{"id":59560,"date":"2016-04-02T09:51:15","date_gmt":"2016-04-02T07:51:15","guid":{"rendered":"http:\/\/wpcalc.com\/?p=59560"},"modified":"2026-09-29T14:57:50","modified_gmt":"2026-09-29T11:57:50","slug":"combined-gas-law","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/chemistry\/combined-gas-law\/","title":{"rendered":"Combined Gas Law 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\">Solve Combined Gas Law Problems<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"59560\" data-favorite-title=\"Combined Gas Law\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/chemistry\/combined-gas-law\/\" data-favorite-excerpt=\"Find an unknown initial or final pressure, volume, or temperature using the combined gas law. Select the value to calculate, then enter the other five values.\" 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\/combined-gas-law\/\" method=\"POST\" class=\"calculator\" id=\"calculator-59560\" data-post=\"59560\"><fieldset class=\"fieldset-input is-1\"><legend class=\"sr-only\">Input Fields<\/legend><div class=\"field is-single\" id=\"input-1\"><label for=\"field-1\">I want to calculate<\/label><div class=\"grid grid-cols-1\"><select id=\"field-1\" name=\"i_want_to_calculate\"><option value=\"vi\">Initial Volume (V\u1d62)<\/option><option value=\"pi\">Initial Pressure (P\u1d62)<\/option><option value=\"ti\">Initial Temperature (T\u1d62)<\/option><option value=\"vf\">Final Volume (Vf)<\/option><option value=\"pf\">Final Pressure (Pf)<\/option><option value=\"tf\">Final Temperature (Tf)<\/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><div class=\"field\" id=\"input-2\" hidden><label for=\"field-2\">Initial Volume (V\u1d62)<\/label><div class=\"field-group\"><input type=\"number\" name=\"initial_volume_v\" id=\"field-2\" step=\"any\" value=\"1\"\/><div class=\"grid grid-cols-1\"><select id=\"field-3\" name=\"unit\" aria-label=\"Unit\"><option value=\"l\">L<\/option><option value=\"ml\">mL<\/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><\/div><div class=\"field\" id=\"input-3\"><label for=\"field-4\">Initial Pressure (P\u1d62)<\/label><div class=\"field-group\"><input type=\"number\" name=\"initial_pressure_p\" id=\"field-4\" step=\"any\" value=\"100\"\/><div class=\"grid grid-cols-1\"><select id=\"field-5\" name=\"unit\" aria-label=\"Unit\"><option value=\"kpa\">kPa<\/option><option value=\"atm\">atm<\/option><option value=\"mmhg\">mmHg<\/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><\/div><div class=\"field\" id=\"input-4\"><label for=\"field-6\">Initial Temperature (T\u1d62)<\/label><input type=\"number\" name=\"initial_temperature_t\" id=\"field-6\" aria-describedby=\"calc-unit-6\" step=\"any\" value=\"273\"\/><div class=\"unit\" id=\"calc-unit-6\">K<\/div><\/div><div class=\"field\" id=\"input-5\"><label for=\"field-7\">Final Volume (Vf)<\/label><div class=\"field-group\"><input type=\"number\" name=\"final_volume_vf\" id=\"field-7\" step=\"any\" value=\"1\"\/><div class=\"grid grid-cols-1\"><select id=\"field-8\" name=\"unit\" aria-label=\"Unit\"><option value=\"l\">L<\/option><option value=\"ml\">mL<\/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><\/div><div class=\"field\" id=\"input-6\"><label for=\"field-9\">Final Pressure (Pf)<\/label><div class=\"field-group\"><input type=\"number\" name=\"final_pressure_pf\" id=\"field-9\" step=\"any\" value=\"100\"\/><div class=\"grid grid-cols-1\"><select id=\"field-10\" name=\"unit\" aria-label=\"Unit\"><option value=\"kpa\">kPa<\/option><option value=\"atm\">atm<\/option><option value=\"mmhg\">mmHg<\/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><\/div><div class=\"field\" id=\"input-7\"><label for=\"field-11\">Final Temperature (Tf)<\/label><input type=\"number\" name=\"final_temperature_tf\" id=\"field-11\" aria-describedby=\"calc-unit-11\" step=\"any\" value=\"293\"\/><div class=\"unit\" id=\"calc-unit-11\">K<\/div><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Re-Calculate\" id=\"calculate-button\" data-post=\"59560\">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> Your Results<\/h3><div class=\"result-box\"><div class=\"field-result is-column is-grid\" id=\"output-1\"><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><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=\"59560\" 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>Combined Gas Law Formula<\/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\\[ \\frac{P_i V_i}{T_i} = \\frac{P_f V_f}{T_f} \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Where:<\/strong><\/p>\n<ul>\n<li>\\(P_i\\) and \\(P_f\\) \u2014 initial and final absolute pressure<\/li>\n<li>\\(V_i\\) and \\(V_f\\) \u2014 initial and final volume<\/li>\n<li>\\(T_i\\) and \\(T_f\\) \u2014 initial and final temperature in kelvins (K)<\/li>\n<\/ul>\n<p>The combined gas law relates two states of the same amount of gas. Rearrange the equation to find any one of the six values when the other five are known.<\/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>Combined Gas Law \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Example:<\/strong> With the calculator\u2019s default values, find the initial volume when a gas starts at 100 kPa and 273 K, then reaches a volume of 1 L at 100 kPa and 293 K.<\/p>\n<p>\\[ V_i = \\frac{P_f V_f T_i}{P_i T_f} = \\frac{(100\\,\\mathrm{kPa})(1\\,\\mathrm{L})(273\\,\\mathrm{K})}{(100\\,\\mathrm{kPa})(293\\,\\mathrm{K})} \\approx 0.9317\\,\\mathrm{L} \\]<\/p>\n<p><strong>Result:<\/strong> The initial volume is 0.9317 L. At unchanged pressure, the gas occupies more space at the higher final temperature.<\/p>\n<p>\n\r\n<\/section>\n<h2>How to use the calculator<\/h2>\n<ol>\n<li>In <strong>I want to calculate<\/strong>, select the unknown: Initial Volume (V\u1d62), Initial Pressure (P\u1d62), Initial Temperature (T\u1d62), Final Volume (Vf), Final Pressure (Pf), or Final Temperature (Tf). The calculator hides the field you selected.<\/li>\n<li>Enter the five known values in the remaining initial and final fields. Use temperatures in K; the temperature fields do not accept Celsius or Fahrenheit as units.<\/li>\n<li>Choose L or mL for each volume field and kPa, atm, or mmHg for each pressure field. If you enter both volumes, give them the <strong>same volume unit<\/strong>: this calculator does not convert between L and mL in its calculation. It does convert pressure units internally.<\/li>\n<li>Read the calculated value in the result. A calculated pressure is displayed in kPa; a calculated volume uses the unit selected for the known volume.<\/li>\n<\/ol>\n<h2>What the combined gas law tells you<\/h2>\n<p>The combined gas law describes how pressure, volume, and absolute temperature change together for a fixed amount of gas. It states that \\(PV\/T\\) remains constant between an initial and a final state, provided the gas can be treated as ideal. Knowing five of the six initial and final values lets you determine the sixth.<\/p>\n<p>The relationship brings together two simpler patterns. At constant temperature, pressure and volume vary inversely, as described by <a href=\"https:\/\/wpcalc.com\/en\/chemistry\/boyles-law\/\">Boyle\u2019s law<\/a>: compressing a gas tends to raise its pressure. At constant pressure, volume is proportional to absolute temperature, as described by <a href=\"https:\/\/wpcalc.com\/en\/chemistry\/charles-law\/\">Charles\u2019 law<\/a>. The combined gas law handles changes in both pressure and temperature at once.<\/p>\n<p>Interpret the result alongside the conditions you entered. In the example, pressure stays at 100 kPa while temperature rises from 273 K to 293 K. The calculated initial volume is smaller than the known final volume, which fits the expectation that a warmer gas occupies more space if its pressure can remain constant. The law compares two states; it does not describe how quickly the gas changes between them.<\/p>\n<p>If you also need to calculate the amount of gas or relate a single state to its pressure, volume, and temperature, use the <a href=\"https:\/\/wpcalc.com\/en\/chemistry\/ideal-gas-law\/\">Ideal Gas Law Calculator<\/a>. The combined gas law does not require the amount of gas as an input because it assumes that amount is unchanged.<\/p>\n<h2>Assumptions and practical tips<\/h2>\n<ul>\n<li><strong>Keep the amount of gas constant.<\/strong> Do not use the combined gas law unchanged if gas enters, escapes, or reacts between the two states.<\/li>\n<li><strong>Use absolute temperature.<\/strong> Enter kelvins, not degrees Celsius. To convert a Celsius temperature to kelvins, add 273.15. Temperatures must be greater than 0 K for a physically meaningful calculation.<\/li>\n<li><strong>Use absolute pressure.<\/strong> A gauge pressure measures pressure relative to its surroundings and cannot be entered directly as though it were absolute pressure. Convert it to absolute pressure first.<\/li>\n<li><strong>Match volume units.<\/strong> Select L for both entered volumes or mL for both. For example, convert 500 mL to 0.5 L before comparing it with a volume entered in L.<\/li>\n<li><strong>Allow for real-gas behavior.<\/strong> The equation is an ideal-gas approximation. Results may be less reliable at high pressures, very low temperatures, or near condensation, where real gases can depart substantially from ideal behavior.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Find an unknown initial or final pressure, volume, or temperature using the combined gas law. Select the value to calculate, then enter the other five values.<\/p>\n","protected":false},"author":70,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[54],"tags":[55],"class_list":["post-59560","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\/59560","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\/70"}],"replies":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/comments?post=59560"}],"version-history":[{"count":5,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/59560\/revisions"}],"predecessor-version":[{"id":65572,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/59560\/revisions\/65572"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=59560"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=59560"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=59560"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}