{"id":66733,"date":"2026-10-13T08:46:20","date_gmt":"2026-10-13T05:46:20","guid":{"rendered":"https:\/\/wpcalc.com\/en\/?p=66733"},"modified":"2026-10-13T08:46:20","modified_gmt":"2026-10-13T05:46:20","slug":"rational-method-runoff","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/engineering\/rational-method-runoff\/","title":{"rendered":"Rational Method Runoff"},"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\">Estimate Peak Stormwater Flow with Q = C\u00b7i\u00b7A<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"66733\" data-favorite-title=\"Runoff Flow\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/engineering\/rational-method-runoff\/\" data-favorite-excerpt=\"Estimate peak stormwater runoff from a small drainage area using the Rational Method Q = C\u00b7i\u00b7A. Enter the drainage area, design rainfall intensity and runoff coefficient to get the peak flow in L\/s, m\u00b3\/s, ft\u00b3\/s and more.\" aria-label=\"Add to Favorites\" data-favorite-icon=\"icon icon-civil\">\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\/engineering\/rational-method-runoff\/\" method=\"POST\" class=\"calculator\" id=\"calculator-66733\" data-post=\"66733\"><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\">Drainage area (A)<\/label><div class=\"term\">A<\/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=\"drainage_area_a\" id=\"field-1\" aria-describedby=\"calc-info-1\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"2\" min=\"0.0001\" value=\"2\"\/><div class=\"grid grid-cols-1\"><select id=\"field-2\" name=\"unit\" aria-label=\"Unit\"><option value=\"ha\" selected>ha<\/option><option value=\"sqm\">m\u00b2<\/option><option value=\"sqkm\">km\u00b2<\/option><option value=\"acre\">acre<\/option><option value=\"sqft\">ft\u00b2<\/option><option value=\"sqmi\">mi\u00b2<\/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\">Contributing watershed area upstream of the design point<\/small><\/div><div class=\"field has-term\" id=\"input-2\"><label for=\"field-3\">Rainfall intensity (i)<\/label><div class=\"term\">i<\/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=\"rainfall_intensity_i\" id=\"field-3\" aria-describedby=\"calc-info-3\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"50\" min=\"0.01\" value=\"50\"\/><div class=\"grid grid-cols-1\"><select id=\"field-4\" name=\"unit\" aria-label=\"Unit\"><option value=\"mmh\" selected>mm\/h<\/option><option value=\"inh\">in\/h<\/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\">Average rainfall intensity for the design storm duration (usually \u2265 the time of concentration)<\/small><\/div><div class=\"field is-single has-term\" id=\"input-3\"><label for=\"field-5\">Runoff coefficient (C)<\/label><div class=\"term\">C<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"runoff_coefficient_c\" id=\"field-5\" aria-describedby=\"calc-info-5\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"0.7\" min=\"0.01\" max=\"1\" value=\"0.7\"\/><small id=\"calc-info-5\">Typical values: asphalt\/roof 0.70\u20130.95, concrete 0.80\u20130.95, gravel 0.50\u20130.70, lawn sandy soil 0.10\u20130.20, lawn heavy soil 0.25\u20130.35, mixed urban 0.50\u20130.70<\/small><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Re-Calculate\" id=\"calculate-button\" data-post=\"66733\">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> Rational Method Results<\/h3><div class=\"result-box\"><div class=\"field-result\" id=\"output-1\"><span class=\"field-title\"><span>Peak runoff rate<\/span><span class=\"result-term\">Q<\/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>Formula and notes<\/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><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=\"66733\" 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>Rational Method 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\\[ Q = C \\, i \\, A \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Where:<\/strong><\/p>\n<ul>\n<li>\\(Q\\) \u2014 peak runoff rate<\/li>\n<li>\\(C\\) \u2014 runoff coefficient (dimensionless, 0\u20131): the fraction of rainfall that becomes surface runoff<\/li>\n<li>\\(i\\) \u2014 average rainfall intensity for the design storm duration (mm\/h or in\/h)<\/li>\n<li>\\(A\\) \u2014 contributing drainage area (ha, m\u00b2, km\u00b2, acre, ft\u00b2 or mi\u00b2)<\/li>\n<\/ul>\n<p>The formula gives the peak flow at a design point when the whole catchment is contributing simultaneously. In convenient mixed units: \\(Q\\) in L\/s when \\(i\\) is in mm\/h and \\(A\\) in hectares (\\(Q \\approx 2.778 \\cdot C \\cdot i \\cdot A\\)), or \\(Q\\) in ft\u00b3\/s when \\(i\\) is in in\/h and \\(A\\) in acres.<\/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>Rational Method \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Example:<\/strong> a 2 ha mixed urban catchment with a runoff coefficient of 0.7 drains to a storm inlet. The local IDF curve gives a design rainfall intensity of 50 mm\/h for a storm duration equal to the time of concentration.<\/p>\n<p>\\[ Q = 2.778 \\times 0.7 \\times 50 \\times 2 \\approx 194.4 \\text{ L\/s} \\]<\/p>\n<p><strong>Result:<\/strong> the peak runoff rate is approximately <strong>194.4 L\/s<\/strong>, i.e. 0.194 m\u00b3\/s, \u2248 6.87 ft\u00b3\/s, or about 3,080 US gallons per minute. This is the flow the inlet, pipe or channel must be sized for.<\/p>\n<p>\n\r\n<\/section>\n<h2>How to use the calculator<\/h2>\n<ol>\n<li>Enter the <strong>Drainage area (A)<\/strong> \u2014 the watershed area upstream of your design point \u2014 and select its unit (ha, m\u00b2, km\u00b2, acre, ft\u00b2 or mi\u00b2).<\/li>\n<li>Enter the <strong>Rainfall intensity (i)<\/strong> from a local IDF curve or stormwater design standard, using a duration equal to or greater than the time of concentration, and choose mm\/h or in\/h.<\/li>\n<li>Enter the <strong>Runoff coefficient (C)<\/strong> between 0 and 1. Use a single value for a uniform surface, or a weighted average if several surface types drain to the same point.<\/li>\n<li>Read the <strong>peak runoff rate<\/strong> and the same flow expressed in m\u00b3\/s, L\/s, ft\u00b3\/s, US gal\/min and other equivalent units.<\/li>\n<\/ol>\n<h2>What the Rational Method is<\/h2>\n<p>The Rational Method is the most widely used technique for estimating peak stormwater runoff from small catchments. It assumes that the peak flow occurs when rainfall of constant intensity falls for at least the time of concentration \u2014 the time needed for water from the hydraulically most distant point to reach the outlet. At that moment every square metre of the catchment is contributing, and the peak flow is simply the rainfall intensity multiplied by the area, scaled by the fraction that actually runs off.<\/p>\n<p>The method matters because peak flow is the number that drives nearly every stormwater design decision: the diameter of a storm sewer, the capacity of a culvert or inlet, the width of a swale or ditch, and the size of detention basins. Once you know \\(Q\\), you can pass it directly into hydraulic design \u2014 for example, sizing an open channel with the <a href=\"https:\/\/wpcalc.com\/en\/engineering\/manning-open-channel-flow\/\">Manning open-channel flow calculator<\/a> or checking losses in a pipe with the <a href=\"https:\/\/wpcalc.com\/en\/engineering\/pipe-pressure-drop\/\">pipe pressure drop calculator<\/a>.<\/p>\n<p>Interpreting the result is straightforward: it is a <em>peak<\/em> rate, not a volume or a hydrograph. The value scales linearly with all three inputs, so doubling the intensity doubles the peak flow. Because it returns a single design number rather than a full runoff simulation, it is best suited for preliminary design and for catchments where storage and routing effects are small.<\/p>\n<h2>Choosing the runoff coefficient<\/h2>\n<p>\\(C\\) represents the fraction of rainfall that appears as surface runoff, and it bundles together infiltration, depression storage and interception losses. Typical values:<\/p>\n<table>\n<thead>\n<tr>\n<th>Surface<\/th>\n<th>Runoff coefficient C<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>Asphalt, roofing<\/td>\n<td>0.70\u20130.95<\/td>\n<\/tr>\n<tr>\n<td>Concrete<\/td>\n<td>0.80\u20130.95<\/td>\n<\/tr>\n<tr>\n<td>Gravel<\/td>\n<td>0.50\u20130.70<\/td>\n<\/tr>\n<tr>\n<td>Lawn, sandy soil<\/td>\n<td>0.10\u20130.20<\/td>\n<\/tr>\n<tr>\n<td>Lawn, heavy soil<\/td>\n<td>0.25\u20130.35<\/td>\n<\/tr>\n<tr>\n<td>Mixed urban areas<\/td>\n<td>0.50\u20130.70<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>For a catchment with several surface types, compute an area-weighted average: \\(C = \\sum C_k A_k \/ \\sum A_k\\). Higher coefficients apply to steeper slopes and less permeable soils.<\/p>\n<h2>Assumptions, limitations and practical tips<\/h2>\n<ul>\n<li><strong>Small catchments only.<\/strong> The Rational Method is normally considered valid up to roughly 50\u2013200 ha (about 50\u2013500 acres). For larger watersheds, rainfall varies too much across the area and routing\/storage effects matter \u2014 use a hydrograph method instead.<\/li>\n<li><strong>Uniform rainfall.<\/strong> The method assumes constant intensity, uniformly distributed over the whole catchment for the duration of the storm. It cannot represent varying or moving storms.<\/li>\n<li><strong>Intensity must match the time of concentration.<\/strong> Always take \\(i\\) from an IDF curve for your chosen return period (e.g. 2-, 10- or 100-year) at a duration equal to \\(t_c\\). Using an intensity for the wrong duration is the most common source of error.<\/li>\n<li><strong>\\(C\\) is assumed constant.<\/strong> In reality runoff coefficients increase as soil saturates and for more extreme storms, so many standards recommend higher \\(C\\) values for rare events; check your local design code.<\/li>\n<li><strong>No storage or routing.<\/strong> Ponds, pipes with significant storage and very flat catchments attenuate the peak, which this method ignores \u2014 it is therefore mildly conservative when such storage exists.<\/li>\n<li><strong>Check the return period.<\/strong> The result is only as good as the design storm behind it: match the return period to the consequence of failure (minor drainage vs. major flood protection).<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Estimate peak stormwater runoff from a small drainage area using the Rational Method Q = C\u00b7i\u00b7A. Enter the drainage area, design rainfall intensity and runoff coefficient to get the peak flow in L\/s, m\u00b3\/s, ft\u00b3\/s and more.<\/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":[4],"tags":[19],"class_list":["post-66733","post","type-post","status-publish","format-standard","hentry","category-engineering","tag-civil"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66733","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=66733"}],"version-history":[{"count":1,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66733\/revisions"}],"predecessor-version":[{"id":66735,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66733\/revisions\/66735"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=66733"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=66733"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=66733"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}