Free Water Deficit Calculator

What is a free water deficit?

A free water deficit is the volume of pure water the body has lost relative to its solutes. When water leaves faster than salt, the remaining fluid becomes more concentrated: plasma sodium and osmolality climb. Estimating the shortfall helps a clinician decide how much water, taken by mouth or given intravenously, would bring concentrations back to normal.

The estimate is most often used when planning treatment of hypernatremia, a serum sodium above the normal range. It covers only the water needed to correct concentration. Ongoing losses from sweat, urine, vomiting or diarrhoea, the maintenance fluid the patient needs anyway, and any restoration of circulating volume have to be added separately.

This calculator is meant for qualified health professionals and for education. It gives an approximate model estimate, not a measurement and not a fluid prescription. Kidney failure, dialysis, uncontrolled diabetes, heart failure and other conditions can make it unreliable. See the disclaimer.

How to use the calculator

1. Choose the unit system, then pick the method under Estimate via: plasma osmolality (Posm, the default) or sodium (Na+).
2. Enter age, sex, weight and height. Use the weight measured while the patient is dehydrated. For an infant under one year old, enter 1 as the age; age only decides which body-water equations are used.
3. For the osmolality method, enter the laboratory-measured plasma osmolality in mOsm/kg. For the sodium method, enter the current serum sodium and the euhydrated sodium. If the patient's own euhydrated value is unknown, keep the standard 140 mEq/L.
4. Press Calculate. You get a range for the share of body weight that is water and a range for the deficit in litres.

The weight unit is read according to the unit system you picked (pounds for US units, kilograms for metric), so make sure the two agree. A negative deficit means the osmolality is below 290 mOsm/kg or the sodium is below the euhydrated value; it should not be read as a validated measure of excess water.

The equations

Both methods share one structure: the estimated volume of body water multiplied by a fraction that says how far the measured concentration sits above its reference value.

water deficit = TBW × (1 − Posm_ref ÷ Posm)Plasma osmolality method, with Posm_ref = 290 mOsm/kg.

water deficit = TBW × (1 − Na_euhydrated ÷ Na_current)Sodium method, with Na_euhydrated normally 140 mEq/L.

The older textbook version of the sodium formula, usually credited to Wynn (1957), fixes total body water (TBW) at 60 percent of body weight, while the osmolality version was published by Cheuvront and colleagues in 2013 after testing several equations against measured fluid losses in dehydrated volunteers. In those experiments the osmolality-based equation tracked free water loss far more closely, because osmolality rises more steeply than sodium as water is lost.

Worked example

A 25-year-old man is 180 cm tall and weighs 80 kg while dehydrated. His plasma osmolality is 310 mOsm/kg.

The three equations give total body water of 44.8 L (Hume and Weyers), 46.3 L (Watson) and 48.1 L (Mellits and Cheek), which is 56.0 to 60.1 percent of his weight. The osmolality factor is 1 − 290 ÷ 310 = 0.0645.

44.8 × 0.0645 ≈ 2.9 L and 48.1 × 0.0645 ≈ 3.1 L

The calculator reports a deficit of about 2.9 L to 3.1 L. With the sodium method and a serum sodium of 150 mEq/L (euhydrated 140), the factor is 1 − 140 ÷ 150 = 0.0667, which gives about 3.0 L to 3.2 L for the same man. The simple textbook version, 0.6 × 80 × 0.0667, lands at 3.2 L.

Why osmolality is the default

The classic sodium formula was designed for patients whose raised sodium comes from losing water alone, and it is widely taught, but it has known weak spots. It underestimates the deficit when the fluid lost also contains sodium, as in sweating or diarrhoea, and it takes no account of other solutes that drag water out of cells. In the Cheuvront study the original sodium equation underestimated free water loss by roughly half, while the osmolality version came close to unbiased.

Use a measured osmolality when you have one. A value calculated from sodium and glucose is only an approximation and may not include urea or other osmoles.

Diabetes and high glucose

Severe hyperglycaemia pulls water out of cells and increases urine output, so a patient in diabetic ketoacidosis or a hyperosmolar state can be many litres short of water while the serum sodium looks only mildly raised or even normal. Sodium-based equations then understate the problem badly, which is another reason this tool leads with osmolality.

Even so, neither equation is validated in hospitalised patients with extreme glucose, very high urea or kidney failure, so the result should be read alongside clinical assessment and the local protocol. Correction is generally gradual: commonly cited guidance for chronic hypernatremia is to lower sodium by no more than about 10 to 12 mEq/L in 24 hours.