About the Free Water Deficit Calculator
Hypernatremia — a serum sodium above 145 mEq/L — almost always reflects a shortage of water relative to the body’s sodium, rather than too much sodium. The free water deficit estimates how many litres of electrolyte-free water the body is short of, assuming total body sodium is unchanged. It is a standard calculation in internal medicine, intensive care and nephrology when assessing patients with hypernatremia from dehydration, diabetes insipidus or inadequate water intake.
The calculation first estimates total body water (TBW) as a fraction of body weight — 0.6 for children and adult men, 0.5 for adult women and older men, and 0.45 for older women — then applies the formula TBW × (current sodium ÷ target sodium − 1). The target defaults to 140 mEq/L, the conventional normal value; you can change it.
The result is an estimate of the existing deficit only. It does not include ongoing losses (urine, stool, insensible losses) and is not a prescription: the fluid used, the route and the safe rate of correction are clinical decisions made by the treating team according to guidelines and close sodium monitoring. Formulas such as Adrogué–Madias are used for that purpose.
With the default inputs, the free water deficit is 6 L. Change any value above to recalculate instantly.
How to use the free water deficit calculator
- 1Enter the current serum sodium.
- 2Enter body weight in kg or lb.
- 3Choose the patient group to set the total body water fraction.
- 4Keep the target at 140 mEq/L or set a different value.
- 5Read the estimated free water deficit and total body water.
Formula and method
Total body water is estimated as a fixed fraction of body weight: 0.6 for children and adult men, 0.5 for adult women and older men, and 0.45 for older women, reflecting differences in muscle and fat mass (the Adrogué–Madias values). Some references instead subtract 5 percentage points for older adults (0.55 for older men), and suggest lower fractions (about 0.5 for men and 0.4 for women) in water-depleted patients, which would shrink the estimate. Sodium is assumed to be distributed throughout total body water, and total body sodium is assumed unchanged.
If current sodium is Na and the normal value is 140 mEq/L, the current water content is TBW and the water needed to dilute sodium back to 140 is TBW × Na ÷ 140. The difference — TBW × (Na ÷ 140 − 1) — is the free water deficit. Weight in pounds is converted with 1 lb = 0.4536 kg.
- TBW
- Total body water (litres)
- Na
- Current serum sodium (mEq/L)
- target Na
- Desired serum sodium, usually 140 mEq/L
Worked examples
70 kg man with sodium 160
TBW = 70 × 0.6 = 42 L. Deficit = 42 × (160 ÷ 140 − 1) = 42 × 0.1429 = 6.0 L of free water.
60 kg woman with sodium 155
TBW = 60 × 0.5 = 30 L. Deficit = 30 × (155 ÷ 140 − 1) = 30 × 0.1071 = 3.2 L.
Older man weighed in pounds
176 lb = 79.8 kg, so TBW = 79.8 × 0.5 = 39.9 L. Deficit = 39.9 × (150 ÷ 140 − 1) = 2.85 L.
Frequently asked questions
What is the free water deficit formula?+
Free water deficit (L) = total body water × (serum sodium ÷ 140 − 1), where total body water is body weight in kg multiplied by 0.6 (men, children), 0.5 (women, older men) or 0.45 (older women).
Why does the total body water fraction vary?+
Water is held mainly in lean tissue. Women and older adults have proportionally more fat and less muscle, so a smaller share of their weight is water. Using the wrong fraction can over- or underestimate the deficit by litres.
Does the free water deficit include ongoing losses?+
No. It only estimates the existing deficit at the moment of measurement. Ongoing losses from urine (especially in diabetes insipidus), the gut, fever and breathing continue and must be assessed separately by the treating team.
How fast should hypernatremia be corrected?+
That is a clinical decision. Guidelines caution against lowering sodium too quickly in chronic hypernatremia because of the risk of cerebral oedema, and recommend frequent sodium checks. This calculator does not provide a correction rate or fluid prescription.
For healthcare professionals and education only. This calculator implements a published formula or score but is not a diagnosis and does not replace clinical judgment. Verify inputs and results against the original source before using them in patient care.