Free Water Deficit
Estimate total body water and the water deficit used to correct hypernatremia.
Standard formula
Uses the Adrogué–Madias approach: deficit = TBW × (current Na ÷ target Na − 1).
Educational estimate
Not a treatment plan. Correction rate and fluid choice are clinical decisions.
What is the free water deficit?
The water missing in hypernatremia
The free water deficit is the amount of electrolyte-free water the body has lost when serum sodium climbs above normal — a state called hypernatremia. Sodium concentration rises when water is lost relative to salt, so replacing that water dilutes the sodium back down. The deficit is estimated from how much water the body holds (total body water) and how far the sodium sits above the goal.
The calculation, described by Adrogué and Madias in the New England Journal of Medicine, has two steps: estimate total body water, then scale it by the relative sodium excess.
FWD = TBW × (current Na ÷ target Na − 1)Total body water (TBW) is body weight multiplied by a fraction that reflects how much of the body is water: about 0.6 for adult men and children, 0.5 for adult women and elderly men, and 0.45 for elderly women, following standard clinical references.
Take a 70 kg man with a measured serum sodium of 160 mmol/L and a target of 140.
Estimate total body water
70 kg × 0.6 = 42 litres of body water.Find the relative sodium excess
160 ÷ 140 − 1 = 0.143, a 14.3 % excess.Multiply
42 × 0.143 = 6 litres — the free water deficit.Pace the correction
Give that water gradually so sodium falls no faster than 8–10 mmol/L per day, plus ongoing losses.
The deficit is a volume, not a rate. How fast you replace it is where the danger lies.
≤ 8–10 mmol/L per day
Lowering sodium faster than this risks cerebral edema, especially in chronic hypernatremia.
Add ongoing losses
The deficit is the existing shortfall only — urine and insensible losses must be replaced on top.
Recheck sodium
Measure sodium repeatedly during correction and adjust; a single calculation is a starting point, not a plan.
Free water is usually given as 5 % dextrose in water intravenously, or plain water enterally when the gut works. Hypotonic saline only partly counts as free water. The fluid, route, and rate are clinical decisions.
A positive deficit means the patient needs that many litres of free water to reach the target sodium. A zero or negative result means the current sodium is already at or below target — there is no free water deficit, and forcing water would be inappropriate. The total body water figure is shown alongside so you can see how the estimate was built. Remember that the population fractions are approximations; an individual's true body water can differ, particularly with obesity, oedema, or dehydration.
This tool sizes the water gap using a standard formula and nothing more.
Not medical advice
This calculator is for education and quick estimation only. It does not account for the cause of hypernatremia, acute versus chronic onset, volume status, or ongoing losses, and it cannot set a safe infusion rate. Management of sodium disorders must be directed by a qualified clinician following local protocols, with repeated laboratory monitoring. Never use this figure to treat a patient without medical supervision.