{"id":59547,"date":"2016-04-01T13:07:57","date_gmt":"2016-04-01T11:07:57","guid":{"rendered":"http:\/\/wpcalc.com\/?p=59547"},"modified":"2026-09-29T14:57:47","modified_gmt":"2026-09-29T11:57:47","slug":"c1v1-c2v2","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/chemistry\/c1v1-c2v2\/","title":{"rendered":"C1V1 = C2V2 Dilution 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 Stock Solution Volume<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"59547\" data-favorite-title=\"C1V1 = C2V2\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/chemistry\/c1v1-c2v2\/\" data-favorite-excerpt=\"Find the volume of stock solution needed for a dilution. Enter the stock concentration, desired concentration, and desired final volume.\" aria-label=\"Add to Favorites\" data-favorite-icon=\"icon icon-chemistry\">\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\/c1v1-c2v2\/\" method=\"POST\" class=\"calculator\" id=\"calculator-59547\" data-post=\"59547\"><fieldset class=\"fieldset-input\"><legend class=\"sr-only\">Input Fields<\/legend><div class=\"field is-single\" id=\"input-1\"><label for=\"field-1\">Stock Concentration (C1)<\/label><div class=\"field-group\"><input type=\"number\" name=\"stock_concentration_c1\" id=\"field-1\" step=\"any\" value=\"1\"\/><div class=\"grid grid-cols-1\"><select id=\"field-2\" name=\"units\" aria-label=\"Units\"><option value=\"mol\/L\">mol\/L<\/option><option value=\"g\/L\">g\/L<\/option><option value=\"mM\">mM<\/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><\/div><div class=\"field is-single\" id=\"input-2\"><label for=\"field-3\">Desired Concentration (C2)<\/label><div class=\"field-group\"><input type=\"number\" name=\"desired_concentration_c2\" id=\"field-3\" step=\"any\" value=\"1\"\/><div class=\"grid grid-cols-1\"><select id=\"field-4\" name=\"units\" aria-label=\"Units\"><option value=\"mol\/L\">mol\/L<\/option><option value=\"g\/L\">g\/L<\/option><option value=\"mM\">mM<\/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><\/div><div class=\"field is-single\" id=\"input-3\"><label for=\"field-5\">Desired Volume (V2)<\/label><div class=\"field-group\"><input type=\"number\" name=\"desired_volume_v2\" id=\"field-5\" step=\"any\" value=\"1\"\/><div class=\"grid grid-cols-1\"><select id=\"field-6\" name=\"units\" aria-label=\"Units\"><option value=\"L\">L<\/option><option value=\"mL\">mL<\/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><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Re-Calculate\" id=\"calculate-button\" data-post=\"59547\">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>Required Volume (V1)<\/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><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=\"59547\" 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\">1<\/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>C1V1 = C2V2 Dilution 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\\[C_1V_1=C_2V_2 \\qquad V_1=\\frac{C_2V_2}{C_1}\\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Where:<\/strong><\/p>\n<ul>\n<li>\\(C_1\\) \u2014 concentration of the stock solution<\/li>\n<li>\\(V_1\\) \u2014 volume of stock solution needed<\/li>\n<li>\\(C_2\\) \u2014 desired concentration of the final solution<\/li>\n<li>\\(V_2\\) \u2014 desired final volume of the diluted solution<\/li>\n<\/ul>\n<p>The equation states that the amount of dissolved substance taken from the stock equals the amount in the final solution. Use compatible concentration units for \\(C_1\\) and \\(C_2\\), and consistent volume units for \\(V_1\\) and \\(V_2\\).<\/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>C1V1 = C2V2 \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Example:<\/strong> You have a 1 mol\/L stock solution and want 1 L of a 0.1 mol\/L solution. Leave Stock Concentration (C1) and Desired Volume (V2) at their defaults, and change Desired Concentration (C2) to 0.1 mol\/L.<\/p>\n<p>\\[V_1=\\frac{C_2V_2}{C_1}=\\frac{(0.1\\,\\mathrm{mol\/L})(1\\,\\mathrm{L})}{1\\,\\mathrm{mol\/L}}=0.1\\,\\mathrm{L}\\]<\/p>\n<p><strong>Result:<\/strong> Use 0.1 L (100 mL) of stock solution, then add diluent until the <em>total<\/em> volume is 1 L.<\/p>\n<p>\n\r\n<\/section>\n<h2>How to use the calculator<\/h2>\n<ol>\n<li>Enter the concentration of the solution you are diluting in <strong>Stock Concentration (C1)<\/strong> and select its <strong>Units<\/strong>.<\/li>\n<li>Enter the concentration you want in <strong>Desired Concentration (C2)<\/strong> and select its <strong>Units<\/strong>. The desired concentration must be lower than the stock concentration after any valid unit conversion.<\/li>\n<li>Enter the final amount of solution to prepare in <strong>Desired Volume (V2)<\/strong> and select L or mL under <strong>Units<\/strong>.<\/li>\n<li>Read <strong>Required Volume (V1)<\/strong> as the amount of stock to measure. If you selected mL for Desired Volume (V2), read the output warning below before using the number.<\/li>\n<\/ol>\n<p>The default concentrations are both 1 mol\/L. Because they are equal, the calculator displays an error until you enter a lower Desired Concentration (C2), such as 0.1 mol\/L.<\/p>\n<h2>What C1V1 = C2V2 means<\/h2>\n<p>Dilution lowers a solution\u2019s concentration by adding solvent, also called diluent. The amount of dissolved substance stays the same: the portion measured from the stock contains the same amount that ends up in the prepared solution. That conservation is what \\(C_1V_1=C_2V_2\\) expresses.<\/p>\n<p>The calculated \\(V_1\\) is the volume of <em>stock solution<\/em>, not the volume of diluent to add. For the example above, measure 100 mL of stock and bring the solution to a final volume of 1 L. Do not simply add 1 L of diluent: doing so would produce more than 1 L of solution and a lower concentration than intended.<\/p>\n<p>The ratio \\(C_2\/C_1\\) is the fraction of the final volume that comes from the stock. For a tenfold dilution, \\(C_2\/C_1=0.1\\), so the stock occupies one-tenth of the final volume. This makes the result easy to check: when the desired concentration is lower than the stock concentration, \\(V_1\\) should be smaller than \\(V_2\\).<\/p>\n<h2>Units, output warning, and practical limits<\/h2>\n<p><strong>Important mL output warning:<\/strong> The calculator converts Desired Volume (V2) to liters for its calculation, but labels the resulting number with the unit you selected for V2. When you select <strong>mL<\/strong>, the displayed number is therefore in <strong>liters despite its mL label<\/strong>. Multiply that number by 1,000 to obtain the required stock volume in mL. For example, with 1 mol\/L stock, 0.1 mol\/L desired concentration, and 100 mL desired volume, the output displays \u201c0.01 mL\u201d; the correct required volume is 0.01 L, or <strong>10 mL<\/strong>. Selecting L for Desired Volume (V2) avoids this labeling issue.<\/p>\n<p>Use concentration units that describe the same kind of quantity. The calculator converts mM to mol\/L correctly, so those two units can be used together. It does <em>not<\/em> use a substance\u2019s molar mass when handling g\/L: although it accepts a mix of g\/L and mol\/L or mM, that mix does not yield a valid conversion. Use g\/L for both concentrations, or use mol\/L and mM as appropriate. Converting g\/L to mol\/L requires the solute\u2019s molar mass.<\/p>\n<p>Enter positive concentrations and a positive final volume. This equation assumes the dissolved substance is conserved during preparation; it does not account for reactions, losses, or changes in concentration after mixing. For accurate work, measure the stock with suitable equipment and bring the mixture to its specified final volume. If you are preparing an acetate solution whose pH also matters, the <a href=\"https:\/\/wpcalc.com\/en\/chemistry\/acetate-buffer-2\/\">acetate buffer composition calculator<\/a> addresses the buffer components. For measurements that relate absorbance to concentration, see the <a href=\"https:\/\/wpcalc.com\/en\/chemistry\/beer-lambert-law\/\">Beer\u2013Lambert law calculator<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Find the volume of stock solution needed for a dilution. Enter the stock concentration, desired concentration, and desired final volume.<\/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":[54],"tags":[56],"class_list":["post-59547","post","type-post","status-publish","format-standard","hentry","category-chemistry","tag-stoichiometry"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/59547","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=59547"}],"version-history":[{"count":5,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/59547\/revisions"}],"predecessor-version":[{"id":65562,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/59547\/revisions\/65562"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=59547"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=59547"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=59547"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}