{"id":61943,"date":"2021-06-01T12:21:21","date_gmt":"2021-06-01T10:21:21","guid":{"rendered":"https:\/\/wpcalc.com\/?p=61943"},"modified":"2026-10-23T16:57:01","modified_gmt":"2026-10-23T13:57:01","slug":"relative-percentage-difference","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/mathematics\/relative-percentage-difference\/","title":{"rendered":"Relative Percent Difference Calculator (RPD)"},"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\">Compare Two Values in Percentages<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"61943\" data-favorite-title=\"Relative Percentage Difference\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/mathematics\/relative-percentage-difference\/\" data-favorite-excerpt=\"Enter two numbers to find their relative percentage difference (RPD): the absolute difference divided by the average of the values, expressed as a percent. Useful for comparing duplicate measurements, lab samples, and two equally valid values.\" 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\/relative-percentage-difference\/\" method=\"POST\" class=\"calculator\" id=\"calculator-61943\" data-post=\"61943\"><fieldset class=\"fieldset-input\"><legend class=\"sr-only\">Input Fields<\/legend><div class=\"field\" id=\"input-1\"><label for=\"field-1\">Original number<\/label><input type=\"number\" name=\"original_number\" id=\"field-1\" placeholder=\"100\" step=\"0.01\" value=\"100\"\/><\/div><div class=\"field\" id=\"input-2\"><label for=\"field-2\">Second number<\/label><input type=\"number\" name=\"second_number\" id=\"field-2\" placeholder=\"90\" step=\"0.01\" value=\"90\"\/><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Re-Calculate\" id=\"calculate-button\" data-post=\"61943\">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>Relative Percentage Difference<\/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=\"61943\" 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>Relative Percentage Difference 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\\[ \\text{RPD} = \\left( \\frac{|\\text{Num}_1 - \\text{Num}_2|}{\\dfrac{\\text{Num}_1 + \\text{Num}_2}{2}} \\right) \\times 100 \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Where:<\/strong><\/p>\n<ul>\n<li>\\( |\\text{Num}_1 - \\text{Num}_2| \\) \u2014 absolute difference between the two numbers<\/li>\n<li>\\( \\dfrac{\\text{Num}_1 + \\text{Num}_2}{2} \\) \u2014 average (mean) of the two numbers<\/li>\n<\/ul>\n<p>The formula expresses the gap between two values as a percentage of their mean. Because the difference is taken as an absolute value, the result is always non-negative and is the same whichever number you enter first.<\/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>Relative Percentage Difference \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Example:<\/strong> two measurements of the same quantity give 100 and 90.<\/p>\n<p>\\[ \\text{diff} = |100 - 90| = 10 \\]<\/p>\n<p>\\[ \\text{avg} = \\frac{100 + 90}{2} = 95 \\]<\/p>\n<p>\\[ \\text{RPD} = \\frac{10}{95} \\times 100 = 10.5263\\% \\]<\/p>\n<p><strong>Result:<\/strong> the relative percentage difference is 10.5263 %.<\/p>\n<p>\n\r\n<\/section>\n<h2>How to use the calculator<\/h2>\n<ol>\n<li>Enter the first value in the <strong>Original number<\/strong> field (e.g. 100).<\/li>\n<li>Enter the second value in the <strong>Second number<\/strong> field (e.g. 90).<\/li>\n<li>The <strong>Relative Percentage Difference<\/strong> is displayed instantly, rounded to four decimal places.<\/li>\n<\/ol>\n<p>The order of the two numbers does not matter: swapping them gives the same result, since the formula uses the absolute difference and the average.<\/p>\n<h2>What is relative percentage difference?<\/h2>\n<p>The relative percentage difference (RPD) measures how far apart two numbers are, expressed as a percentage of their average. It answers the question: \"How large is the disagreement between these two values relative to their size?\" A result of 0 % means the numbers are identical; larger values mean greater disagreement.<\/p>\n<p>RPD is the standard tool when neither value can serve as a reference. If you compare a measurement against a known true value, <a href=\"https:\/\/wpcalc.com\/en\/mathematics\/percentage-error-calculator\/\">percentage error<\/a> is the right choice. But when you compare two measurements of equal standing \u2014 for instance, duplicate lab samples analyzed by the same method, results from two different instruments, or two analysts measuring the same thing \u2014 there is no \"correct\" value to compare against, and RPD is the symmetric, order-independent alternative.<\/p>\n<p>Because RPD is always non-negative, it tells you the size of the difference but not its direction. If you need to know whether a value increased or decreased from a starting point, use <a href=\"https:\/\/wpcalc.com\/en\/mathematics\/percentage-change-calculator\/\">percentage change<\/a> instead.<\/p>\n<h2>How to interpret the result<\/h2>\n<p>The result is a percentage of the mean of the two values. In the example above, 10.5263 % means the two numbers differ by about one tenth of their average. Common acceptance thresholds depend on the field: in environmental and analytical chemistry, duplicate samples with an RPD below 10\u201320 % are often considered acceptable, while stricter work may require values under 5 %.<\/p>\n<p>Note that RPD is more forgiving than a simple relative change when the values are large, and more sensitive when they are small. Comparing 100 and 90 gives 10.53 %, but comparing 10 and 0 gives 200 % \u2014 the same absolute gap of 10 produces very different percentages because the average differs.<\/p>\n<h2>Assumptions, limitations and tips<\/h2>\n<ul>\n<li><strong>Zero average:<\/strong> the formula is undefined when the two numbers sum to zero (e.g. 5 and \u22125), because you would divide by zero. In that case RPD cannot be computed.<\/li>\n<li><strong>Negative numbers:<\/strong> the calculator handles negative inputs, but be cautious when the values straddle zero \u2014 the average can be very small, producing misleadingly huge percentages.<\/li>\n<li><strong>No direction:<\/strong> RPD never tells you which value is larger. Use it for magnitude of agreement only.<\/li>\n<li><strong>Two values only:<\/strong> for more than two measurements, consider a mean-based statistic such as the <a href=\"https:\/\/wpcalc.com\/en\/mathematics\/quadratic-mean-calculator-root-mean-square\/\">quadratic mean<\/a> or <a href=\"https:\/\/wpcalc.com\/en\/mathematics\/weighted-mean\/\">weighted mean<\/a> as a companion measure.<\/li>\n<li><strong>Naming:<\/strong> RPD is sometimes used interchangeably with <a href=\"https:\/\/wpcalc.com\/en\/mathematics\/percentage-difference-calculator\/\">percentage difference<\/a>. Both divide the absolute difference by the average of the two values, so the results match.<\/li>\n<\/ul>\n<h2>Quick reference values<\/h2>\n<table>\n<thead>\n<tr>\n<th>Num 1<\/th>\n<th>Num 2<\/th>\n<th>Average<\/th>\n<th>Abs. difference<\/th>\n<th>RPD<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>100<\/td>\n<td>90<\/td>\n<td>95<\/td>\n<td>10<\/td>\n<td>10.5263 %<\/td>\n<\/tr>\n<tr>\n<td>100<\/td>\n<td>95<\/td>\n<td>97.5<\/td>\n<td>5<\/td>\n<td>5.1282 %<\/td>\n<\/tr>\n<tr>\n<td>100<\/td>\n<td>100<\/td>\n<td>100<\/td>\n<td>0<\/td>\n<td>0 %<\/td>\n<\/tr>\n<tr>\n<td>100<\/td>\n<td>50<\/td>\n<td>75<\/td>\n<td>50<\/td>\n<td>66.6667 %<\/td>\n<\/tr>\n<tr>\n<td>10<\/td>\n<td>0<\/td>\n<td>5<\/td>\n<td>10<\/td>\n<td>200 %<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"excerpt":{"rendered":"<p>Enter two numbers to find their relative percentage difference (RPD): the absolute difference divided by the average of the values, expressed as a percent. Useful for comparing duplicate measurements, lab samples, and two equally valid values.<\/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":[71],"class_list":["post-61943","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\/61943","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=61943"}],"version-history":[{"count":5,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/61943\/revisions"}],"predecessor-version":[{"id":67494,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/61943\/revisions\/67494"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=61943"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=61943"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=61943"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}