Free water deficit (hypernatraemia)
Estimated water deficit in hypernatraemia from sodium, weight and total body water fraction
Sources last checked: 2026-11-03
Free water deficit (hypernatraemia)
Estimated water deficit in hypernatraemia from sodium, weight and total body water fraction
An estimate of the current deficit only. It ignores ongoing renal, gastrointestinal and insensible losses, assumes a pure water deficit (it underestimates the deficit after hypotonic fluid loss), and is not an infusion plan. The total body water fraction is an assumption that dominates the result.
What is the Free water deficit (hypernatraemia)?
The free water deficit estimates how much water a hypernatraemic patient has lost relative to body sodium — the positive water balance needed to bring serum sodium back to 140 mmol/L. It multiplies an assumed total body water (a fraction of body weight that falls with female sex, age and dehydration) by the relative sodium excess. The equation is a standard teaching formula; the fractions used here follow the 2023 review by Yun, Baek and Kim.
When to use it
- Hypernatraemia (Na > 145 mmol/L), to estimate the size of the water deficit
- Documenting the magnitude of a pure water deficit, e.g. in diabetes insipidus or inadequate intake
- Teaching and checking the order of magnitude of a fluid plan written elsewhere
When not to use it
- As an infusion prescription — ongoing losses, the type of fluid and the correction rate are separate decisions
- Hypernatraemia from sodium gain (hypertonic saline, sodium bicarbonate), where the problem is excess sodium rather than missing water
- Hypovolaemic shock, where volume restoration comes first
How it is calculated
Total body water (L) = fraction × body weight (kg) Free water deficit (L) = total body water × (Na / 140 − 1)
Clinical pearls and limitations
- An estimate of the current deficit only. It ignores ongoing renal, gastrointestinal and insensible losses, assumes a pure water deficit (it underestimates the deficit after hypotonic fluid loss), and is not an infusion plan. The total body water fraction is an assumption that dominates the result.
- The result is very sensitive to the assumed body water fraction: in a 70 kg patient with Na 160, choosing 0.6 instead of 0.45 changes the estimate by more than 2 L.
- After hypotonic fluid loss (diarrhoea, osmotic diuresis) the formula underestimates the true deficit, because sodium was lost as well.
- Recheck sodium frequently: the formula predicts a static deficit, while renal and insensible losses continue.
- Review articles describe chronic hypernatraemia as being corrected over 48–72 hours; the rate is a clinical decision this tool does not make.
Frequently asked questions
How do you calculate free water deficit?
Total body water × (sodium / 140 − 1), where total body water = fraction × body weight (0.6 in adult men, 0.5 in women, lower in the elderly and in water-depleted patients).
What total body water fraction should I use in the elderly?
Adrogué and Madias give 0.5 for elderly men and 0.45 for elderly women; water-depleted patients have still lower fractions.
Is free water deficit the same as the amount of fluid to give?
No. It is the deficit at one point in time; ongoing losses must be added and the free-water content of the chosen fluid taken into account.
Why does the formula use 140 mmol/L?
It estimates the water needed to bring sodium back to a normal reference value of 140 mmol/L.
Evidence and guidelines
- Primary source: Yun G, Baek SH, Kim S. Evaluation and management of hypernatremia in adults: clinical perspectives. Korean J Intern Med 2023;38(3):290 (Eq. 5 and worked example).
- Kim SW. Hypernatremia: successful treatment. Electrolyte Blood Press 2006;4(2):66-71 (worked example with 40 % total body water in a water-depleted woman).
- Adrogué HJ, Madias NE. Hypernatremia. N Engl J Med 2000;342(20):1493-1499.
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