Free Water Deficit Calculator (hypernatraemia)

Understanding the free water deficit calculator — concept and principle

The free water deficit estimates how many litres of water a person with a high blood sodium (hypernatraemia) would need to bring sodium back to 140 mmol/L. It is used in hospitals when planning oral, enteral or intravenous water replacement for dehydrated patients, older adults with poor intake, or people with diabetes insipidus.

The deficit is the extra water that would dilute sodium back to 140; the default works out to about 4.8 L.

How it is calculated

Free water deficit (L) = TBW × (Na ÷ 140 − 1)

TBW (total body water) = weight (kg) × factor

Factor 0.6 for men and 0.5 for women up to age 65.
Factor 0.5 for men and 0.45 for women over 65.
Sodium in mmol/L; 140 is the target concentration.

The principle

Sodium is mainly an extracellular ion, but water moves freely between all body compartments, so serum sodium reflects the ratio of total body sodium to total body water. If the amount of sodium in the body stays the same, concentration × volume is constant: current Na × current TBW = 140 × target TBW. Rearranging gives the extra water needed, TBW × (Na ÷ 140 − 1). The TBW factors reflect that lean tissue is water-rich and fat is not; women and older adults have proportionally more fat and less water.

Worked example

Male, age 35, so the factor is 0.6.
TBW = 75 × 0.6 = 45 L.
Na ÷ 140 = 155 ÷ 140 = 1.1071; minus 1 gives 0.1071.
Deficit = 45 × 0.1071 = 4.82, so about 4.82 L of free water.

Each point is the calculator re-run with only “Sodium (mmol/L)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

Sodium (mmol/L)	Free water deficit (L)
38.8	-32.54
77.5	-20.09
116	-7.63
155	4.82
194	17.28
232	29.73
310	54.64

How to read the result

The result is the existing deficit only. It does not include ongoing losses from urine, fever, breathing or diarrhoea, which must be added, often 1 L per day or more. In chronic hypernatraemia, the correction is usually spread over at least 48 hours and limited to about 10–12 mmol/L per 24 hours, because the brain adapts to high sodium and correcting too fast can cause cerebral oedema. Acute hypernatraemia that developed over hours may be corrected faster under specialist care.

Common mistakes

Replacing the entire deficit at once rather than over the planned period.
Forgetting ongoing losses, so sodium fails to fall as expected.
Treating the result as a volume of saline; the formula is for electrolyte-free water such as 5% dextrose or enteral water.

Keep in mind: This is an estimate, not a diagnosis or a prescription. TBW fractions are approximations and sodium must be rechecked often during treatment. Fluid therapy should be directed by a clinician.

Frequently asked questions

Why use 140 as the target?

It is a convenient midpoint of the normal 135–145 mmol/L range.

How fast should sodium be lowered?

In chronic cases, typically no more than about 10–12 mmol/L in 24 hours, as the calculator notes.

Is free water the same as drinking water?

Free water means water without sodium; drinking water or 5% dextrose both provide it.

Sources: Adrogué HJ, Madias NE. Hypernatremia. N Engl J Med 2000.

Checked 8 Nov 2026. Published formulas cited on the page. For information only — not medical advice.

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