Free Water Deficit Calculator

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Created by Georgi Georgiev
Last updated: Aug 13, 2026

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1. Water deficit and dehydration
2. How to use the free water deficit calculator
3. Free water deficit equations
• Sodium concentration formula
• Plasma osmolality formula
4. Advantages of using plasma osmolality in WD estimation
5. Water deficit estimation for patients with diabetes

    Water deficit and dehydration

In medicine, water deficit (WD) is the volume of water required to correct dehydration during the initial stages of fluid-replacement therapy in electrolyte disorders. A free water deficit estimate is most often used to determine the amount of free water needed to correct hypernatremia.

FWD is used to manage hypernatremia when deciding fluid replenishment which is done by oral intake in less severe cases and can demand intravenous (IV) delivery in more severe ones. Hypernatremia management in general requires replacement of water deficit, ongoing losses and insensible losses, alongside identification of the underlying cause. Although some sources state that rapid over-correction can result in cerebral edema others state that "In adults, rapid correction does not appear to cause poor neurologic outcomes, and failure to correct hypernatremia within 72 hours has been associated with worsening mortality in hospitalized patients." and further "Although a correction of less than 10 mEq per L per 24 hours has been recommended based on expert opinion, more recent evidence suggests that hypernatremia in adults can be corrected at a rate of 12 mEq per L over 24 hours." ^[1].

    How to use the free water deficit calculator

This tool should only be used by qualified medical professionals. The outputs are to be interpreted in light of the totality of the available information, particularly because certain conditions such as advanced kidney disease/dialysis and others may render them unreliable.

Enter the patient's measured and known demographic characteristics: age, sex, weight, and height. If using plasma osmolality, enter its measured value in mOsm/kg H₂O. Cheuvront et al. in deriving and testing free water deficit equations measured plasma osmolality directly ^[3]. For closest correspondence to the original methodology, a laboratory-measured serum/plasma osmolality should be used where available, over a calculated estimate.

If using the sodium concentration method, enter a laboratory-measured plasma sodium or serum sodium concentration in mEq/L. Then enter a laboratory-measured serum/plasma sodium concentration of the patient in euhydrated state, if it is known. Otherwise the recommendation is to use the reference value of 140 mEq/L.

The tool outputs a low and high estimate of body water percentage obtained from applicable TBW equations (either 2 or 3, depending on age) ^[7][8][9]. The calculator outputs a low and high estimate of free water deficit, in litres, based on the body water percentage estimates. Negative numbers indicate that P_osm is below the 290 mOsm/kg reference used by the equation or that sodium is below the specified euhydrated value. It should not be interpreted as a validated quantitative estimate of free water excess.

With either approach the result is an approximate model estimate with substantial clinical uncertainty rather than a direct measurement of total body-water loss. Specifics of the equations used to estimate FWD are in the sections that follow. The calculated water deficit is not a fluid prescription. It does not determine fluid type, infusion rate, timing, or the amount of additional fluid required for intravascular volume restoration, ongoing losses, or maintenance.

    Free water deficit equations

This calculator supports two equations for estimating free water deficit: one based on plasma osmolality and one based on sodium concentration.

    Sodium concentration formula

The most-commonly cited water deficit equation is the one put forth in Wynn (1957) ^[4]:

WD = 0.6 · Body Mass × (1 - 140 / Na⁺)

in which Na⁺ stands for measured serum sodium or plasma sodium concentration with the two generally being treated equivalently for this calculation. In often-used modifications the body water fraction 0.6 is replaced by an average based on a few general groups by sex and age (0.6 for adult male, 0.5 for adult female, and a few others). In this free-water deficit calculator we use anthropomorphic measurements to estimate TBW instead of these broad-scope averages.

The modified equation used in this calculator is:

WD = Body Water Fraction_est. · Body Mass · (1 - 140 / Na⁺)

Despite its apparent widespread use, the original formula and several of its modifications have been criticized on various grounds. For example, Adrogué and Madias (2000) consider it adequate for estimating the water deficit in patients with hypernatremia caused by pure water loss, but show that it underestimates the deficit in patients with hypotonic fluid loss ^[2]. Some of its shortcomings were also explored in Barsoum and Levine (2002) ^[5] who also recommended against its use. Voets (2025) ^[6], outright says it should not be used for patients suffering from glycaemic dysregulation due to resulting vast underestimation of water loss in such patients.

For the above reasons and others explored below, the plasma osmolality approach and not the sodium concentration one is the default in this calculator.

    Plasma osmolality formula

This tool uses a modification of the equation named "WD₆" in the Cheuvront et al. (2013) ^[3] paper. It establishes WD₆ as a more accurate alternative to the commonly used formulas based on sodium concentration. The original WD₆ equation is as follows:

WD = 0.6 · Body Mass · (1 - 290 / P_osm)

where Body mass is measured in kg, _osm stands for Plasma osmolality in mOsm/kg H₂O (mmol/kg in the paper). In the formula the number 290 is the 290 mOsm/kg reference value used in Cheuvront et al.'s model of plasma osmolality proposed as appropriate by the authors.

The modified equation used in this calculator is:

WD = Body Water Fraction_est. · Body Mass · (1 - 290 / P_osm)

The Body Water Fraction_est. is the estimated body water percentage expressed as a fraction (60% equals 0.6). Instead of relying on general rules such as using 0.6 for males and 0.5 for females, the body water fraction is estimated using TBW equations applicable to the patient depending on their specified age. The different TBW equations used and their applicability are explained in detail in our total body water calculator page.

In doing this we disregard Cheuvront et al.'s ^[3] finding that using TBW estimated from individual characteristics failed to improve the accuracy of free water deficit prediction. We hypothesize that the lack of improvement is partly due to the limited age range of their sample (18 to 32 years) in which the average value of 0.6 in their equation is exactly the population average. The average TBW fraction varies with age group as seen in our table of average body water percentage by age and gender. Another highly likely explanation is that variation in the TBW fraction was not the dominant source of estimation error in the equation, given the substantially larger improvement observed when plasma osmolality was substituted for sodium. To a lesser extent it could have been due to the sample size being insufficient to detect small improvements in free water estimation accuracy.

    Advantages of using plasma osmolality in WD estimation

On top of the issues with the sodium concentration equation discussed above, an important piece of evidence against its utility comes in Cheuvront et al. ^[3]. The paper presents a systematic experimental exploration of the accuracy of the main sodium concentration formula and four of its modifications in healthy adults. These modifications were:

• using the known euhydrated body mass, instead of current body mass
• a correction for an unknown euhydrated body mass
• using TBW estimated from the measured body composition instead of a fixed 60% value
• using the actual euhydrated plasma sodium level instead of 140 mEq/L

The original water deficit equation turned out to underestimate total water deficit (TWD) as expected, but in this study it also underestimated free water loss by 50%. From the above adjustments the substitution of euhydrated plasma sodium was the only one resulting in a meaningful and statistically significant improvement in accuracy, but it still underestimated water loss by more than 0.5 l, on average. Also, it is not that often in practice that a measure of euhydrated Na⁺ is available.

In the same paper the authors proposed an equation in which sodium is substituted with plasma osmolality and it resulted in a nearly unbiased free water loss estimate with an error with the acceptable range of measurement uncertainty. It still underestimated total body water deficit by 40%, but even so it is more accurate than all sodium-based formulae and also "provides a more accurate estimate of FW losses than does plasma sodium in response to hypotonic TBW losses" addressing two of the important shortcomings of the conventional formula. This is the major reason why we choose to use the plasma osmolality estimate in this free water deficit calculator.

Why plasma osmolality outperformed plasma sodium

Cheuvront et al. ^[3] in their Figures 3 and 4 explore the main reason the equation based on plasma osmolality (P_osm) outperformed the ones using Na⁺. Although both plasma sodium and osmolality increased in response to dehydration, the function is disproportional and P_osm increased substantially more than Na⁺ as the level of dehydration increased. Figure 4 is particularly telling as it shows how significantly different the two regression slopes are.

As a physiological mechanism, the authors propose that "sodium is lost in sweat in amounts much larger than other substances that contribute to Posm (cations, anions, proteins, and nonionized organic substances) (2, 40, 41), and thus, Posm increases as water is lost despite progressive sweat-sodium losses in the ordinary physiologic range" ^[3].

Section summary: a controlled experimental dehydration study of healthy young adults, the plasma-osmolality-based WD₆ equation estimated free-water loss substantially more accurately than the sodium-based equations tested. Its clinical performance in hospitalized patients and in conditions such as severe hypernatremia, hyponatremia, DKA/HHS, renal failure and fluid-overloaded states has not been established to the same extent.

    Water deficit estimation for patients with diabetes

Patients with diabetes are a special subgroup which might suffer from dehydration induced by their condition. Total body water balance and glycaemic regulation are closely intertwined and during glycaemic dysregulation, a large water deficit can occur as a result of osmotic diuresis ^[6]. Diabetic ketoacidosis (DKA) and hyperosmotic hyperglycaemic state (HHS), two of the most serious and potentially life-threatening complications of diabetes mellitus produce, on average, TBW deficits of 6–7 L and 9–10 L, respectively ^[6].

According to Voets (2025) ^[6], patients suffering from glycaemic dysregulation should not be diagnosed using the commonly cited water deficit equation as it results in vast underestimation with potentially serious health consequences due to either misdiagnosis or inadequate treatment. His illustrative example features a 75 year old female patient with a body mass at admission of 78 kg, plasma sodium concentration of 142 mEq/L and plasma osmolality (estimated as plasma glucose concentration plus twice plasma sodium concentration) of 340 mmol/kg. The patient was admitted to the emergency ward because of HHS and thirst, nausea and a plasma glucose concentration of 54.6 mEq/L. Since typically plasma osmolality includes urea and other osmotically active substances, the 340 mmol/kg estimate seems to correspond to effective osmolality which is different from measured total osmolality and is likely underestimating the value required for input in P_osm-based equation, but we use it below for illustrative purposes.

The standard water deficit equation was used to estimate the patient's water deficit at just about 0.7 L (0.67 L). There was considerable underestimation of the actual TBW deficit because of the lack of plasma sodium correction for the osmotic water shift induced by severe hyperglycaemia ^[6]. Voets describes this underestimation as contributing to inadequate treatment and clinical deterioration.

Voets proposes a modified equation which takes into account both sodium and glucose plasma levels and arrives at an estimate for the patient's water deficit of 8.6 L. The original Cheuvront et al. equation the estimated free water deficit of this patient is 6.9 L. Information about the patient's height needed to apply our calculator to the case is missing, but if she is between 170 cm and 180 cm tall the estimated free water deficit is between 5.2 L and 6.0 L. As shown, plasma-osmolality-based equations give a substantially larger estimate in the published HHS example and therefore avoid the marked underestimation produced by the conventional sodium-based equation, making them potentially suitable for this population.