{"id":59970,"date":"2016-12-29T11:40:40","date_gmt":"2016-12-29T09:40:40","guid":{"rendered":"https:\/\/wpcalc.com\/?p=59970"},"modified":"2025-05-09T09:34:58","modified_gmt":"2025-05-09T06:34:58","slug":"crest-vertical-curve-length","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/engineering\/crest-vertical-curve-length\/","title":{"rendered":"Crest Vertical Curve Length 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 class=\"text-lg font-display font-bold\">Vertical Curve Length Estimator<\/h2><\/div><div class=\"relative group inline-block\">\n  <button class=\"favorite\" id=\"favorite\" data-favorite-id=\"59970\" data-favorite-title=\"Crest Vertical Curve Length\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/engineering\/crest-vertical-curve-length\/\" data-favorite-excerpt=\"This calculator estimates the minimum required length of a crest vertical curve on roads to ensure sufficient sight distance for safe vehicle operation. It helps highway designers evaluate visibility constraints and alignments based on grades, stopping sight distance, and driver eye\/obstruction height.\" aria-label=\"Add to Favorites\" data-favorite-icon=\"icon icon-roadways\">\n    <span class=\"icon icon-shape-star-empty\"><\/span>\n  <\/button>\n  <div class=\"absolute right-full -translate-y-1\/2 top-1\/2 mr-2 w-max max-w-xs px-3 py-2 bg-gray-800 text-white text-xs rounded shadow-lg opacity-0 group-hover:opacity-100 transition-opacity duration-200 z-10 pointer-events-none\">\n   <span class=\"favorite-tooltip\" id=\"favorite-tooltip\"><\/span>\n  <\/div>\n<\/div><\/div><form action=\"https:\/\/wpcalc.com\/en\/engineering\/crest-vertical-curve-length\/\" method=\"POST\" class=\"calculator\" id=\"calculator-59970\" data-post=\"59970\"><fieldset class=\"fieldset-input\"><legend class=\"sr-only\">Input Fields<\/legend><div class=\"field has-term\" id=\"input-1\"><label for=\"field-1\">Sight distance<\/label><div class=\"term\">S<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"number\" name=\"sight_distance\" id=\"field-1\" step=\"1\" value=\"160\"\/><div class=\"unit\">m<\/div><\/div><div class=\"field has-term\" id=\"input-2\"><label for=\"field-2\">Initial roadway grade<\/label><div class=\"term\">g\u2081<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"number\" name=\"initial_roadway_grade\" id=\"field-2\" step=\"0.1\" value=\"3\"\/><div class=\"unit\">%<\/div><\/div><div class=\"field has-term\" id=\"input-3\"><label for=\"field-3\">Final roadway grade<\/label><div class=\"term\">g\u2082<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"number\" name=\"final_roadway_grade\" id=\"field-3\" step=\"0.1\" value=\"-2\"\/><div class=\"unit\">%<\/div><\/div><div class=\"field has-term\" id=\"input-4\"><label for=\"field-4\">Driver&#039;s eye height<\/label><div class=\"term\">h\u2081<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"number\" name=\"drivers_eye_height\" id=\"field-4\" step=\"0.01\" value=\"1.2\"\/><div class=\"unit\">m<\/div><\/div><div class=\"field has-term\" id=\"input-5\"><label for=\"field-5\">Object height<\/label><div class=\"term\">h\u2082<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"number\" name=\"object_height\" id=\"field-5\" step=\"0.01\" value=\"0.15\"\/><div class=\"unit\">m<\/div><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Re-Calculate\" id=\"calculate-button\" data-post=\"59970\">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>Minimum curve length<\/span><\/span><span class=\"field-value\" id=\"result-1\" data-unit=\"meters\"><\/span><button class=\"copy-result\" data-tooltip=\"Copy Result\"><span class=\"copy-icon icon icon-document-copy\"><\/span><\/button><\/div><div class=\"field-result\" id=\"output-2\"><span class=\"field-title\"><span>Minimum curve length<\/span><\/span><span class=\"field-value\" id=\"result-2\" data-unit=\"feet\"><\/span><button class=\"copy-result\" data-tooltip=\"Copy Result\"><span class=\"copy-icon icon icon-document-copy\"><\/span><\/button><\/div><\/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=\"59970\" aria-live=\"polite\"><h2 class=\"text-sm text-gray-500 text-center mb-2\">How did this result make you feel?<\/h2><div class=\"grid grid-cols-3 sm:flex sm:flex-row sm:justify-around gap-4 sm:items-center sm:flex-wrap\"><button 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\">\ud83d\ude00 <\/span><span class=\"reaction-description font-medium\">Like <\/span><\/button><button 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\">\ud83d\udca1 <\/span><span class=\"reaction-description font-medium\">Helpful <\/span><\/button><button 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\">\ud83d\ude15 <\/span><span class=\"reaction-description font-medium\">Confused <\/span><\/button><button 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\">\ud83d\ude1e <\/span><span class=\"reaction-description font-medium\">Disappointed <\/span><\/button><button 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\">\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><ins class=\"adsbygoogle\"\n     style=\"display:block; text-align:center; margin: 32px 0;\"\n     data-ad-layout=\"in-article\"\n     data-ad-format=\"fluid\"\n     data-ad-client=\"ca-pub-1721569815777345\"\n     data-ad-slot=\"6317458308\"><\/ins>\n<script>\n     (adsbygoogle = window.adsbygoogle || []).push({});\n<\/script>\n<p><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>Crest Vertical Curve Length 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\">\\[\\text{If } S < L_m: \\quad L_m = \\frac{A \\cdot S^2}{200 \\cdot (\\sqrt{h_1} + \\sqrt{h_2})^2}\\]\\[\\text{If } S > L_m: \\quad L_m = 2S &#8211; \\frac{200 \\cdot (\\sqrt{h_1} + \\sqrt{h_2})^2}{A}\\]<\/div>\r\n\t<\/figure>\r\n\t<br \/>\n<strong>Where:<\/strong> <\/p>\n<ul>\n<li>$$L_m$$ = minimum length of crest curve (m)<\/li>\n<li>$$A$$ = absolute grade difference (%), $$|g<em>1 &#8211; g<\/em>2|$$<\/li>\n<li>$$S$$ = stopping sight distance (m)<\/li>\n<li>$$h_1$$ = driver\u2019s eye height (m)<\/li>\n<li>$$h_2$$ = object height (m)<\/li>\n<\/ul>\n<p>\r\n<\/section><br \/>\nCrest vertical curves are used in road design where two opposing gradients meet. These curves must be long enough to provide clear visibility for drivers. The equations differ depending on whether the stopping sight distance S is less than or greater than the curve length $$L_m$$. This calculator supports quick estimation for engineers, enhancing road safety and compliance with geometric design standards.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>This calculator estimates the minimum required length of a crest vertical curve on roads to ensure sufficient sight distance for safe vehicle operation. It helps highway designers evaluate visibility constraints and alignments based on grades, stopping sight distance, and driver eye\/obstruction height.<\/p>\n","protected":false},"author":70,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[4],"tags":[37],"class_list":["post-59970","post","type-post","status-publish","format-standard","hentry","category-engineering","tag-roadways"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/59970","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=59970"}],"version-history":[{"count":1,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/59970\/revisions"}],"predecessor-version":[{"id":63934,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/59970\/revisions\/63934"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=59970"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=59970"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=59970"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}