{"id":61923,"date":"2021-05-28T09:31:09","date_gmt":"2021-05-28T07:31:09","guid":{"rendered":"https:\/\/wpcalc.com\/?p=61923"},"modified":"2026-09-30T20:45:06","modified_gmt":"2026-09-30T17:45:06","slug":"proportion-calculator","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/mathematics\/proportion-calculator\/","title":{"rendered":"Proportion 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\">Solve for the Missing Value<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"61923\" data-favorite-title=\"Proportion\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/mathematics\/proportion-calculator\/\" data-favorite-excerpt=\"This proportion calculator finds the missing value in a proportion of the form A\/B = C\/D. Enter any three known values (A, B, C) and it computes the fourth (D) using cross-multiplication.\" aria-label=\"Add to Favorites\" data-favorite-icon=\"icon icon-algebra\">\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\/mathematics\/proportion-calculator\/\" method=\"POST\" class=\"calculator\" id=\"calculator-61923\" data-post=\"61923\"><fieldset class=\"fieldset-input is-3\"><legend class=\"sr-only\">Input Fields<\/legend><div class=\"field\" id=\"input-1\"><label for=\"field-1\">A<\/label><input type=\"number\" name=\"a\" id=\"field-1\" placeholder=\"2\" step=\"1\" value=\"2\"\/><\/div><div class=\"field\" id=\"input-2\"><label for=\"field-2\">B<\/label><input type=\"number\" name=\"b\" id=\"field-2\" placeholder=\"3\" step=\"1\" value=\"3\"\/><\/div><div class=\"field\" id=\"input-3\"><label for=\"field-3\">C<\/label><input type=\"number\" name=\"c\" id=\"field-3\" placeholder=\"4\" step=\"1\" value=\"4\"\/><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Re-Calculate\" id=\"calculate-button\" data-post=\"61923\">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>D (value that completes the proportion)<\/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=\"61923\" 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>Proportion 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\\[ \\frac{A}{B} = \\frac{C}{D} \\quad \\Rightarrow \\quad D = \\frac{B \\cdot C}{A} \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Where:<\/strong><\/p>\n<ul>\n<li>\\(A\\) \u2014 first term of the proportion (cannot be zero)<\/li>\n<li>\\(B\\) \u2014 second term of the proportion<\/li>\n<li>\\(C\\) \u2014 third term of the proportion<\/li>\n<li>\\(D\\) \u2014 the unknown value that completes the proportion<\/li>\n<\/ul>\n<p>The formula follows from the cross-multiplication rule: since \\(A \\cdot D = B \\cdot C\\), dividing both sides by \\(A\\) gives the missing value.<\/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>Proportion \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Example:<\/strong> in a proportion, \\(A = 2\\), \\(B = 3\\), and \\(C = 4\\). Find \\(D\\).<\/p>\n<p>\\[ D = \\frac{B \\cdot C}{A} = \\frac{3 \\cdot 4}{2} = \\frac{12}{2} = 6 \\]<\/p>\n<p><strong>Result:<\/strong> \\(D = 6\\), so the complete proportion is \\(\\frac{2}{3} = \\frac{4}{6}\\).<\/p>\n<p>\n\r\n<\/section>\n<h2>How to use the calculator<\/h2>\n<ol>\n<li>Enter the value of \\(A\\) in the first field (it must not be zero).<\/li>\n<li>Enter the value of \\(B\\) in the second field.<\/li>\n<li>Enter the value of \\(C\\) in the third field.<\/li>\n<li>The result field \"D (value that completes the proportion)\" updates automatically, showing the number rounded to four decimal places.<\/li>\n<\/ol>\n<h2>What is a proportion?<\/h2>\n<p>A proportion is a statement that two ratios are equal: \\(\\frac{A}{B} = \\frac{C}{D}\\). It expresses a relationship of equivalence between two pairs of quantities: whenever \\(A\\) relates to \\(B\\) the same way \\(C\\) relates to \\(D\\), the four numbers form a proportion. In the classical notation \\(A : B = C : D\\), the terms \\(A\\) and \\(D\\) are called the <em>extremes<\/em> and \\(B\\) and \\(C\\) the <em>means<\/em>.<\/p>\n<p>The defining property of any proportion is that the product of the extremes equals the product of the means: \\(A \\cdot D = B \\cdot C\\). This is the cross-multiplication rule, and it is what lets you recover any one missing term from the other three. The calculator applies \\(D = \\frac{B \\cdot C}{A}\\), which is simply this rule solved for \\(D\\).<\/p>\n<p>Proportions appear everywhere quantities scale together. If a map uses a 1:1000 scale, real distances are found proportionally. Doubling a recipe, converting units, mixing paint in a fixed ratio, resizing an image while keeping its aspect ratio, or computing unit prices all reduce to finding the fourth term of a proportion. The same idea underlies <a href=\"https:\/\/wpcalc.com\/en\/mathematics\/direct-variation\/\">direct variation<\/a>, where two variables always change at a constant ratio.<\/p>\n<p>Interpreting the result is straightforward: the computed \\(D\\) tells you exactly what value keeps the two ratios equal. If \\(D\\) comes out larger than \\(C\\), the second ratio involves bigger numbers than the first at the same relative scale; if smaller, the opposite. A negative \\(D\\) simply means the proportion includes negative terms \u2014 the arithmetic is unchanged.<\/p>\n<h2>Assumptions, limitations and tips<\/h2>\n<ul>\n<li><strong>A cannot be zero.<\/strong> The formula divides by \\(A\\), so the calculator returns an error if \\(A = 0\\). If your known values leave a different term unknown, rearrange the proportion first so the missing value plays the role of \\(D\\).<\/li>\n<li><strong>Any three of the four terms can be used.<\/strong> If you know \\(B\\), \\(C\\), and \\(D\\) instead, invert the proportion: \\(\\frac{B}{A} = \\frac{D}{C}\\) is equivalent, so entering \\(B\\), \\(D\\), \\(C\\) as \\(A\\), \\(B\\), \\(C\\) recovers \\(A\\).<\/li>\n<li><strong>Precision.<\/strong> Results are rounded to four decimal places, which is enough for most practical uses. For exact fractions, work with whole-number inputs where possible.<\/li>\n<li><strong>Order matters.<\/strong> The fields must match the layout of the proportion: \\(A\\) over \\(B\\) equals \\(C\\) over \\(D\\). Swapping values between the numerator and denominator positions changes the answer.<\/li>\n<li><strong>Units.<\/strong> For the result to be meaningful, quantities in the same position across the two ratios must share the same unit (e.g., both numerators in kilometers, both denominators in hours).<\/li>\n<\/ul>\n<p>Proportions are also the gateway to broader algebra: the same ratio reasoning supports <a href=\"https:\/\/wpcalc.com\/en\/mathematics\/geometric-progression\/\">geometric progressions<\/a>, whose consecutive terms always form a constant ratio, and it appears in the cross-multiplication steps used when solving <a href=\"https:\/\/wpcalc.com\/en\/mathematics\/linear-inequalities-calculator\/\">linear inequalities<\/a> or systems by the <a href=\"https:\/\/wpcalc.com\/en\/mathematics\/elimination-method\/\">elimination method<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>This proportion calculator finds the missing value in a proportion of the form A\/B = C\/D. Enter any three known values (A, B, C) and it computes the fourth (D) using cross-multiplication.<\/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":[7],"tags":[11],"class_list":["post-61923","post","type-post","status-publish","format-standard","hentry","category-mathematics","tag-algebra"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/61923","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=61923"}],"version-history":[{"count":3,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/61923\/revisions"}],"predecessor-version":[{"id":66279,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/61923\/revisions\/66279"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=61923"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=61923"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=61923"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}