{"id":66930,"date":"2026-10-13T10:31:56","date_gmt":"2026-10-13T07:31:56","guid":{"rendered":"https:\/\/wpcalc.com\/en\/?p=66930"},"modified":"2026-10-13T10:31:56","modified_gmt":"2026-10-13T07:31:56","slug":"mach-number-calculator","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/physics\/mach-number-calculator\/","title":{"rendered":"Mach 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\">Convert an Object&#039;s Speed into a Mach Number<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"66930\" data-favorite-title=\"Mach Number\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/physics\/mach-number-calculator\/\" data-favorite-excerpt=\"Enter an object&#039;s speed and the local speed of sound to get its Mach number, speed unit conversions, Mach cone angle, and the flow regime (subsonic, transonic, supersonic, hypersonic).\" aria-label=\"Add to Favorites\" data-favorite-icon=\"icon icon-spectrum\">\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\/mach-number-calculator\/\" method=\"POST\" class=\"calculator\" id=\"calculator-66930\" data-post=\"66930\"><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\">Object 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=\"object_speed_v\" id=\"field-1\" aria-describedby=\"calc-info-1\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 900\" min=\"0\" value=\"900\"\/><div class=\"grid grid-cols-1\"><select id=\"field-2\" name=\"unit\" aria-label=\"Unit\"><option value=\"kmh\" selected>km\/h<\/option><option value=\"ms\">m\/s<\/option><option value=\"mph\">mph<\/option><option value=\"fts\">ft\/s<\/option><option value=\"kn\">knots<\/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\">Speed of the moving object (aircraft, projectile, vehicle) relative to the surrounding air.<\/small><\/div><div class=\"field has-term\" id=\"input-2\"><label for=\"field-3\">Local speed of sound (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=\"local_speed_of_sound_a\" id=\"field-3\" aria-describedby=\"calc-info-3\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 343\" min=\"0\" value=\"343\"\/><div class=\"grid grid-cols-1\"><select id=\"field-4\" name=\"unit\" aria-label=\"Unit\"><option value=\"ms\" selected>m\/s<\/option><option value=\"kmh\">km\/h<\/option><option value=\"mph\">mph<\/option><option value=\"fts\">ft\/s<\/option><option value=\"kn\">knots<\/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\">Speed of sound in the surrounding air. At sea level it is about 343 m\/s at 20 \u00b0C (340 m\/s at 15 \u00b0C) and it drops with altitude and temperature.<\/small><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Re-Calculate\" id=\"calculate-button\" data-post=\"66930\">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> Mach Number Results<\/h3><div class=\"result-box\"><div class=\"field-result is-column\" id=\"output-1\"><span class=\"field-title\"><span>Mach number and speed conversions<\/span><span class=\"result-term\">M<\/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><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=\"66930\" 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>Mach 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\\[ M = \\frac{v}{a} \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Where:<\/strong><\/p>\n<ul>\n<li>\\(M\\) \u2014 Mach number (dimensionless)<\/li>\n<li>\\(v\\) \u2014 speed of the object relative to the surrounding air (m\/s)<\/li>\n<li>\\(a\\) \u2014 local speed of sound in the surrounding air (m\/s)<\/li>\n<\/ul>\n<p>The formula expresses how many times faster (or slower) than sound an object is travelling through the air. Both speeds must be in the same unit \u2014 the calculator converts your inputs to m\/s before dividing.<\/p>\n<p>The speed of sound itself depends only on the air temperature:<\/p>\n<p>\\[ a = \\sqrt{\\gamma R T} \\]<\/p>\n<p>where \\(\\gamma = 1.4\\) and \\(R = 287.058\\ \\mathrm{J\/(kg\\cdot K)}\\) for air, and \\(T\\) is the absolute temperature in kelvin.<\/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>Mach Number \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Example:<\/strong> an airliner cruises at 900 km\/h through air in which sound travels at 343 m\/s (roughly sea level at 20 \u00b0C).<\/p>\n<p>\\[ v = 900\\ \\mathrm{km\/h} = \\frac{900}{3.6} = 250\\ \\mathrm{m\/s} \\]<\/p>\n<p>\\[ M = \\frac{v}{a} = \\frac{250}{343} \\approx 0.729 \\]<\/p>\n<p><strong>Result:<\/strong> \\(M \\approx 0.729\\) \u2014 the aircraft flies at Mach 0.73, about 73 % of the local speed of sound. This falls in the subsonic regime (0.3 \u2264 M &lt; 0.8).<\/p>\n<p>\n\r\n<\/section>\n<h2>How to Use the Calculator<\/h2>\n<ol>\n<li>Enter the <strong>Object speed (v)<\/strong> \u2014 the speed of the aircraft, projectile or vehicle relative to the air \u2014 and pick its unit (km\/h, m\/s, mph, ft\/s or knots) from the dropdown.<\/li>\n<li>Enter the <strong>Local speed of sound (a)<\/strong> and its unit. If you don't know it, use 343 m\/s for warm sea-level air (20 \u00b0C), 340 m\/s at 15 \u00b0C, or about 295 m\/s near the stratosphere.<\/li>\n<li>Read the <strong>Mach number<\/strong>, the object speed converted into m\/s, km\/h, mph and knots, and \u2014 for M \u2265 1 \u2014 the <strong>Mach cone half-angle<\/strong> \\(\\mu = \\arcsin(1\/M)\\).<\/li>\n<li>Check the <strong>Flow regime classification<\/strong> to see whether the flow is subsonic, transonic, supersonic or hypersonic, along with the implied air temperature for the speed of sound you entered.<\/li>\n<\/ol>\n<h2>What Is the Mach Number?<\/h2>\n<p>The Mach number is the ratio of an object's speed to the speed of sound in the surrounding air. It is named after the Austrian physicist Ernst Mach. Because it is a ratio of two speeds, it has no units: Mach 1 means the object moves exactly at the speed of sound, Mach 2 twice as fast, and Mach 0.5 half as fast.<\/p>\n<p>What makes the Mach number so important in aerodynamics is that the speed of sound is not constant. Sound travels at about 343 m\/s in warm sea-level air, but only about 295 m\/s in the cold stratosphere. Since \\(a\\) depends only on temperature, the same true airspeed produces a <em>higher<\/em> Mach number at high altitude. That is why airliners cruising around Mach 0.8 at 11 km altitude fly at roughly 900\u2013950 km\/h, while the same Mach number at sea level would require over 1,200 km\/h.<\/p>\n<p>The Mach number determines how air behaves around the object. Below about Mach 0.3, air can be treated as incompressible and flow is smooth. As speed rises, compressibility effects appear, and near Mach 1 shock waves form \u2014 the source of the sonic boom. This is why engineers classify flight into regimes: <strong>subsonic<\/strong> (M &lt; 0.8), <strong>transonic<\/strong> (0.8 \u2264 M &lt; 1.2), <strong>supersonic<\/strong> (1.2 \u2264 M &lt; 5) and <strong>hypersonic<\/strong> (M \u2265 5). Each regime brings very different drag, heating and structural challenges.<\/p>\n<p>For supersonic flight (M \u2265 1) the calculator also gives the <strong>Mach angle<\/strong> \\(\\mu = \\arcsin(1\/M)\\) \u2014 the half-angle of the cone-shaped shock wave trailing the object. The faster the object, the narrower the cone: at Mach 2 the half-angle is 30\u00b0, while at Mach 5 it shrinks to about 11.5\u00b0.<\/p>\n<h2>Reference: Speed of Sound and Flight Regimes<\/h2>\n<table>\n<thead>\n<tr>\n<th>Air temperature<\/th>\n<th>Speed of sound<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>\u221255 \u00b0C (stratosphere, ~11 km)<\/td>\n<td>\u2248 295 m\/s (1,062 km\/h)<\/td>\n<\/tr>\n<tr>\n<td>0 \u00b0C<\/td>\n<td>\u2248 331 m\/s (1,193 km\/h)<\/td>\n<\/tr>\n<tr>\n<td>15 \u00b0C (ISA sea level)<\/td>\n<td>\u2248 340 m\/s (1,225 km\/h)<\/td>\n<\/tr>\n<tr>\n<td>20 \u00b0C<\/td>\n<td>\u2248 343 m\/s (1,235 km\/h)<\/td>\n<\/tr>\n<tr>\n<td>30 \u00b0C<\/td>\n<td>\u2248 349 m\/s (1,256 km\/h)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Assumptions and Limitations<\/h2>\n<ul>\n<li>The calculator divides two speeds; it assumes you supply the <em>local<\/em> speed of sound, i.e. the value at the object's altitude and temperature. Using the sea-level value for a high-altitude aircraft understates the true Mach number.<\/li>\n<li>The speed of the object must be measured <strong>relative to the air<\/strong> (true airspeed), not relative to the ground. A tailwind or headwind changes ground speed but not the Mach number.<\/li>\n<li>The implied temperature in the results assumes dry air with \\(\\gamma = 1.4\\) and \\(R = 287.058\\ \\mathrm{J\/(kg\\cdot K)}\\). Humidity and real-gas effects at hypersonic speeds slightly change the actual speed of sound.<\/li>\n<li>The regime boundaries (0.3, 0.8, 1.2, 5) are conventional aerospace definitions; the exact transition depends on the object's shape, especially in transonic flow, where local supersonic pockets appear on the wings well before the aircraft itself reaches Mach 1.<\/li>\n<\/ul>\n<p>If you need the object's average speed from a distance and time, or want to explore other wave phenomena, try our <a href=\"https:\/\/wpcalc.com\/en\/physics\/average-speed-calculator\/\">average speed calculator<\/a>, the <a href=\"https:\/\/wpcalc.com\/en\/physics\/doppler-effect-calculator\/\">Doppler effect calculator<\/a>, or the <a href=\"https:\/\/wpcalc.com\/en\/physics\/wave-speed-calculator-wavelength-frequency\/\">wave speed calculator<\/a>. For high-speed flight you may also find the <a href=\"https:\/\/wpcalc.com\/en\/physics\/g-force-calculator\/\">g-force calculator<\/a> useful.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Enter an object's speed and the local speed of sound to get its Mach number, speed unit conversions, Mach cone angle, and the flow regime (subsonic, transonic, supersonic, hypersonic).<\/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":[87],"class_list":["post-66930","post","type-post","status-publish","format-standard","hentry","category-physics","tag-waves-optics"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66930","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=66930"}],"version-history":[{"count":1,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66930\/revisions"}],"predecessor-version":[{"id":66932,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66930\/revisions\/66932"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=66930"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=66930"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=66930"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}