Free Water Deficit Calculator

Free water deficit = total body water × (serum sodium ÷ 140 − 1) · total body water = weight × water fraction

weight

Body weight. Total body water is this weight multiplied by the water fraction below, which is why the same deficit can be a bigger share of one body than of another (kg)

fraction

The share of body weight that is water: 0.6 for men of 65 and under, 0.5 for women of 65 and under and for men over 65, and 0.45 for women over 65. This page is the only one of the four that changes the answer by sex and age, and it is the assumption the result is most sensitive to

serum sodium

Serum sodium in mmol/L, as printed on the lab report. 140 is the reference value the page divides by, not a measured quantity

deficit

Free water deficit in litres of water — not litres of fluid, and not the volume of anything to be infused (L)

Use it when a sodium result has come back above the reference range and you want to see how much water that concentration stands for — usually because someone has quoted a free water deficit to you and you want to know what the figure is made of. It is also the quickest way to see how much the answer depends on the assumptions rather than on the measurement: read a row of the table below and watch the same sodium produce four different deficits, then look at how little a change of target from 140 to 145 does to the answer — it nearly halves it. Do not use it to plan a correction. This is the arithmetic a clinician starts from and then adjusts, because the body is treated as a closed system here and the fluid that carries free water always carries something else with it.

1. 70 kg, man of 40, sodium 150

   1. Water fraction: 0.6, because this is a man of 65 or under
   2. Total body water: 70 × 0.6 = 42.0 L
   3. Deficit: 42.0 × (150 ÷ 140 − 1) = 42.0 × 0.0714 = 3.0 L

   This is the combination the page opens with, so the first figure you see on a fresh screen is this one. The sodium of 150 is 10 above the reference value of 140, and 10 over 140 is a little more than seven per cent, which applied to 42 litres is three litres.

2. 60 kg, woman of 45, sodium 166

   1. Water fraction: 0.5, because this is a woman of 65 or under
   2. Total body water: 60 × 0.5 = 30.0 L
   3. Deficit: 30.0 × (166 ÷ 140 − 1) = 30.0 × 0.1857 = 5.57 L

   This is a worked example printed in a clinical review of hypernatremia, which gives the answer as 5.6 L — the same figure to the precision it quotes. A 60 kg body holding 30 litres is missing more than five and a half of them, which is the reason these patients are managed with a plan rather than with a glass of water.

3. 60 kg, woman of 75, sodium 155

   1. Water fraction: 0.45, because this is a woman over 65 — the only group that uses 0.45
   2. Total body water: 60 × 0.45 = 27.0 L
   3. Deficit: 27.0 × (155 ÷ 140 − 1) = 27.0 × 0.1071 = 2.89 L

   The same 60 kg and a lower sodium than the example above, but seventeen years older: at the younger fraction this sodium would give 3.21 L, and here it gives 2.89 L, because the fraction moved by a tenth of body weight. That is the whole reason the four water fractions are printed in the table below rather than hidden inside the calculator.

This page computes a free water deficit and stops there. Several things a correction plan needs are not in the figure, and the first of them is ongoing loss: the formula treats the body as a closed system, so urine, stool, sweat and the water lost in breathing are all missing from it. In practice those losses are estimated separately and added, which is why the fluid actually prescribed is always more than the number printed here. The second is that total body water is extrapolated from weight and ignores body composition — fat holds little water, so a heavy body with a high fat mass holds less water than the fraction assumes, and a very muscular one holds more. The third is the fluid itself: free water is not given as water. It is carried in a solution — 5 per cent dextrose, which brings a glucose load, or a dilute saline, which brings sodium — and drinking the equivalent volume is not practical in the quantities involved. The fourth is time: a deficit of this size is replaced over two or three days, not at once, because the sodium has to come down slowly. How slowly is a matter of expert opinion rather than trial evidence, and it depends on how the hypernatremia arose: for a sodium that rose over more than 48 hours or over an unknown period the usual ceiling is about 0.5 mmol/L per hour, or roughly 10 to 12 mmol/L per day, while a rise of less than 48 hours may be corrected faster in its first hours. The fifth is that hypernatremia is not one condition. A sodium elevated because water was lost is not the same as one elevated while the body holds excess water, as happens with corticosteroid treatment in critical illness, and in that second setting the volume of free water given and the fall in sodium are not even proportional. Finally, the formulas of this family are imprecise at the level of one person — deviations above 10 mmol/L have been described — and a serum sodium can itself be a measurement artefact. This is a number to discuss, not to act on alone, and it is an adult calculation: under 18 the paediatric rule applies and this page declines to guess at it.

What is free water deficit?

It is the amount of water a body is short of, expressed in litres, at a moment when the sodium dissolved in that water has become too concentrated. The word free means water on its own — water that is not carrying sodium with it — and that is the form the body needs to be given. The figure is not a measurement; nothing measures it directly. It is worked out from two things that can be measured or assumed: how much water the body holds, from the weight and the water fraction, and how far the sodium has been concentrated, from the lab result against its reference value.

Why does the reference sodium of 140 matter so much?

Because it is the number the sodium is measured against, and the deficit is proportional to how far above it the result sits. Take the same 60 kg woman: at a sodium of 166 the deficit comes out at 5.57 L against a reference of 140, but the same result worked against a target of 145 gives 2.9 L — barely half as much. Both conventions are in use: 140 is the usual target, and it is the one printed in the clinical references behind this page, while at least one recent paper works to 145 and some calculators let you set the target yourself. So when someone quotes you a free water deficit, the target behind it is part of the answer, and it is worth asking for. This page uses 140 throughout.

Why do my sex and age change the answer?

Because they change how much of your body weight is water, and the sodium is dissolved in that water rather than spread through the whole body. The four fractions used here — 0.6 for men of 65 and under, 0.5 for women of 65 and under and for men over 65, and 0.45 for women over 65 — are a published convention, quoted from a clinical review, and they are the only reason the same weight and the same sodium give different answers to different people. One reading of them is worth correcting: 0.45 is not the value for older people in general, it is the value for older women. Men over 65 use the same 0.5 as a younger woman. Other published sources divide the groups differently, and one gives older women 0.4, so the four numbers here are one convention rather than the only one.

Is this how much fluid I should be given?

No, and the gap is not small. Free water is not administered as water: it is delivered in a solution that brings something with it, either dextrose, which adds a glucose load, or a diluted saline, which adds sodium, and that choice belongs to whoever is treating you. Fluid you have lost since the sample was taken is not in the figure either, and neither is the ongoing loss that continues while a correction is under way; both are estimated separately and added to what this page prints. The rate matters as much as the total: a deficit of this size is normally made up over two or three days so that the sodium falls slowly, and the fluid is often given by a route you cannot use at home. Use the number to understand a plan, never as one.

Can I use this if my sodium is normal or low?

Only at or above the reference value of 140 — the calculator refuses anything lower. Below that, the formula does not return a small deficit, it returns a negative one: a body with a sodium of 120 in 42 litres of water comes out at minus 6 L, which means water is in excess, not in deficit. That is a different problem with different rules, and it is one of the few places where a formula this simple can say something actively misleading if it is allowed to run. If your result is below the reference range, this page is not the page you want.

How fast should a high sodium be corrected?

Slowly, and by how much is a matter of expert opinion rather than settled evidence. The ceiling usually quoted is about 0.5 mmol/L per hour, or roughly 10 to 12 per day, whenever the sodium rose over more than 48 hours or over an unknown time. If the rise was recent — within about 48 hours — a faster fall in the first hours is accepted practice. The reason for the caution is that the brain adapts to a high sodium over days, and pulling the level down faster than it adapted has caused cerebral oedema and lasting neurological damage, which is why this is set by protocol and monitored rather than calculated at home. It is worth knowing that the ceiling is contested: a large study of severe hypernatremia found slower correction was associated with higher mortality, not lower, and said in as many words that the rate limit rests on opinion.

Can I use it for a child?

No. The four water fractions here are adult ones, and the paediatric rule is different in a way this page cannot express: for children the fraction is a single value of 0.6, used regardless of sex, whereas the four numbers here are divided by sex as well as by age. A teenage girl entered here would be given the adult female fraction of 0.5 when the paediatric convention says 0.6, so the page refuses anyone under 18 instead of returning a figure that looks right. Children with a sodium disorder need a paediatric assessment, and the volume questions in that setting are different ones.

• Diagnosis and management of sodium disorders: hyponatremia and hypernatremia — Braun MM, Barstow CH, Pyzocha NJ — American Family Physician, 2015;91(5):299-307 — the source of the four water fractions on this page, quoted verbatim, and of the reference sodium of 140
• Evaluation and management of hypernatremia in adults: clinical perspectives — Yun G, Baek SH, Kim S — Korean Journal of Internal Medicine, 2023;38(3):290-302 — the worked example in the second example above, the fluid-is-not-water caveat, and the correction rate for sodium that rose over more than 48 hours
• Rate of Correction and All-Cause Mortality in Patients With Severe Hypernatremia — Feigin E, Feigin L, Ingbir M et al. — JAMA Network Open, 2023;6(9):e2335415 — why the rate limit above is described as expert opinion rather than as evidence: this study found slower correction associated with higher mortality, and states plainly that the ceiling is opinion