{"id":66508,"date":"2026-10-06T17:38:54","date_gmt":"2026-10-06T14:38:54","guid":{"rendered":"https:\/\/wpcalc.com\/en\/?p=66508"},"modified":"2026-10-06T17:38:54","modified_gmt":"2026-10-06T14:38:54","slug":"degree-of-unsaturation-calculator","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/chemistry\/degree-of-unsaturation-calculator\/","title":{"rendered":"Degree of Unsaturation 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\">Count Rings and \u03c0 Bonds from a Molecular Formula<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"66508\" data-favorite-title=\"Degree of Unsaturation\" data-favorite-url=\"https:\/\/wpcalc.com\/en\/chemistry\/degree-of-unsaturation-calculator\/\" data-favorite-excerpt=\"Enter the counts of carbon, hydrogen, nitrogen and halogen atoms from a molecular formula to find the degree of unsaturation (DBE\/IHD) \u2014 the total number of rings and \u03c0 bonds the molecule must contain.\" aria-label=\"Add to Favorites\" data-favorite-icon=\"icon icon-molecule\">\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\/degree-of-unsaturation-calculator\/\" method=\"POST\" class=\"calculator\" id=\"calculator-66508\" data-post=\"66508\"><fieldset class=\"fieldset-input is-2\"><legend class=\"sr-only\">Input Fields<\/legend><div class=\"is-single field\" id=\"input-1\"><span class=\"font-semibold\">Atom Counts from the Molecular Formula<\/span><\/div><div class=\"field has-term\" id=\"input-2\"><label for=\"field-2\">Carbon (C)<\/label><div class=\"term\">C<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"carbon_c\" id=\"field-2\" aria-describedby=\"calc-info-2\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 6\" min=\"1\" value=\"6\"\/><small id=\"calc-info-2\">Number of carbon atoms in the formula<\/small><\/div><div class=\"field has-term\" id=\"input-3\"><label for=\"field-3\">Hydrogen (H)<\/label><div class=\"term\">H<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"hydrogen_h\" id=\"field-3\" aria-describedby=\"calc-info-3\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 6\" min=\"0\" value=\"6\"\/><small id=\"calc-info-3\">Number of hydrogen atoms<\/small><\/div><div class=\"field has-term\" id=\"input-4\"><label for=\"field-4\">Nitrogen (N)<\/label><div class=\"term\">N<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"nitrogen_n\" id=\"field-4\" aria-describedby=\"calc-info-4\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 0\" min=\"0\" value=\"0\"\/><small id=\"calc-info-4\">Number of nitrogen atoms (trivalent)<\/small><\/div><div class=\"field has-term\" id=\"input-5\"><label for=\"field-5\">Halogens (X)<\/label><div class=\"term\">X<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"text\" name=\"halogens_x\" id=\"field-5\" aria-describedby=\"calc-info-5\" data-number inputmode=\"decimal\" autocomplete=\"off\" spellcheck=\"false\" placeholder=\"e.g. 0\" min=\"0\" value=\"0\"\/><small id=\"calc-info-5\">Total F, Cl, Br and I atoms \u2014 they count like hydrogens<\/small><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Re-Calculate\" id=\"calculate-button\" data-post=\"66508\">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> Unsaturation Analysis<\/h3><div class=\"result-box\"><div class=\"field-result\" id=\"output-1\"><span class=\"field-title\"><span>Degree of Unsaturation<\/span><span class=\"result-term\">DoU<\/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\" id=\"output-2\"><span class=\"field-title\"><span>Maximum Possible Rings<\/span><span class=\"result-term\">rings<\/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 class=\"field-result is-column\" id=\"output-3\"><span class=\"field-title\"><span>Interpretation<\/span><\/span><span class=\"field-value\" id=\"result-3\"><\/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-4\"><span class=\"field-title\"><span>Calculation Details<\/span><\/span><span class=\"field-value\" id=\"result-4\"><\/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=\"66508\" 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>Degree of Unsaturation 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{DoU} = C - \\frac{H + X}{2} + \\frac{N}{2} + 1 = \\frac{2C + 2 + N - H - X}{2} \\]<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Where:<\/strong><\/p>\n<ul>\n<li>\\(C\\) \u2014 number of carbon atoms<\/li>\n<li>\\(H\\) \u2014 number of hydrogen atoms<\/li>\n<li>\\(N\\) \u2014 number of nitrogen atoms<\/li>\n<li>\\(X\\) \u2014 total number of halogen atoms (F, Cl, Br, I)<\/li>\n<\/ul>\n<p>The formula gives the total number of rings and \\(\\pi\\) bonds in a neutral, closed-shell molecule containing only C, H, N, halogens, O and S. Oxygen and sulfur atoms are ignored because their typical valences cancel out of the hydrogen balance.<\/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>Degree of Unsaturation \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Example:<\/strong> a compound with the molecular formula C<sub>6<\/sub>H<sub>6<\/sub> (benzene). Enter C = 6, H = 6, N = 0, X = 0.<\/p>\n<p>\\[ \\text{DoU} = \\frac{2(6) + 2 + 0 - 6 - 0}{2} = \\frac{14 - 6}{2} = \\frac{8}{2} = 4 \\]<\/p>\n<p><strong>Result:<\/strong> DoU = 4. Benzene must contain 4 degrees of unsaturation in total \u2014 indeed one ring plus three double bonds (1 + 3 = 4).<\/p>\n<p>\n\r\n<\/section>\n<h2>How to Use the Calculator<\/h2>\n<ol>\n<li>Read the molecular formula of your compound and count the carbon atoms; enter this number in the <strong>Carbon (C)<\/strong> field.<\/li>\n<li>Count the hydrogen atoms and enter the total in the <strong>Hydrogen (H)<\/strong> field.<\/li>\n<li>Count all nitrogen atoms and enter the total in the <strong>Nitrogen (N)<\/strong> field (enter 0 if there are none).<\/li>\n<li>Add up every fluorine, chlorine, bromine and iodine atom and enter the sum in the <strong>Halogens (X)<\/strong> field. Do not enter them one at a time.<\/li>\n<li>Leave out oxygen and sulfur entirely \u2014 they have no effect on the result.<\/li>\n<li>Read the <strong>Degree of Unsaturation<\/strong>, the <strong>Maximum Possible Rings<\/strong>, the <strong>Interpretation<\/strong> and the step-by-step <strong>Calculation Details<\/strong> below the inputs.<\/li>\n<\/ol>\n<h2>What Is the Degree of Unsaturation?<\/h2>\n<p>The degree of unsaturation (also called the index of hydrogen deficiency, IHD, or double bond equivalents, DBE) tells you how many rings and \\(\\pi\\) bonds a molecule contains, based only on its molecular formula. Every ring \"costs\" one degree, every double bond (C=C, C=O, C=N, N=N) costs one degree, and every triple bond (C\u2261C, C\u2261N) costs two degrees because it contains two \\(\\pi\\) bonds.<\/p>\n<p>The idea comes from hydrogen counting. An acyclic saturated alkane with \\(n\\) carbons holds the maximum possible number of hydrogens: \\(2n + 2\\). Every ring or \\(\\pi\\) bond removes two hydrogens from that maximum. By comparing the hydrogens (plus halogens, which behave like hydrogens) your formula actually has against the saturated maximum, you can count the missing \"units of saturation\" \u2014 hence the name index of hydrogen deficiency.<\/p>\n<p>The result is a constraint, not a structure. A DoU of 4 for C<sub>6<\/sub>H<sub>6<\/sub> is consistent with benzene, but also with, say, two rings plus two double bonds. Spectroscopy (NMR, IR) and chemical intuition are needed to pin down the actual arrangement. Still, the DoU is one of the first checks chemists make when solving an unknown-structure problem, because it immediately rules out impossible skeletons and flags aromatic systems (a benzene ring alone always contributes 4).<\/p>\n<p>A useful sanity check: DoU = 0 means the molecule is fully saturated and acyclic \u2014 an alkane or haloalkane with only single bonds. A half-integer result (such as 2.5) is a red flag: neutral closed-shell molecules always give whole numbers, so a fractional value points to a radical, an ion, or a typo in the formula.<\/p>\n<h2>Assumptions, Limitations and Tips<\/h2>\n<ul>\n<li><strong>Valence assumptions:<\/strong> the formula assumes carbon is tetravalent, nitrogen trivalent, and hydrogen and halogens monovalent \u2014 the normal valences in neutral organic molecules. Unusual valences (e.g., nitro groups written in charge-separated form still work, but exotic species may not) can break the count.<\/li>\n<li><strong>Oxygen and sulfur are ignored:<\/strong> O and S atoms (divalent) do not appear in the formula, so you do not need to count them. The same result holds whether the compound is C<sub>6<\/sub>H<sub>6<\/sub>, C<sub>6<\/sub>H<sub>6<\/sub>O or C<sub>6<\/sub>H<sub>6<\/sub>O<sub>2<\/sub>.<\/li>\n<li><strong>Halogens count as hydrogens:<\/strong> chloroform CHCl<sub>3<\/sub> is treated like CH<sub>4<\/sub> (H + X = 4), giving DoU = 0. Enter the sum of all F, Cl, Br and I atoms in a single field.<\/li>\n<li><strong>Phosphorus and boron:<\/strong> the calculator does not handle P or B. For P (trivalent, like N) an approximate extension adds +\u00bd per P atom; boron (trivalent but electron-deficient) does not fit the simple rule.<\/li>\n<li><strong>Maximum Possible Rings:<\/strong> since each ring uses exactly one degree of unsaturation, the ring count can never exceed the DoU \u2014 that is what the second result field shows. The actual number of rings could be anything from 0 up to this value.<\/li>\n<li><strong>Ions and radicals:<\/strong> the formula is derived for neutral, closed-shell molecules. Charged species or radicals often give half-integer or otherwise misleading values; interpret such results with care.<\/li>\n<\/ul>\n<p>If you are also working out the composition of a compound, the <a href=\"https:\/\/wpcalc.com\/en\/chemistry\/empirical-formula-calculator\/\">Empirical Formula Calculator<\/a> pairs well with this tool, and the <a href=\"https:\/\/wpcalc.com\/en\/chemistry\/formal-charge-calculator\/\">Formal Charge Calculator<\/a> helps when you suspect your species is an ion. For reaction planning, see the <a href=\"https:\/\/wpcalc.com\/en\/chemistry\/limiting-reactant-calculator\/\">Limiting Reactant Calculator<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Enter the counts of carbon, hydrogen, nitrogen and halogen atoms from a molecular formula to find the degree of unsaturation (DBE\/IHD) \u2014 the total number of rings and \u03c0 bonds the molecule must contain.<\/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":[54],"tags":[61],"class_list":["post-66508","post","type-post","status-publish","format-standard","hentry","category-chemistry","tag-bonding"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66508","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=66508"}],"version-history":[{"count":1,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66508\/revisions"}],"predecessor-version":[{"id":66509,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/66508\/revisions\/66509"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=66508"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=66508"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=66508"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}