{"id":66973,"date":"2026-10-13T10:44:30","date_gmt":"2026-10-13T07:44:30","guid":{"rendered":"https:\/\/wpcalc.com\/en\/?p=66973"},"modified":"2026-10-13T10:44:30","modified_gmt":"2026-10-13T07:44:30","slug":"froude-number-calculator","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/physics\/froude-number-calculator\/","title":{"rendered":"Froude Number 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\">Check Whether Open-Channel Flow Is Subcritical, Critical or Supercritical<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"66973\" data-favorite-title=\"Froude Number\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/physics\/froude-number-calculator\/\" data-favorite-excerpt=\"Enter the flow speed, flow depth and gravity to compute the Froude number and find out whether your open-channel flow is subcritical, critical or supercritical, with critical-speed details.\" aria-label=\"Add to Favorites\" data-favorite-icon=\"icon icon-drop\">\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\/physics\/froude-number-calculator\/\" method=\"POST\" class=\"calculator\" id=\"calculator-66973\" data-post=\"66973\"><fieldset class=\"fieldset-input is-1\"><legend class=\"sr-only\">Input Fields<\/legend><div class=\"field has-term\" id=\"input-1\"><label for=\"field-1\">Flow speed (v)<\/label><div class=\"term\">v<\/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=\"flow_speed_v\" id=\"field-1\" aria-describedby=\"calc-info-1\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 2\" min=\"0\" value=\"2\"\/><div class=\"grid grid-cols-1\"><select id=\"field-2\" name=\"unit\" aria-label=\"Unit\"><option value=\"ms\" selected>m\/s<\/option><option value=\"fts\">ft\/s<\/option><option value=\"kmh\">km\/h<\/option><option value=\"mph\">mph<\/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\">Average velocity of the water. Can be measured with a float or flow meter.<\/small><\/div><div class=\"field has-term\" id=\"input-2\"><label for=\"field-3\">Characteristic length \/ flow depth (L)<\/label><div class=\"term\">L<\/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=\"characteristic_length_flow_depth_l\" id=\"field-3\" aria-describedby=\"calc-info-3\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 1.2\" min=\"0\" value=\"1.2\"\/><div class=\"grid grid-cols-1\"><select id=\"field-4\" name=\"unit\" aria-label=\"Unit\"><option value=\"m\" selected>m<\/option><option value=\"cm\">cm<\/option><option value=\"ft\">ft<\/option><option value=\"in\">in<\/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\">For open-channel flow use the mean flow depth (hydraulic depth = area \/ top width). For a rectangular channel this is simply the water depth.<\/small><\/div><div class=\"field has-term\" id=\"input-3\"><label for=\"field-5\">Gravitational acceleration (g)<\/label><div class=\"term\">g<\/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=\"gravitational_acceleration_g\" id=\"field-5\" aria-describedby=\"calc-info-5\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 9.81\" min=\"0\" value=\"9.81\"\/><div class=\"grid grid-cols-1\"><select id=\"field-6\" name=\"unit\" aria-label=\"Unit\"><option value=\"ms2\" selected>m\/s\u00b2<\/option><option value=\"fts2\">ft\/s\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-5\">Standard gravity on Earth is 9.81 m\/s\u00b2 (32.2 ft\/s\u00b2).<\/small><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Re-Calculate\" id=\"calculate-button\" data-post=\"66973\">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> Froude Number Results<\/h3><div class=\"result-box\"><div class=\"field-result is-column\" id=\"output-1\"><span class=\"field-title\"><span>Froude number<\/span><span class=\"result-term\">Fr<\/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>Flow-regime classification<\/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>Critical speed and 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><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=\"66973\" 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>Froude Number 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\\[ Fr = \\frac{v}{\\sqrt{g \\, L}} \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Where:<\/strong><\/p>\n<ul>\n<li>\\(Fr\\) \u2014 Froude number (dimensionless)<\/li>\n<li>\\(v\\) \u2014 mean flow velocity (m\/s)<\/li>\n<li>\\(g\\) \u2014 gravitational acceleration (m\/s\u00b2)<\/li>\n<li>\\(L\\) \u2014 characteristic length: for open-channel flow, the mean flow depth or hydraulic depth (m)<\/li>\n<\/ul>\n<p>The formula compares the speed of the flow with the speed of a small gravity (surface) wave travelling on the water surface, \\(v_c = \\sqrt{gL}\\). This wave speed is the natural information speed of a free-surface flow, so the ratio tells you whether disturbances can propagate upstream (\\(Fr &lt; 1\\)) or are swept downstream (\\(Fr &gt; 1\\)).<\/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>Froude Number \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Example:<\/strong> water flows at an average speed of 2 m\/s in a rectangular channel with a water depth of 1.2 m. Take \\(g = 9.81\\ \\text{m\/s}^2\\).<\/p>\n<p>\\[ Fr = \\frac{v}{\\sqrt{g \\, L}} = \\frac{2}{\\sqrt{9.81 \\times 1.2}} = \\frac{2}{\\sqrt{11.772}} = \\frac{2}{3.431} \\approx 0.583 \\]<\/p>\n<p><strong>Result:<\/strong> \\(Fr \\approx 0.583 &lt; 1\\), so the flow is <strong>subcritical (tranquil)<\/strong>. The critical speed at this depth is \\(v_c = \\sqrt{9.81 \\times 1.2} \\approx 3.431\\ \\text{m\/s}\\); the flow would have to accelerate to that speed to reach the critical state.<\/p>\n<p>\n\r\n<\/section>\n<h2>How to Use the Calculator<\/h2>\n<ol>\n<li>Enter the <strong>Flow speed (v)<\/strong> and choose its unit (m\/s, ft\/s, km\/h or mph). You can estimate it by timing a floating object over a known distance or measure it with a flow meter.<\/li>\n<li>Enter the <strong>Characteristic length \/ flow depth (L)<\/strong> and its unit. For a rectangular channel this is simply the water depth; for other cross-sections use the hydraulic depth (flow area divided by top width).<\/li>\n<li>Enter the <strong>Gravitational acceleration (g)<\/strong> \u2014 the default 9.81 m\/s\u00b2 (or 32.2 ft\/s\u00b2) is standard on Earth and can be left as is.<\/li>\n<li>Read the results: the <strong>Froude number<\/strong>, the <strong>flow-regime classification<\/strong> (subcritical, near-critical or supercritical), and the <strong>critical speed and details<\/strong>, which include the critical speed at your depth, the specific energy head, and the critical depth for your speed.<\/li>\n<\/ol>\n<h2>What Is the Froude Number?<\/h2>\n<p>The Froude number is the standard dimensionless number for open-channel and free-surface flow. Just as the <a href=\"https:\/\/wpcalc.com\/en\/physics\/mach-number-calculator\/\">Mach number<\/a> compares a gas flow speed to the speed of sound, the Froude number compares a water flow speed to the celerity of a small surface wave, \\(\\sqrt{gL}\\). It measures the relative importance of inertia versus gravity: at low Fr, gravity dominates and the water surface adjusts gently; at high Fr, inertia dominates and the surface becomes steep and choppy.<\/p>\n<p>The classification is straightforward. <strong>Subcritical flow<\/strong> (\\(Fr &lt; 1\\)) is tranquil: waves can travel both upstream and downstream, so the flow depth is controlled by downstream conditions \u2014 this is why a weir or obstruction raises the water level far upstream (the backwater effect). <strong>Critical flow<\/strong> (\\(Fr = 1\\)) is an unstable transition where the depth equals the critical depth and the flow is extremely sensitive to small changes in slope or geometry. <strong>Supercritical flow<\/strong> (\\(Fr &gt; 1\\)) is rapid: no disturbance can travel upstream, so the flow is controlled entirely by upstream conditions.<\/p>\n<p>The transition from supercritical back to subcritical cannot happen smoothly \u2014 it occurs abruptly through a <strong>hydraulic jump<\/strong>, a standing wave that dissipates energy. Hydraulic jumps are seen downstream of spillways and sluice gates and are deliberately used in stilling basins to destroy the destructive energy of fast flow. The calculator's near-critical band (0.95\u20131.05) reflects the practical difficulty of holding flow exactly at \\(Fr = 1\\).<\/p>\n<p>The result table also shows two useful derived quantities: the <strong>specific energy head<\/strong> \\(E = L + v^2\/(2g)\\), the sum of depth and velocity head relative to the channel bottom, and the <strong>critical depth<\/strong> \\(L_c = v^2\/g\\), the depth at which your current speed would be exactly critical. Comparing your actual depth with the critical depth is often the quickest way to judge the regime.<\/p>\n<h2>Assumptions, Limitations and Tips<\/h2>\n<ul>\n<li><strong>Use the right length.<\/strong> This calculator implements the depth-based Froude number for open-channel flow. For a rectangular channel, \\(L\\) is the water depth; for other shapes use the hydraulic depth \\(A\/T\\) (flow area divided by top width). Ship and hull hydrodynamics uses a different, length-based Froude number \u2014 the two are not interchangeable.<\/li>\n<li><strong>Use consistent reality.<\/strong> The calculator converts units internally, so you only need to enter values in whatever units you measured \u2014 just pick the matching unit in each dropdown.<\/li>\n<li><strong>Uniform, gradually varied flow assumed.<\/strong> The classification assumes the velocity is reasonably representative of the cross-section. In highly non-uniform flow (near drops, junctions or jumps), Fr varies from point to point.<\/li>\n<li><strong>Keep g realistic.<\/strong> Changing g only makes sense for other planets or teaching examples; on Earth use 9.81 m\/s\u00b2 (32.2 ft\/s\u00b2).<\/li>\n<li>Depth and velocity interact with channel resistance: to explore related flow physics, see the <a href=\"https:\/\/wpcalc.com\/en\/physics\/drag-force-calculator\/\">Drag Force Calculator<\/a> or the <a href=\"https:\/\/wpcalc.com\/en\/physics\/speed-of-sound-in-air-calculator\/\">Speed of Sound in Air Calculator<\/a>.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Enter the flow speed, flow depth and gravity to compute the Froude number and find out whether your open-channel flow is subcritical, critical or supercritical, with critical-speed details.<\/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":[62],"tags":[88],"class_list":["post-66973","post","type-post","status-publish","format-standard","hentry","category-physics","tag-fluids"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66973","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=66973"}],"version-history":[{"count":1,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66973\/revisions"}],"predecessor-version":[{"id":66974,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66973\/revisions\/66974"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=66973"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=66973"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=66973"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}