Free water deficit calculator: the formula and its limits
For healthcare professionals and students. Check results against your local protocols and clinical judgement; this tool does not give medical advice.
This free water deficit calculator estimates how much water a patient with hypernatraemia has lost relative to a target sodium, using the classic equation free water deficit = total body water × (Na ÷ 140 − 1). Total body water comes from weight and the age- and sex-specific fractions in Adrogué and Madias’s 2000 review. Alongside it, the tool gives the alternative form of the equation, a glucose-corrected sodium for hyperglycaemic states such as DKA or HHS, and the Adrogué–Madias estimate of how much one litre of a chosen fluid would change the serum sodium.
It is designed for students and clinicians checking the arithmetic and understanding why different references quote different numbers. It does not write a fluid prescription. Everything runs in your browser.
How to use the Free Water Deficit Calculator
- Enter the serum sodium in mmol/L (identical to mEq/L) and the body weight in kg or lb.
- Choose the total body water fraction for the patient group, or type another fraction.
- Keep the target sodium at 140 mmol/L or set the value your protocol uses.
- If glucose is high, choose a glucose-corrected sodium (Katz 1.6 or Hillier 2.4) and enter the glucose in mg/dL or mmol/L.
- Pick a fluid to see the Adrogué–Madias change in sodium per litre, then read the warnings.
Free Water Deficit Calculator features
Body water by group
Fractions of 0.6 for children and adult men, 0.5 for adult women and older men, and 0.45 for older women, or your own value.
Both equation forms
TBW × (Na/140 − 1) and TBW × (1 − 140/Na), so you can see how far apart they are for your patient.
Glucose correction
Katz (1.6 mmol/L per 100 mg/dL) or Hillier (2.4) correction for hyperglycaemia, with glucose in mg/dL or mmol/L.
Adrogué–Madias per litre
Expected change in sodium after one litre of 5% dextrose, 0.2%, 0.45% or 0.9% saline, Ringer’s lactate or a custom fluid.
Full working
Every step is written out with your numbers and can be copied as one line.
Formulas used
Total body water (L) = fraction × weight (kg). Adrogué HJ and Madias NE, “Hypernatremia”, N Engl J Med 2000;342(20):1493–1499, estimate the fraction as 0.6 in children, 0.6 and 0.5 in non-elderly men and women, and 0.5 and 0.45 in elderly men and women.
Free water deficit (L) = TBW × (Na ÷ target − 1), with a target of 140 mmol/L. Some texts write it as TBW × (1 − 140 ÷ Na); the second form gives a smaller number because it uses the body water that would be present after correction. Worked example (hand-calculated, used in the self-test): a 70 kg man with sodium 160 mmol/L has TBW 0.6 × 70 = 42 L and a deficit of 42 × (160 ÷ 140 − 1) = 6.0 L; the alternative form gives 5.25 L.
Change in serum sodium after 1 L of fluid = (fluid Na + fluid K − serum Na) ÷ (TBW + 1) (Adrogué–Madias). For the same man and 1 L of 5% dextrose: (0 − 160) ÷ 43 = −3.7 mmol/L. Adrogué and Madias offered it as a more practical guide than the classic deficit equation, but it assumes the whole litre is retained with no other losses.
Hyperglycaemia, DKA and the corrected sodium
High glucose draws water out of cells and lowers the measured sodium, hiding the true water deficit. Katz (1973) calculated a fall of 1.6 mmol/L for each 100 mg/dL rise in glucose; Hillier et al. (1999) measured about 2.4 mmol/L. The tool adds factor × (glucose − 100) ÷ 100 to the measured sodium and converts mmol/L glucose with 1 mmol/L = 18.016 mg/dL. Example: sodium 150 and glucose 600 mg/dL gives 158 (Katz) or 162 (Hillier).
| Fluid (Adrogué & Madias table) | Sodium, mmol/L | Change per litre for a 70 kg man, Na 160 |
|---|---|---|
| 5% dextrose in water | 0 | −3.72 |
| 0.2% sodium chloride | 34 | −2.93 |
| 0.45% sodium chloride | 77 | −1.93 |
| Ringer’s lactate (with K 4) | 130 | −0.60 |
| 0.9% sodium chloride | 154 | −0.14 |
How accurate is the free water deficit?
Not very, which is why the result should start a plan rather than fix it. Cheuvront SN et al., Am J Clin Nutr 2013;97(1):79–85, dehydrated 36 healthy volunteers and found that the water-deficit equation grossly underestimated both free-water and total body water losses. The equation ignores ongoing urine, stool and insensible losses, and body water fractions vary with body fat. Measure sodium repeatedly and follow your protocol for the safe rate of fall, which is generally slower when hypernatraemia has developed over days or its duration is unknown.
Free Water Deficit Calculator FAQ
What is the free water deficit formula?
Free water deficit = total body water × (serum Na ÷ 140 − 1), where total body water is weight × 0.6, 0.5 or 0.45 depending on age and sex. The free water deficit calculator above shows each step.
Should I use the measured or the corrected sodium in DKA?
In marked hyperglycaemia the measured sodium understates the water deficit, so many clinicians look at the glucose-corrected sodium. The tool lets you choose Katz (1.6) or Hillier (2.4); follow your local DKA or HHS protocol.
Why do two formulas give different answers?
TBW × (Na/140 − 1) and TBW × (1 − 140/Na) use body water before and after correction. For sodium 160 in a 70 kg man they give 6.0 and 5.25 L.
Does the deficit include ongoing losses?
No. It estimates the existing deficit only. Urine, stool and insensible losses continue and must be added, and the patient’s sodium must be rechecked.
Can I use it for cats or dogs?
The arithmetic is the same, but body water fractions and fluid plans for animals differ. Use your veterinary reference or ask your vet.
How does this relate to serum osmolality?
Sodium is the main determinant of serum osmolality. The osmolality calculator shows the calculated value and the osmolal gap.