{"id":59528,"date":"2016-03-24T18:19:20","date_gmt":"2016-03-24T16:19:20","guid":{"rendered":"http:\/\/wpcalc.com\/?p=59528"},"modified":"2026-09-28T14:17:08","modified_gmt":"2026-09-28T11:17:08","slug":"arrhenius-equation-2","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/chemistry\/arrhenius-equation-2\/","title":{"rendered":"Arrhenius Equation 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\">Calculate Reaction Rate Constant Using Arrhenius Equation<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"59528\" data-favorite-title=\"Arrhenius Equation\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/chemistry\/arrhenius-equation-2\/\" data-favorite-excerpt=\"Calculate a reaction rate constant with the Arrhenius equation. Enter the frequency factor, activation energy in kJ\/mol, and temperature in kelvin.\" aria-label=\"Add to Favorites\" data-favorite-icon=\"icon icon-chemistry-1\">\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\/arrhenius-equation-2\/\" method=\"POST\" class=\"calculator\" id=\"calculator-59528\" data-post=\"59528\"><fieldset class=\"fieldset-input is-3\"><legend class=\"sr-only\">Input Fields<\/legend><div class=\"field\" id=\"input-1\"><label for=\"field-1\">Frequency Factor (A)<\/label><input type=\"number\" name=\"frequency_factor_a\" id=\"field-1\" step=\"any\" value=\"1e7\"\/><\/div><div class=\"field\" id=\"input-2\"><label for=\"field-2\">Activation Energy (Ea)<\/label><input type=\"number\" name=\"activation_energy_ea\" id=\"field-2\" aria-describedby=\"calc-unit-2\" step=\"0.01\" value=\"50\"\/><div class=\"unit\" id=\"calc-unit-2\">kJ\/mol<\/div><\/div><div class=\"field\" id=\"input-3\"><label for=\"field-3\">Temperature (T)<\/label><input type=\"number\" name=\"temperature_t\" id=\"field-3\" aria-describedby=\"calc-unit-3\" step=\"0.01\" value=\"298.15\"\/><div class=\"unit\" id=\"calc-unit-3\">K<\/div><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Re-Calculate\" id=\"calculate-button\" data-post=\"59528\">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\" id=\"output-1\"><span class=\"field-title\"><span>Reaction Rate Constant (k)<\/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><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=\"59528\" 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>Arrhenius Equation 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\\[ k = A e^{-\\frac{1000E_a}{RT}} \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Where:<\/strong><\/p>\n<ul>\n<li>\\(k\\) \u2014 reaction rate constant<\/li>\n<li>\\(A\\) \u2014 frequency factor, or pre-exponential factor<\/li>\n<li>\\(E_a\\) \u2014 activation energy entered in kJ\/mol<\/li>\n<li>\\(R\\) \u2014 gas constant, 8.314 J\/(mol\u00b7K)<\/li>\n<li>\\(T\\) \u2014 absolute temperature in kelvin (K)<\/li>\n<\/ul>\n<p>The factor of 1000 converts the entered activation energy from kJ\/mol to J\/mol so its units match \\(R\\). The equation describes how the rate constant depends on temperature when \\(A\\) and \\(E_a\\) are treated as constant.<\/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>Arrhenius Equation \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Example:<\/strong> A reaction has a frequency factor of \\(1\\times10^7\\) s\u207b\u00b9 and an activation energy of 50 kJ\/mol. Find its rate constant at 298.15 K.<\/p>\n<p>\\[ E_a=50\\times1000=50{,}000\\ \\text{J\/mol} \\]<\/p>\n<p>\\[ k=(1\\times10^7)e^{-\\frac{50{,}000}{8.314\\times298.15}}\\approx1.7374\\times10^{-2}\\ \\text{s}^{-1} \\]<\/p>\n<p><strong>Result:<\/strong> \\(k\\approx0.017374\\) s\u207b\u00b9, displayed by the calculator as approximately 1.7374e-2 sec\u207b\u00b9.<\/p>\n<p>\n\r\n<\/section>\n<h2>How to use the calculator<\/h2>\n<ol>\n<li>Enter the <strong>Frequency Factor (A)<\/strong>. For a first-order reaction, use a value in s\u207b\u00b9.<\/li>\n<li>Enter the <strong>Activation Energy (Ea)<\/strong> in kJ\/mol. The calculator converts it to J\/mol internally; do not convert it before entering it.<\/li>\n<li>Enter the <strong>Temperature (T)<\/strong> in kelvin. To convert from degrees Celsius, add 273.15.<\/li>\n<li>Read the <strong>Reaction Rate Constant (k)<\/strong>. The result is shown in scientific notation and labeled sec\u207b\u00b9.<\/li>\n<\/ol>\n<h2>What the Arrhenius equation tells you<\/h2>\n<p>The Arrhenius equation connects temperature with a chemical reaction\u2019s rate constant. Activation energy represents an energy barrier associated with the reaction. At a higher temperature, the exponential factor \\(e^{-E_a\/(RT)}\\) is larger, so the calculated rate constant increases when the other inputs stay the same. The frequency factor \\(A\\) sets the scale of the result; it is a fitted parameter, not simply a count of collisions.<\/p>\n<p>A rate constant is not the same as a reaction rate. The rate constant is a parameter in a rate law, while the rate at a particular moment can also depend on reactant concentrations and the reaction orders. A larger \\(k\\) generally indicates a faster reaction under comparable conditions, but comparing constants from different rate laws requires care. Balancing a reaction with the <a href=\"https:\/\/wpcalc.com\/en\/chemistry\/balancing-chemical-equations\/\">Chemical Equation Balancer<\/a> establishes its stoichiometry; it does not determine its rate law or activation energy.<\/p>\n<p>Activation energy controls how strongly the rate constant responds to a temperature change. When two reactions have the same starting temperature and comparable activation energies, the one with the higher activation energy generally has the larger proportional change in \\(k\\) for a given temperature increase. The equation is therefore useful for estimating a rate constant at a specified temperature when appropriate values of \\(A\\) and \\(E_a\\) are known.<\/p>\n<h2>Assumptions and practical limits<\/h2>\n<ul>\n<li><strong>Use absolute temperature.<\/strong> Enter kelvin, not degrees Celsius or Fahrenheit. Temperature must be greater than 0 K.<\/li>\n<li><strong>Check the units of \\(A\\).<\/strong> The rate constant has the same units as \\(A\\). This calculator always labels its output sec\u207b\u00b9, which is appropriate for a first-order rate constant. For other reaction orders, the numerical calculation still follows the equation, but the displayed unit may be incorrect.<\/li>\n<li><strong>Use parameters for the same reaction and conditions.<\/strong> Values of \\(A\\) and \\(E_a\\) are usually obtained from experimental data. A reaction mechanism, catalyst, or medium change can make previously fitted values unsuitable.<\/li>\n<li><strong>Avoid extrapolating too far.<\/strong> Treating \\(A\\) and \\(E_a\\) as constant may give a poor estimate outside the temperature range used to determine them.<\/li>\n<li><strong>Expect scientific notation.<\/strong> A result such as 1.7374e-2 means \\(1.7374\\times10^{-2}\\), or 0.017374. The calculator displays four digits after the decimal point in its scientific-notation value; this formatting does not indicate the precision of the inputs.<\/li>\n<\/ul>\n<p>The gas constant also appears in calculations such as the <a href=\"https:\/\/wpcalc.com\/en\/chemistry\/ideal-gas-law\/\">Ideal Gas Law<\/a>, but here it must be expressed in J\/(mol\u00b7K) to match the activation energy after conversion. If you are working from measured temperatures, check the temperature scale before using either equation.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Calculate a reaction rate constant with the Arrhenius equation. Enter the frequency factor, activation energy in kJ\/mol, and temperature in kelvin.<\/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":[57],"class_list":["post-59528","post","type-post","status-publish","format-standard","hentry","category-chemistry","tag-reactions"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/59528","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=59528"}],"version-history":[{"count":3,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/59528\/revisions"}],"predecessor-version":[{"id":65392,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/59528\/revisions\/65392"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=59528"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=59528"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=59528"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}