to roughly \u00b120%.<\/li>\n<li><strong>Dilute, ideal gas:<\/strong> the formula assumes \\(\\lambda \\gg d\\), i.e. collisions are brief binary events. It fails for dense gases and near condensation; for dense or non-ideal conditions see the <a href=\"https:\/\/wpcalc.com\/en\/chemistry\/van-der-waals-equation-calculator\/\">Van der Waals Equation calculator<\/a>.<\/li>\n<li><strong>Single-component gas:<\/strong> one uniform diameter is assumed. For gas mixtures, an effective diameter must be estimated (e.g. from viscosity data of the mixture).<\/li>\n<li><strong>Maxwell\u2013Boltzmann distribution:<\/strong> the \\(\\sqrt{2}\\) factor relies on the equilibrium velocity distribution, which holds for most practical conditions.<\/li>\n<li><strong>Absolute pressure required:<\/strong> gauge pressure reads zero at 1 atm but the physics depends on absolute pressure. Subtract nothing \u2014 if your gauge reads 0 bar at ambient, enter ~1 atm, not 0 (zero pressure is rejected anyway).<\/li>\n<\/ul>\n<h2>Typical Values at 25 \u00b0C<\/h2>\n<table>\n<thead>\n<tr>\n<th>Pressure<\/th>\n<th>\u03bb for N\u2082 (d = 0.37 nm)<\/th>\n<th>Regime<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>1 atm (101 325 Pa)<\/td>\n<td>\u2248 67 nm<\/td>\n<td>Continuum flow<\/td>\n<\/tr>\n<tr>\n<td>1\/100 atm \u2248 1 013 Pa<\/td>\n<td>\u2248 6.7 \u00b5m<\/td>\n<td>Transitional<\/td>\n<\/tr>\n<tr>\n<td>1 Pa<\/td>\n<td>\u2248 6.8 \u00b5m<\/td>\n<td>Knudsen flow begins<\/td>\n<\/tr>\n<tr>\n<td>10\u207b\u2076 atm (high vacuum)<\/td>\n<td>\u2248 6.7 cm<\/td>\n<td>Molecular flow<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Note how quickly \u03bb grows as pressure drops \u2014 a factor of 10 in pressure gives a factor of 10 in mean free path at constant temperature.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Calculate the mean free path of gas molecules from temperature, pressure, and collision diameter. Enter the gas conditions in any common unit and get \u03bb in nm, \u00b5m, mm, or m.<\/p>\n","protected":false},"author":3168,"featured_media":0,"comment_status":"open","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[54],"tags":[55],"class_list":["post-66915","post","type-post","status-publish","format-standard","hentry","category-chemistry","tag-gases"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66915","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/users\/3168"}],"replies":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/comments?post=66915"}],"version-history":[{"count":1,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66915\/revisions"}],"predecessor-version":[{"id":66916,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66915\/revisions\/66916"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=66915"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=66915"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=66915"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}