Free Water Deficit Calculator (Hypernatraemia)
Free water deficit in hypernatraemia from total body water, current and target sodium — with safe correction rate (≤ 10–12 mmol/L per day), hourly infusion rate and ongoing losses.
How it works
Deficit = TBW × (Na current ÷ Na target − 1); TBW = weight × 0.6 (men) / 0.5 (women, elderly men) / 0.45 (elderly women); correction ≤ 10–12 mmol/L per day
Hypernatraemia almost always means a shortage of water rather than an excess of salt, and the free water deficit estimates how much water would bring the sodium back to target if total body solute stays constant. Total body water is a fraction of weight that falls with age and is lower in women. The deficit is only a starting point: ongoing losses through skin, breath and dilute urine (especially in diabetes insipidus) must be added, and any isotonic fluid given for volume depletion does not count as free water. The pace matters more than the number — brain cells adapt to chronic hypernatraemia by accumulating osmolytes, so lowering sodium faster than 10–12 mmol/L a day risks cerebral oedema. Acute hypernatraemia (under 48 hours) can be corrected faster.
Worked example
A 70 kg man with sodium 158, target 145: TBW 42 L; deficit = 42 × (158/145 − 1) = 3.77 L. Correcting at 10 mmol/L/day takes 31 hours; with 1 L/day of losses that is about 3.9 L/day, or 163 mL/h of free water.
Frequently asked questions
Should I use the Adrogue-Madias formula instead?
Adrogue-Madias predicts the sodium change from one litre of a chosen fluid and is better for choosing the infusate; the free water deficit gives the total volume. Use both and, above all, remeasure often.
What target should I choose?
Aim for 145 mmol/L rather than normal in the first day; the goal is a safe rate, not rapid normalisation.
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Clinical decision tool for education and for use by trained clinicians alongside judgement — not a diagnosis and not a substitute for medical assessment. Scores validated in specific populations may not apply to every patient.