Free Water Deficit Calculator

Find the free water deficit in hypernatremia.

How it is calculated

The tool estimates total body water as a fixed fraction of body weight, then scales it by how far serum sodium sits above the target: TBW = 0.6 × W and deficit = TBW × (Na ÷ Natarget − 1). W is weight in kilograms, Na is the current serum sodium and Natarget the desired value, both in mmol/L (the same unit for both). Results are in litres, to two decimals. The 0.6 factor is always used; it is not adjusted for sex, age or frailty. All three inputs must be above zero. If sodium is below the target the deficit comes out negative, meaning no free water deficit. The figure is an estimate, not a prescription.

Worked example

An adult weighing 70 kg has a serum sodium of 150 mmol/L, and the target is 140. Total body water is 0.6 × 70 = 42.00 L. The sodium ratio is 150 ÷ 140 = 1.0714, so subtracting 1 gives 0.0714. The deficit is 42 × 0.0714 = 3.00 L of free water.

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Common mistakes

  • Entering weight in pounds. The 0.6 × weight step assumes kilograms, so pounds overstate the deficit by more than double.
  • Mixing sodium units, such as mg/dL for one value and mmol/L for the other. Both must share a unit.
  • Treating the result as the volume to give at once. It is the estimated total deficit, and the tool says nothing about the rate of correction.
  • Expecting an adjustment for sex or age. The tool always uses 0.6, so elderly or female patients, who have lower body water fractions, are overestimated.
  • Swapping current and target sodium. A negative result then appears for a patient who is actually hypernatraemic.

About this calculator

This calculator estimates the free water deficit in hypernatremia using Deficit = TBW × (Na⁺current/Na⁺target − 1), where TBW (total body water) is approximated as a fraction of body weight (roughly 0.6 for men, 0.5 for women, adjusted lower for the elderly), and Na⁺ values are the patient's current and target serum sodium in mEq/L. The result estimates how much pure water is missing relative to sodium, guiding how much free water needs to be replaced.

Emergency medicine and internal medicine physicians, ICU and nephrology nurses, and medical students on clinical rotations use this to guide correction of hypernatremia — a calculation that must be paired with a safe correction rate (typically no faster than 10–12 mEq/L per 24 hours) to avoid cerebral edema from correcting too quickly. Enter the patient's weight, sex, current sodium, and target sodium to get the estimated deficit.

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