Free Water Deficit Calculator
The free water deficit estimates how much electrolyte-free water, in litres, a patient needs to lower an elevated serum sodium toward normal. It is used in managing hypernatremia. As with sodium correction, the rate of replacement matters, and over-rapid lowering risks cerebral edema, so this is a clinician-managed process. This tool computes the deficit from weight, the total body water fraction, and current and target sodium. It is arithmetic only.
Free water deficit formula
Free water deficit (L) = total body water fraction * weight_kg * ((current Na / target Na) - 1)
Weight is in kilograms and sodium in mmol/L. The total body water fraction is editable, commonly about 0.6 in men and children and 0.5 in women, lower in the elderly. The result is the litres of free water needed to bring sodium to the target if ongoing losses are replaced separately.
Worked example
For a 70 kg patient, fraction 0.6, current sodium 160, target 140 mmol/L: deficit = 0.6 * 70 * ((160 / 140) - 1) = 42 * (1.142857 - 1) = 42 * 0.142857 = 6.00 L. This is the estimated free water needed, to be given at a clinician-controlled rate.
Frequently asked questions
What is free water?
Free water is water without electrolytes. In practice the deficit is replaced with hypotonic fluids such as 5% dextrose or by the enteral route. The calculator gives the volume of pure water equivalent.
How fast should the deficit be corrected?
Guidelines typically limit the fall in serum sodium to a set amount per 24 hours to avoid cerebral edema. The total deficit from this tool does not set the rate; that is a clinical decision based on how acute the hypernatremia is.
Does this account for ongoing losses?
No. The formula estimates the existing deficit only. Insensible losses and continuing urinary or gastrointestinal losses must be added separately when planning fluids.
Is this a treatment recommendation?
No. It is an arithmetic estimate of a deficit. Diagnosis, fluid choice, rate, and monitoring are clinical decisions made by a qualified clinician.
Sources
- U.S. National Library of Medicine, StatPearls: Hypernatremia.
- U.S. National Library of Medicine, MedlinePlus: Fluid and Electrolyte Balance.
Reviewed by the CalculatorHub team, edited by James Graham, 19 June 2026. Educational tool, not medical advice. See our methodology.