Free Water Deficit Calculator
Water deficit in hypernatremia from serum sodium and weight
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Free Water Deficit Calculator turns the numbers behind water deficit in hypernatremia from serum sodium and weight into a result, step by step. You supply Serum Sodium (mEq/L) and Weight (kg) to Free Water Deficit; the answer follows at once. Nothing in Free Water Deficit is a black box. Students and professionals reach for Free Water Deficit when speed matters. Free Water Deficit runs in your browser. Health data stays in the tab. Free Water Deficit is part of the Health collection on CalcProMaster, alongside free water deficit calculator hypernatremia sodium correction, free calculators and more. Keep Free Water Deficit bookmarked for next time. Free Water Deficit stays bookmarked for next time.
What the defaults give
A serum sodium of 155 mEq/L in a 70 kg adult implies a free water deficit of about 4.5 litres.
Free water deficit is the amount of pure water missing relative to the body’s normal sodium concentration. It is not the same as the fluid you would give quickly — correction is deliberately slow.
The formula
Deficit = TBW × (Na measured ÷ 140 − 1), where total body water (TBW) is about 0.6 × body weight in an adult male.
TBW = 0.6 × 70 = 42 L. 155 ÷ 140 = 1.1071, minus 1 = 0.1071. 42 × 0.1071 = 4.5 L.
Worked example
Serum sodium 155 mEq/L
Weight 70 kg → TBW 42 L
Ratio 155/140 = 1.1071
Deficit = 42 × 0.1071 = 4.5 L
Why the correction is slow
Rapid correction of hypernatraemia can cause cerebral oedema, because the brain has adapted to a high-osmolality environment by generating its own osmolytes. The usual target is a fall of no more than 10 mEq/L per 24 hours, and slower in chronic cases — which means a deficit of this size is replaced over a day or more, not in an hour.
What changes the TBW fraction
- Age and sex — 0.5 for adult women, 0.45–0.5 for older adults, and 0.6 for children, whose water fraction is higher.
- Obesity — fat holds little water, so 0.6 × actual weight overestimates TBW; lean body weight is the better basis.
- Fluid losses — ongoing fever, diarrhoea or diuresis means the calculated deficit is a snapshot that shrinks as losses continue.
- Sodium intake — the deficit is a water problem, not a salt one, and adding salt to the fluid makes it worse.
What this is not
It is not a prescription. The fluid type, the rate and the monitoring plan depend on why the sodium is high — dehydration, diabetes insipidus, osmotic diuresis or a solute load all need different handling.
Frequently Asked Questions
Why 4.5 L for a sodium of 155?
TBW is 0.6 × 70 = 42 L, and 155/140 − 1 = 0.1071. 42 × 0.1071 = 4.5 litres of free water deficit.
How fast should the deficit be replaced?
No faster than about 10 mEq/L of sodium correction per 24 hours, and more slowly in chronic hypernatraemia, to avoid cerebral oedema.
What TBW fraction should I use?
0.6 for an adult male, 0.5 for an adult female, lower in older adults and higher in children. For obesity, base the calculation on lean body weight.
Does the deficit mean I should give 4.5 L of saline?
No. The deficit is water, and saline adds sodium. The replacement fluid is usually free water or a hypotonic solution, chosen with the underlying cause in mind.
Is this the same as the water deficit in DKA?
Related but not identical. DKA calculations usually use a corrected sodium and a different TBW assumption, and the fluid plan also has to account for ongoing osmotic diuresis.
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