{"id":65015,"date":"2025-07-18T13:38:41","date_gmt":"2025-07-18T10:38:41","guid":{"rendered":"https:\/\/wpcalc.com\/en\/?p=65015"},"modified":"2026-09-30T20:48:27","modified_gmt":"2026-09-30T17:48:27","slug":"reverse-percentage-calculator","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/mathematics\/reverse-percentage-calculator\/","title":{"rendered":"Reverse Percentage 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 the Original Value from Final and Percentage<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"65015\" data-favorite-title=\"Reverse Percentage\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/mathematics\/reverse-percentage-calculator\/\" data-favorite-excerpt=\"Find the original value before a percentage increase or decrease was applied. Enter the final value, the percentage change, and whether it was an increase or a decrease \u2014 the calculator reverses the change to reveal the starting number.\" aria-label=\"Add to Favorites\" data-favorite-icon=\"icon icon-percent-sign\">\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\/reverse-percentage-calculator\/\" method=\"POST\" class=\"calculator\" id=\"calculator-65015\" data-post=\"65015\"><fieldset class=\"fieldset-input\"><legend class=\"sr-only\">Input Fields<\/legend><div class=\"field has-term\" id=\"input-1\"><label for=\"field-1\">Final value<\/label><div class=\"term\">Final<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"final_value\" id=\"field-1\" aria-describedby=\"calc-info-1\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" min=\"0\" value=\"120\"\/><small id=\"calc-info-1\">Enter the final value after the percentage change<\/small><\/div><div class=\"field has-term\" id=\"input-2\"><label for=\"field-2\">Percentage change<\/label><div class=\"term\">%<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"number\" name=\"percentage_change\" id=\"field-2\" aria-describedby=\"calc-info-2\" step=\"any\" value=\"20\"\/><small id=\"calc-info-2\">Enter the percentage increase or decrease<\/small><\/div><div class=\"field is-single\" id=\"input-3\"><label for=\"field-3\">Change type<\/label><div class=\"grid grid-cols-1\"><select id=\"field-3\" name=\"change_type\"><option value=\"increase\">Increase<\/option><option value=\"decrease\">Decrease<\/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><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Re-Calculate\" id=\"calculate-button\" data-post=\"65015\">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>Original value<\/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=\"65015\" 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\">1<\/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>Reverse Percentage 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\\[\n\\text{After an increase:} \\quad \\text{Original} = \\frac{\\text{Final}}{1 + \\frac{p}{100}} \\\\[1.2em]\n\\text{After a decrease:} \\quad \\text{Original} = \\frac{\\text{Final}}{1 - \\frac{p}{100}}\n\\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Where:<\/strong><\/p>\n<ul>\n<li>\\(\\text{Final}\\) \u2014 the value you have after the percentage change was applied<\/li>\n<li>\\(p\\) \u2014 the percentage change (e.g. 20 for 20%)<\/li>\n<li>\\(\\text{Original}\\) \u2014 the starting value before the change<\/li>\n<\/ul>\n<p>Dividing the final value by the growth or shrink factor converts the result back to the base it was calculated from. Note that you divide by \\(1 \\pm p\/100\\), not by simply subtracting or adding \\(p\\%\\) of the final value \u2014 that is the most common mistake with reverse percentages.<\/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>Reverse Percentage \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Example:<\/strong> a price rose by 20% and is now 120. What was the original price?<\/p>\n<p>\\[ 1 + \\frac{20}{100} = 1.20 \\]<\/p>\n<p>\\[ \\text{Original} = \\frac{120}{1.20} = 100 \\]<\/p>\n<p><strong>Result:<\/strong> the original value was 100.<\/p>\n<p><strong>Example 2:<\/strong> a price fell by 20% and is now 80. Then \\(1 - 20\/100 = 0.80\\), so \\(\\text{Original} = 80 \/ 0.80 = 100\\). A 20% decrease followed by a 20% increase does <em>not<\/em> return 100 \u2014 the decrease costs 20 units, but the increase only adds back 16.<\/p>\n<p>\n\r\n<\/section>\n<h2>How to Use the Reverse Percentage Calculator<\/h2>\n<ol>\n<li>Enter the <strong>Final value<\/strong> \u2014 the number you have after the change (e.g. a discounted price or a tax-inclusive amount).<\/li>\n<li>Enter the <strong>Percentage change<\/strong> that was applied, as a plain number (e.g. 20 for 20%, not 0.2).<\/li>\n<li>Choose the <strong>Change type<\/strong>: <em>Increase<\/em> if the value went up, <em>Decrease<\/em> if it went down.<\/li>\n<li>Read the <strong>Original value<\/strong> \u2014 the number before the percentage was applied.<\/li>\n<\/ol>\n<h2>What Is a Reverse Percentage?<\/h2>\n<p>A reverse percentage (also called \"finding the original value\" or \"working backwards from a percentage\") answers the question: <em>I know the number after a percentage change \u2014 what was it before?<\/em> This comes up constantly: restoring a sale price to its full price, extracting the net price from a gross price that includes VAT or sales tax, or finding a company's revenue before a reported growth rate.<\/p>\n<p>The key insight is that a percentage change is always calculated <em>from the original value<\/em>, not from the final one. When a price increases by 20%, the final price is 120% of the original \u2014 a multiplier of 1.20. To undo the change, you divide by that multiplier. Multiplying by 1.20 and dividing by 1.20 are inverse operations, so you land exactly back on the starting number.<\/p>\n<p>This is also why you cannot simply subtract 20% of the final value. Taking 20% off 120 gives 96, not 100 \u2014 because 20% of 120 (24) is larger than 20% of 100 (20). The base matters, and reverse percentage is the method that respects the correct base.<\/p>\n<p>If you need to go the other direction \u2014 from an original value to a new one \u2014 use the <a href=\"https:\/\/wpcalc.com\/en\/mathematics\/percentage-change-calculator\/\">Percentage Change calculator<\/a>, or the dedicated <a href=\"https:\/\/wpcalc.com\/en\/mathematics\/percentage-increase-calculator\/\">Percentage Increase<\/a> and <a href=\"https:\/\/wpcalc.com\/en\/mathematics\/percentage-decrease-calculator\/\">Percentage Decrease<\/a> calculators. For everyday percentage problems in both directions, the general <a href=\"https:\/\/wpcalc.com\/en\/mathematics\/percentage-calculator\/\">Percentage calculator<\/a> is a good starting point.<\/p>\n<h2>Common Uses<\/h2>\n<ul>\n<li><strong>Sale prices:<\/strong> an item costs 80 after a 20% discount; the pre-sale price was 100.<\/li>\n<li><strong>Tax-inclusive amounts:<\/strong> a gross price of 120 with 20% VAT means a net price of 100 (VAT is 20% of the net, not of the gross).<\/li>\n<li><strong>Markups:<\/strong> a retail price of 138 with a 15% markup on cost means the cost was 120.<\/li>\n<li><strong>Financial reports:<\/strong> revenue of 1.15 million after 15% growth means last year's revenue was 1 million.<\/li>\n<\/ul>\n<h2>Assumptions and Limitations<\/h2>\n<ul>\n<li>The calculator assumes the percentage was applied exactly once to the original value, using the original as the base (the standard convention).<\/li>\n<li>A value cannot be decreased by 100% or more and remain positive \u2014 the calculator will warn you if you try a 100% decrease, since dividing by zero is undefined. Decreases over 100% would imply a negative original value, which rarely makes sense in practice.<\/li>\n<li>Compound changes must be undone one step at a time. If a value increased by 10% and then by another 10%, you cannot reverse it with a single 20% change: the combined multiplier is \\(1.10 \\times 1.10 = 1.21\\), not 1.20.<\/li>\n<li>Results are rounded to 4 decimal places, which is enough for money and most practical applications; tiny rounding differences may appear with repeating decimals.<\/li>\n<\/ul>\n<h2>Quick Reference Table<\/h2>\n<table>\n<thead>\n<tr>\n<th>Change<\/th>\n<th>Multiplier<\/th>\n<th>To reverse<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>+10%<\/td>\n<td>\\(1.10\\)<\/td>\n<td>Divide by 1.10<\/td>\n<\/tr>\n<tr>\n<td>+20%<\/td>\n<td>\\(1.20\\)<\/td>\n<td>Divide by 1.20<\/td>\n<\/tr>\n<tr>\n<td>+50%<\/td>\n<td>\\(1.50\\)<\/td>\n<td>Divide by 1.50<\/td>\n<\/tr>\n<tr>\n<td>\u221210%<\/td>\n<td>\\(0.90\\)<\/td>\n<td>Divide by 0.90<\/td>\n<\/tr>\n<tr>\n<td>\u221220%<\/td>\n<td>\\(0.80\\)<\/td>\n<td>Divide by 0.80<\/td>\n<\/tr>\n<tr>\n<td>\u221225%<\/td>\n<td>\\(0.75\\)<\/td>\n<td>Divide by 0.75<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Notice the asymmetry: reversing a 20% increase requires dividing by 1.20 (about a 16.67% reduction), while reversing a 20% decrease requires dividing by 0.80 (a 25% increase). Percentage changes are not symmetric in the two directions, and this table makes the pattern easy to check at a glance.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Find the original value before a percentage increase or decrease was applied. Enter the final value, the percentage change, and whether it was an increase or a decrease \u2014 the calculator reverses the change to reveal the starting number.<\/p>\n","protected":false},"author":3168,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[7],"tags":[71],"class_list":["post-65015","post","type-post","status-publish","format-standard","hentry","category-mathematics","tag-percentages-calculators"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/65015","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=65015"}],"version-history":[{"count":3,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/65015\/revisions"}],"predecessor-version":[{"id":66286,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/65015\/revisions\/66286"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=65015"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=65015"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=65015"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}