{"id":66877,"date":"2026-10-13T10:04:15","date_gmt":"2026-10-13T07:04:15","guid":{"rendered":"https:\/\/wpcalc.com\/en\/?p=66877"},"modified":"2026-10-13T10:04:15","modified_gmt":"2026-10-13T07:04:15","slug":"reaction-order-from-initial-rates-calculator","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/chemistry\/reaction-order-from-initial-rates-calculator\/","title":{"rendered":"Reaction Order from Initial Rates 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 Reaction Order from a Table of Initial Rates<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"66877\" data-favorite-title=\"Reaction Order from Initial Rates\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/chemistry\/reaction-order-from-initial-rates-calculator\/\" data-favorite-excerpt=\"Enter the concentration and initial rate measured in each experiment, and this calculator determines the reaction order n, the rate constant k, and the full rate law using the method of initial rates.\" 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\/reaction-order-from-initial-rates-calculator\/\" method=\"POST\" class=\"calculator\" id=\"calculator-66877\" data-post=\"66877\"><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\">Experiments \u2014 Concentration ; Initial Rate<\/label><textarea id=\"field-1\" name=\"experiments_concentration_initial_rate\">0.10; 5.0e-4; 0.20; 1.0e-3; 0.40; 2.0e-3<\/textarea><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Re-Calculate\" id=\"calculate-button\" data-post=\"66877\">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> Reaction Order and Rate Constant<\/h3><div class=\"result-box\"><div class=\"field-result\" id=\"output-1\"><span class=\"field-title\"><span>Reaction Order<\/span><span class=\"result-term\">n<\/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\" id=\"output-2\"><span class=\"field-title\"><span>Rate Constant<\/span><span class=\"result-term\">k<\/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>Rate Law<\/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>Experiments and Pairwise Orders<\/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 class=\"field-result is-column\" id=\"output-5\"><span class=\"field-title\"><span>Calculation Details<\/span><\/span><span class=\"field-value\" id=\"result-5\"><\/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=\"66877\" 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>Reaction Order from Initial Rates 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\\[ r = k\\,[A]^n \\quad\\Longrightarrow\\quad n = \\frac{\\ln(r_2\/r_1)}{\\ln([A]_2\/[A]_1)}, \\qquad k = \\frac{r}{[A]^n} \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Where:<\/strong><\/p>\n<ul>\n<li>\\(r_1, r_2\\) \u2014 initial rates measured in two experiments (mol\u00b7L\u207b\u00b9\u00b7s\u207b\u00b9)<\/li>\n<li>\\([A]_1, [A]_2\\) \u2014 the corresponding reactant concentrations (mol\/L)<\/li>\n<li>\\(n\\) \u2014 reaction order with respect to reactant A<\/li>\n<li>\\(k\\) \u2014 rate constant (unit depends on \\(n\\))<\/li>\n<\/ul>\n<p>The formula follows from taking the logarithm of the rate law \\(r = k[A]^n\\): since \\(k\\) cancels when the concentration of A is the only thing that changes between two runs, the ratio of the two rates isolates the order \\(n\\).<\/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>Reaction Order \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Example:<\/strong> three experiments were run at 25 \u00b0C with only the concentration of reactant A varied. The initial rates were: [A] = 0.10 M gives 5.0\u00d710\u207b\u2074 M\/s; [A] = 0.20 M gives 1.0\u00d710\u207b\u00b3 M\/s; [A] = 0.40 M gives 2.0\u00d710\u207b\u00b3 M\/s.<\/p>\n<p>\\[ n = \\frac{\\ln\\left(1.0\\times10^{-3} \/ 5.0\\times10^{-4}\\right)}{\\ln(0.20\/0.10)} = \\frac{\\ln 2}{\\ln 2} = 1 \\]<\/p>\n<p>The other pair (0.20 \u2192 0.40 M) gives the same result, so the mean order is \\(n = 1\\). The rate constant from each run:<\/p>\n<p>\\[ k = \\frac{r}{[A]^1} = \\frac{5.0\\times10^{-4}}{0.10} = \\frac{1.0\\times10^{-3}}{0.20} = \\frac{2.0\\times10^{-3}}{0.40} = 5.0\\times10^{-3}\\ \\text{s}^{-1} \\]<\/p>\n<p><strong>Result:<\/strong> \\(n = 1\\) (first order with respect to A), \\(k = 5.0\\times10^{-3}\\ \\text{s}^{-1}\\), and the rate law is \\(r = 5.0\\times10^{-3}[A]\\). Doubling [A] doubles the rate.<\/p>\n<p>\n\r\n<\/section>\n<h2>How to Use the Calculator<\/h2>\n<ol>\n<li>In the <strong>Experiments \u2014 Concentration ; Initial Rate<\/strong> field, enter the data as pairs: the reactant concentration in mol\/L followed by its measured initial rate in mol\/(L\u00b7s).<\/li>\n<li>Separate the values with spaces, semicolons or new lines \u2014 the default entry <code>0.10; 5.0e-4; 0.20; 1.0e-3; 0.40; 2.0e-3<\/code> shows the expected format.<\/li>\n<li>Scientific notation (<code>5.0e-4<\/code>) and decimal commas (<code>0,10<\/code>) are both accepted.<\/li>\n<li>Provide at least two experiments with <em>different<\/em> concentrations; more data points give a more reliable order.<\/li>\n<li>Read the results: the <strong>Reaction Order<\/strong> \\(n\\), the <strong>Rate Constant<\/strong> \\(k\\) with its unit, the fitted <strong>Rate Law<\/strong>, a table of <strong>Experiments and Pairwise Orders<\/strong>, and the <strong>Calculation Details<\/strong> explaining every step.<\/li>\n<\/ol>\n<h2>What Is Reaction Order and Why Does It Matter?<\/h2>\n<p>The <strong>order of a reaction<\/strong> with respect to a reactant A is the exponent \\(n\\) in the rate law \\(r = k[A]^n\\). It tells you how sensitively the rate responds to a change in concentration: when [A] doubles, a zero-order rate stays the same, a first-order rate doubles, and a second-order rate quadruples. The order is an <em>experimental<\/em> quantity \u2014 it cannot be read off the balanced equation, because it reflects the actual mechanism by which the reaction proceeds, not just its overall stoichiometry.<\/p>\n<p>The <strong>method of initial rates<\/strong> is the classic way to measure it. You run the reaction several times, changing only the initial concentration of A while keeping everything else \u2014 other reactants, temperature, solvent \u2014 fixed. Because you compare the very first moments of the reaction (\\(t \\approx 0\\)), the concentrations are still essentially the ones you prepared, reverse reactions have not yet built up products, and complications from changing concentrations during the run are avoided.<\/p>\n<p>The calculator compares every pair of consecutive distinct concentrations, computes an order for each pair, and averages them. If all pairs agree, the data are consistent with a single rate law, and the mean value is reported together with the rate constant \\(k\\), obtained by dividing each measured rate by \\([A]^n\\). Interpreting the result is straightforward: \\(n = 0\\), 1, 2 or 3 means zero-, first-, second- or third-order behavior; a value near 0.5 or other fractions often signals a chain or complex mechanism, while wildly inconsistent pairwise orders point to bad data or a rate law that is not a simple power of [A].<\/p>\n<p>Once \\(n\\) and \\(k\\) are known, you can predict the rate at any concentration, compare the speed of different reactants in the same process, or plug the order into kinetic models \u2014 for example, a first-order reaction has the well-known constant half-life you can explore with the <a href=\"https:\/\/wpcalc.com\/en\/chemistry\/reaction-half-life-calculator\/\">Reaction Half-Life Calculator<\/a>.<\/p>\n<h2>Assumptions, Limitations and Practical Tips<\/h2>\n<ul>\n<li><strong>One reactant at a time.<\/strong> The calculator finds the order with respect to A only. To get the overall order of a multi-reactant reaction, repeat the experiments varying each reactant separately while the others are held constant (or kept in large excess). The individual orders then add up to the overall order.<\/li>\n<li><strong>Concentrations in mol\/L and rates in mol\u00b7L\u207b\u00b9\u00b7s\u207b\u00b9<\/strong> are assumed, so \\(k\\) carries the unit s\u207b\u00b9 for first order, M\u00b7s\u207b\u00b9 for zero order, M\u207b\u00b9\u00b7s\u207b\u00b9 for second order, and in general M<sup>1\u2212n<\/sup>\u00b7s\u207b\u00b9.<\/li>\n<li><strong>Constant temperature is essential.<\/strong> \\(k\\) is strongly temperature-dependent (see the <a href=\"https:\/\/wpcalc.com\/en\/chemistry\/van-t-hoff-equation-calculator\/\">Van 't Hoff Equation Calculator<\/a> for how equilibrium constants, and similarly rate constants, change with temperature). All experiments should be run at the same temperature.<\/li>\n<li><strong>True initial rates.<\/strong> The tabulated rate must be the instantaneous rate at \\(t \\approx 0\\), usually obtained from the slope of a concentration\u2013time curve at the start. Rates averaged over a long interval will distort the order.<\/li>\n<li><strong>Repeated concentrations are averaged.<\/strong> If two experiments share the same [A], their rates are averaged before the order is computed; a warning appears if the duplicate rates disagree strongly.<\/li>\n<li><strong>Check the spread.<\/strong> If the calculator reports pairwise orders that differ by more than about 0.1, the data are not internally consistent \u2014 re-measure the rates or consider that the order may change with concentration (e.g. saturation kinetics).<\/li>\n<li><strong>Fractional and negative orders exist.<\/strong> Orders like \u00bd (chain reactions, thermal decomposition) or \u22121 (inhibition by a product or catalyst poison) are chemically real, but they should be confirmed with extra data points.<\/li>\n<\/ul>\n<h2>Typical Orders and Their Meaning<\/h2>\n<table>\n<thead>\n<tr>\n<th>Order n<\/th>\n<th>Effect of doubling [A]<\/th>\n<th>Unit of k<\/th>\n<th>Common example<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>0<\/td>\n<td>rate unchanged<\/td>\n<td>M\u00b7s\u207b\u00b9<\/td>\n<td>photochemical reactions; enzyme saturation<\/td>\n<\/tr>\n<tr>\n<td>1<\/td>\n<td>rate \u00d72<\/td>\n<td>s\u207b\u00b9<\/td>\n<td>radioactive-style decay; many decompositions<\/td>\n<\/tr>\n<tr>\n<td>2<\/td>\n<td>rate \u00d74<\/td>\n<td>M\u207b\u00b9\u00b7s\u207b\u00b9<\/td>\n<td>dimerization; HI decomposition<\/td>\n<\/tr>\n<tr>\n<td>3<\/td>\n<td>rate \u00d78<\/td>\n<td>M\u207b\u00b2\u00b7s\u207b\u00b9<\/td>\n<td>reaction of NO with certain gases<\/td>\n<\/tr>\n<tr>\n<td>\u00bd<\/td>\n<td>rate \u00d71.41<\/td>\n<td>M<sup>\u00bd<\/sup>\u00b7s\u207b\u00b9<\/td>\n<td>thermal decomposition of acetaldehyde<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>For related calculations, the <a href=\"https:\/\/wpcalc.com\/en\/chemistry\/reaction-enthalpy-from-bond-energies-calculator\/\">Bond Energy Reaction Enthalpy Calculator<\/a> estimates the heat of a reaction from its bonds, complementing the kinetic information you obtain here.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Enter the concentration and initial rate measured in each experiment, and this calculator determines the reaction order n, the rate constant k, and the full rate law using the method of initial rates.<\/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":[57],"class_list":["post-66877","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\/66877","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=66877"}],"version-history":[{"count":1,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66877\/revisions"}],"predecessor-version":[{"id":66878,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66877\/revisions\/66878"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=66877"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=66877"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=66877"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}