Free water deficit calculator

Why the water deficit is only a starting point

Hypernatremia means too little water for the amount of sodium in the body. Students meet it first as a formula with one neat answer in liters, and this is where the danger lies: the number looks exact and invites action. The formula only says how much water is missing at this moment. It says nothing about how long the sodium has been high, which determines how quickly the brain can safely adapt, and nothing about what is still being lost. The review we cite makes the point repeatedly. Read the sections below before using any figure.

What is the free water deficit?

The free water deficit is the amount of pure water, with no salt, that a person with a high blood sodium level (hypernatremia) is estimated to be missing relative to their salt. It is the water that would bring the serum sodium back to 140 mmol/L if it were added and nothing else changed. It is a teaching estimate of the size of the problem, not a prescription.

What is the formula?

Free water deficit (liters) = total body water (TBW, liters) × (serum sodium ÷ 140 − 1). TBW is body weight in kilograms multiplied by a fraction that depends on age and sex. For a 60 kg woman with a sodium of 166 mmol/L and a TBW fraction of 0.5, TBW is 30 L and the deficit is 30 × (166 ÷ 140 − 1) = 5.6 L. That example comes from a 2023 review in the Korean Journal of Internal Medicine.

Which total body water fraction is used?

The page offers the fractions that Adrogué and Madias gave in the New England Journal of Medicine in 2000: 0.6 for children, 0.6 for adult men, 0.5 for adult women, 0.5 for older men and 0.45 for older women. (We read these as quoted in a later paper; the original is behind a paywall.) The sources do not agree on every number. The 2023 review writes TBW as 60 percent of body weight for men and 50 percent for women, with 5 percent deducted in older people, which gives 0.55 for older men rather than 0.5. It also says that in patients with water depletion lower values, 50 percent for men and 40 percent for women, are usually applied. You can enter your own fraction.

How fast can sodium be corrected?

The review describes two situations. In acute symptomatic hypernatremia that developed within 48 hours, a more rapid fall of 1 to 2 mmol/L per hour for the first 6 to 8 hours has been reported to improve prognosis without raising the risk of brain swelling. In hypernatremia lasting longer than 48 hours or of unknown duration, the review says the correction rate should be under 0.5 mmol/L per hour (12 mmol/L per day), based on data from children, particularly infants. It then adds that several adult studies found faster correction not linked to more deaths or brain injury, while too slow a correction (under 0.25 mmol/L per hour, or 6 mmol/L per day) was linked to higher mortality. It also says the calculated water is typically given over 48 to 72 hours. The rate and the plan belong to the treating team.

What is the Adrogué–Madias formula?

It estimates what 1 liter of a given IV fluid does to the serum sodium: change in sodium = (sodium plus potassium of the fluid − current serum sodium) ÷ (TBW + 1). Fluids differ in their sodium: 5 percent dextrose in water has none, a 0.9 percent sodium chloride solution has about 154 mmol/L (9 g per liter divided by 58.44 g per mole, our arithmetic) and 0.45 percent has about 77. For the 60 kg woman above, 1 liter of 0.9 percent saline changes her sodium by -0.4 mmol/L, and 1 liter of dextrose in water by -5.4 mmol/L. The page has a second mode for this calculation.

Why is the formula only approximate?

A 2021 paper in Kidney360 (Chen and colleagues) states that the Adrogué–Madias formula works exactly only when 1 liter of fluid is given; for other volumes it is an approximation that drifts further from the truth as the volume grows. The 2023 review adds that the formula did not predict sodium changes accurately in a group of patients with hypernatremia, severe loss of extracellular volume and markedly reduced kidney function. Neither formula accounts for ongoing urine, stool, sweat and breathing losses.

What if the sodium is below 140?

Then there is no free water deficit to calculate, and the page says so. Low sodium (hyponatremia) is a separate problem with different guidelines, such as the European guideline from 2014, and different dangers when sodium is corrected too fast. Nothing on this page applies to it. For related lab arithmetic, see the corrected sodium and serum osmolality calculators.

Worked example

A 60 kg woman has a sodium of 166 mmol/L. TBW = 60 × 0.5 = 30 L. Sodium ÷ 140 = 1.186, minus 1 gives 0.186, and 30 × 0.186 = 5.6 L. In the 2023 review, this deficit is spread across 48 to 72 hours with allowance for ongoing losses, not given at once. A man weighing 80 kg with a sodium of 155 mmol/L and a fraction of 0.6 has TBW of 48 L and a deficit of 5.1 L. Changing the fraction from 0.6 to 0.5 for the same man would lower that to 4.3 L, so the fraction matters.

Limits of this method

The formula treats TBW as fixed. In reality, a person who is dehydrated has less water than the fraction suggests, which is why the review quotes lower fractions for water-depleted patients. The formula also assumes sodium is the only change. It does not know the duration of hypernatremia, which the review uses to set the safe correction rate, nor the patient’s volume status, nor what is still being lost. The review reports that mortality in adults was higher with excessively slow correction in several studies, so a smaller number on a page is not automatically a safer one.

Common mistakes

Using pounds as if they were kilograms doubles the result; the unit switch converts a typed weight. Entering the TBW (a volume) instead of body weight is another slip. A third is treating the deficit as the volume of fluid to run in one day: the 2023 review adds insensible loss and ongoing renal or other losses to the deficit when it calculates the total water, and it describes correction over 48 to 72 hours. The total body water calculator on this site estimates TBW in liters from height and weight with the Watson equations, a different method from the fixed fractions used here; do not mix the two without saying which was used.

Sources: Adrogué HJ, Madias NE, “Hypernatremia,” N Engl J Med 2000;342:1493–1499 (total body water fractions as quoted by later papers; the original was not opened); Yun G, Baek SH, Kim S, “Evaluation and management of hypernatremia in adults: clinical perspectives,” Korean J Intern Med 2023;38:290–302 (equations, correction rates, worked example; paraphrased); Chen S, Shieh M, Chiaramonte R, Shey J, “Improving on the Adrogué–Madias formula,” Kidney360 2021;2:365–370 (abstract). Related: total body water, corrected sodium, serum osmolality.

For general information only — not medical advice, and not a tool for patient care decisions. Talk with a doctor about any sodium result, and call emergency services if someone is severely unwell. How we check our calculators.