{"id":61696,"date":"2021-04-21T14:29:02","date_gmt":"2021-04-21T12:29:02","guid":{"rendered":"https:\/\/wpcalc.com\/?p=61696"},"modified":"2026-10-01T13:29:41","modified_gmt":"2026-10-01T10:29:41","slug":"free-water-deficit","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/en\/medical\/free-water-deficit\/","title":{"rendered":"Free Water Deficit \u2013 Hypernatremia 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\">Free Water Deficit \u2013 Hypernatremia<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"61696\" data-favorite-title=\"Free Water Deficit \u2013 Hypernatremia \" data-favorite-url=\"https:\/\/wpcalc.com\/en\/medical\/free-water-deficit\/\" data-favorite-excerpt=\"This calculator estimates the free water deficit in patients with hypernatremia. Select the patient type and enter weight, current serum sodium, and target sodium to find how much free water is needed to correct the sodium level.\" aria-label=\"Add to Favorites\" data-favorite-icon=\"icon icon-pharmacology\">\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\/medical\/free-water-deficit\/\" method=\"POST\" class=\"calculator\" id=\"calculator-61696\" data-post=\"61696\"><fieldset class=\"fieldset-input is-1\"><legend class=\"sr-only\">Input Fields<\/legend><div class=\"field\" id=\"input-1\"><label for=\"field-1\">Patient type<\/label><div class=\"grid grid-cols-1\"><select id=\"field-1\" name=\"patient_type\"><option value=\"1\" selected>Adult Male<\/option><option value=\"2\">Adult Female<\/option><option value=\"3\">Elderly Male<\/option><option value=\"4\">Elderly Female<\/option><option value=\"5\">Child<\/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 class=\"field\" id=\"input-2\"><label for=\"field-2\">Weight<\/label><input type=\"number\" name=\"weight\" id=\"field-2\" aria-describedby=\"calc-unit-2\" placeholder=\"Weight\" step=\"any\" value=\"70\"\/><div class=\"unit\" id=\"calc-unit-2\">kg<\/div><\/div><div class=\"field has-term\" id=\"input-3\"><label for=\"field-3\">Current sodium<\/label><div class=\"term\">Na<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"number\" name=\"current_sodium\" id=\"field-3\" aria-describedby=\"calc-unit-3\" placeholder=\"Current Na\" step=\"any\" value=\"160\"\/><div class=\"unit\" id=\"calc-unit-3\">mEq\/L<\/div><\/div><div class=\"field has-term\" id=\"input-4\"><label for=\"field-4\">Desired sodium<\/label><div class=\"term\">Na<\/div>  <div class=\"absolute bottom-0 left-16 top-8 w-2 h-0.5 bg-blue-500\"><\/div><input type=\"number\" name=\"desired_sodium\" id=\"field-4\" aria-describedby=\"calc-unit-4\" placeholder=\"Desired Na\" step=\"any\" value=\"140\"\/><div class=\"unit\" id=\"calc-unit-4\">mEq\/L<\/div><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Re-Calculate\" id=\"calculate-button\" data-post=\"61696\">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>Free water deficit:<\/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=\"61696\" 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>Free Water Deficit 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{Free Water Deficit} = TBW \\times \\left( \\frac{\\text{Na}_{\\text{current}}}{\\text{Na}_{\\text{desired}}} - 1 \\right) \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>Where:<\/strong><\/p>\n<ul>\n<li>\\(TBW\\) \u2014 total body water in liters, estimated as body weight multiplied by a factor based on patient type: 0.6 for adult males and children, 0.5 for adult females and elderly males, 0.45 for elderly females<\/li>\n<li>\\(\\text{Na}_{\\text{current}}\\) \u2014 current serum sodium concentration (mEq\/L)<\/li>\n<li>\\(\\text{Na}_{\\text{desired}}\\) \u2014 target serum sodium concentration, usually around 140 mEq\/L<\/li>\n<\/ul>\n<p>The formula estimates the volume of free water (pure water, without electrolytes) that must be replaced to bring the serum sodium concentration down to the desired 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>Free Water Deficit \u2013 Calculation Example<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Example:<\/strong> an adult male weighing 70 kg has a serum sodium of 160 mEq\/L, and the treatment goal is to lower it to 140 mEq\/L.<\/p>\n<p>\\[ TBW = 0.6 \\times 70 = 42 \\text{ L} \\]<\/p>\n<p>\\[ \\text{Free Water Deficit} = 42 \\times \\left( \\frac{160}{140} - 1 \\right) = 42 \\times 0.1429 \\approx 6.0 \\text{ L} \\]<\/p>\n<p><strong>Result:<\/strong> the free water deficit is approximately 6.0 liters.<\/p>\n<p>\n\r\n<\/section>\n<h2>How to use the calculator<\/h2>\n<ol>\n<li>Open the <strong>Patient type<\/strong> dropdown and select Adult Male, Adult Female, Elderly Male, Elderly Female, or Child. This sets the total body water fraction used in the formula.<\/li>\n<li>Enter the patient's <strong>Weight<\/strong> in kilograms.<\/li>\n<li>Enter the <strong>Current sodium<\/strong> level in mEq\/L from the most recent laboratory result.<\/li>\n<li>Enter the <strong>Desired sodium<\/strong> target in mEq\/L \u2014 typically 140 mEq\/L, or a safe intermediate goal.<\/li>\n<li>Read the <strong>Free water deficit<\/strong> result, shown in liters.<\/li>\n<\/ol>\n<h2>What is free water deficit?<\/h2>\n<p>Free water deficit is the amount of water the body is missing relative to its electrolyte content. Hypernatremia \u2014 a serum sodium above roughly 145 mEq\/L \u2014 almost always reflects a deficit of water rather than an excess of sodium. Because sodium is dissolved in body water, the ratio between sodium and water determines the measured concentration. When water is lost faster than sodium (through inadequate intake, diabetes insipidus, osmotic diuresis, or excessive losses from skin and gut), the sodium concentration rises even though total body sodium may be normal.<\/p>\n<p>The free water deficit formula works backwards from that ratio. Total body water (TBW) is estimated from weight using population averages: about 60% of body weight in adult men and children, 50% in adult women and elderly men, and 45% in elderly women, since body water content falls with age and varies with body composition. The formula then asks how much pure water must be added so that the current amount of sodium is diluted to the target concentration.<\/p>\n<p>The result should be interpreted as a total correction volume, not a dose to give all at once. Serum sodium must be lowered slowly \u2014 typically no faster than 10\u201312 mEq\/L in 24 hours \u2014 because rapid correction can cause cerebral edema and seizures. In practice, clinicians divide the deficit over 48\u201372 hours and reassess sodium levels frequently, adjusting fluids to ongoing losses. The choice of fluid (usually hypotonic saline or dextrose-containing solutions rather than sterile water) also affects how quickly the deficit is corrected, and ongoing water losses must be replaced in addition to the calculated deficit.<\/p>\n<h2>Assumptions and limitations<\/h2>\n<ul>\n<li><strong>TBW estimates are approximations.<\/strong> The fraction of body weight that is water varies with obesity, muscle mass, and hydration status. In obese patients, using actual weight may overestimate TBW; some clinicians use adjusted body weight.<\/li>\n<li><strong>The formula assumes a steady state.<\/strong> It does not account for ongoing free water losses (urine output, fever, ventilator losses), which must be measured and added separately.<\/li>\n<li><strong>It ignores sodium and potassium changes.<\/strong> The classic Adrogu\u00e9\u2013Madias approach, which factors in the sodium and potassium content of the replacement fluid, may predict correction rates more accurately than the simple deficit formula.<\/li>\n<li><strong>Not all hypernatremia is treated the same way.<\/strong> In hypovolemic patients, volume must be restored with isotonic fluids before free water deficit is corrected; in diabetes insipidus, the underlying cause must be addressed.<\/li>\n<li><strong>This tool is for education and reference.<\/strong> It does not replace clinical judgment, and any fluid plan for hypernatremia should be managed by a physician with serial sodium monitoring.<\/li>\n<\/ul>\n<h2>Related calculators<\/h2>\n<p>For related assessments, you may also find these useful: the <a href=\"https:\/\/wpcalc.com\/en\/medical\/hyperglycemia-sodium-correction\/\">Corrected Sodium (Hyperglycemia) Calculator<\/a> adjusts sodium readings when glucose is elevated, the <a href=\"https:\/\/wpcalc.com\/en\/medical\/clinical-dehydration-scale\/\">Clinical Dehydration Scale<\/a> grades the severity of dehydration in children, and the <a href=\"https:\/\/wpcalc.com\/en\/medical\/dosage-infusion\/\">Dosage Infusion Calculator<\/a> helps set up the intravenous fluid rates needed to deliver the calculated replacement volume.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>This calculator estimates the free water deficit in patients with hypernatremia. Select the patient type and enter weight, current serum sodium, and target sodium to find how much free water is needed to correct the sodium level.<\/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":[8],"tags":[32],"class_list":["post-61696","post","type-post","status-publish","format-standard","hentry","category-medical","tag-pharmacology"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/61696","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=61696"}],"version-history":[{"count":3,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/61696\/revisions"}],"predecessor-version":[{"id":66325,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/posts\/61696\/revisions\/66325"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/media?parent=61696"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/categories?post=61696"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/en\/wp-json\/wp\/v2\/tags?post=61696"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}