Estimates how much water is missing in hypernatremia, from the serum sodium, body weight and total body water.
Result
Enter sodium and weight and choose the body water group.
Sources
3 studies
3
studies
913
citations
58
PubMed papers
Evidence
Known limitations
This review sets out the causes and treatment of hypernatremia, the body water fractions by age and sex, and the case for slow correction when hypernatremia has developed over days.
N Engl J Med: Journal Metrics Score 29.8, Q1 · cited 913 times
A review of hypernatremia in intensive care, where it is common and an independent risk factor for death; it notes that the rate of correction must match how fast the hypernatremia developed.
J Crit Care: Journal Metrics Score 1.7, Q2 · cited 270 times
From published dilution measurements in 458 men and 265 women, the authors derived equations for total body water from age, height and weight that outperformed earlier equations in independent data.
Am J Clin Nutr: Journal Metrics Score 5.0, Q1 · cited 1,477 times
The key review has been cited 913 times, and 58 PubMed articles mention the free water deficit in their title or abstract. Citation counts from OpenAlex and article counts from PubMed, retrieved November 11, 2026. Journal Metrics Scores and quartiles are from this site’s current release; follow the journal name for details.
After the result
Sodium 160 or higher · Sodium above 145 and below 160 · Any result
Severe hypernatremia. Find the cause of the water loss. The deficit is a starting estimate.
Next steps
Avoid common errors
5 common errors to avoid
and 3 more
When the estimate misleads
1Ongoing losses
The deficit is a snapshot. In diabetes insipidus or an osmotic diuresis, urine losses during treatment can exceed the deficit itself.
2Hypotonic fluid losses
Vomiting, diarrhea and osmotic diuresis lose sodium and potassium as well as water, so the formula underestimates what is missing.
3Body water estimate
The fraction of weight that is water varies with age, sex and body build; in obesity the usual fractions overestimate body water.
4Hyperglycemia
High glucose pulls water out of cells and lowers the measured sodium, so the formula based on measured sodium can understate the water deficit.
5Not a fluid order
The result says nothing about which fluid to give or how fast. Correction rate depends on how quickly the hypernatremia developed.
Formula
Total body water × (sodium / 140 − 1), with total body water = weight × 0.6, 0.5 or 0.45.
TBW × (Na / 140 − 1)
Total body water × (sodium / 140 − 1), with total body water = weight × 0.6, 0.5 or 0.45.
Formula and body water fractions
| Value | Formula |
|---|---|
| Free water deficit (L) | total body water × (serum sodium / target sodium − 1); target 140 mmol/L unless you enter another |
| Total body water (L) | weight (kg) × fraction from the table below |
| Watson equations, for comparison | men: 2.447 − 0.09516 × age + 0.1074 × height (cm) + 0.3362 × weight (kg); women: −2.097 + 0.1069 × height (cm) + 0.2466 × weight (kg) (TBW in L, age in years) |
| Group | Fraction | Share of body weight |
|---|---|---|
| Child, or man under 65 | 0.6 | 60% of body weight |
| Woman under 65, or man 65 or older | 0.5 | 50% of body weight |
| Woman 65 or older | 0.45 | 45% of body weight |
Adrogué and Madias 2000
Why 140
Watson equations
Test cases
3 published cases, each also a test case
3 published cases; the calculator reproduces every result.
Worked examples
A 61-year-old man with schizophrenia on lithium developed recurrent hypernatremia after pancreatectomy, with a peak sodium of 165.5 mmol/L. The authors estimated total body water as 50% of his 82 kg (41 L) and the free water deficit as about 7.5 L.
“the estimated free-water deficit was approximately 7.5 L”
The authors used 0.5 for a 61-year-old man; the calculator’s usual choice for a man under 65 is 0.6, which would give 9.0 L. The fraction is an estimate either way.
Entered as: Serum sodium: 165.5 mmol/L (mEq/L); Body weight: 82 kg; Total body water: Woman under 65, or man 65 or older (0.5).
Source: He Y et al., Front Med (Lausanne) 2026 (PubMed · Free full text · DOI)
A 40-year-old woman with metastatic breast cancer weighed 48 kg and had a sodium of 167 mEq/L from central diabetes insipidus, worsened by hypercalcemia. The report gives a free water deficit of 5.6 L.
“She had a free water deficit of 5.6 L.”
The 5.6 L matches total body water at 60% of weight (28.8 L). With 50%, the usual fraction for a woman, the deficit is 4.6 L.
Entered as: Serum sodium: 167 mmol/L (mEq/L); Body weight: 48 kg; Total body water: Child, or man under 65 (0.6).
Source: Zain MA et al., Am J Case Rep 2018 (PubMed · Free full text · DOI)
A 58-year-old man weighing 54.1 kg presented with a sodium of 191 mmol/L and a glucose of 31 mmol/L. Using 60% of body weight, the authors estimated the water deficit at 11.8 L, yet he had gained 18 kg by day 9 of treatment.
“Using Adrogue's equation, the estimated water deficit was 11.8 L”
The 11.8 L comes from the measured sodium of 191; the authors’ glucose-corrected sodium of 202 gives 14.4 L. Both are far below the 18 kg he gained by day 9; the authors note that combined high sodium and glucose can lead to underestimating the actual water deficit.
Entered as: Serum sodium: 191 mmol/L (mEq/L); Body weight: 54.1 kg; Total body water: Child, or man under 65 (0.6).
Source: Xiao H et al., Case Rep Endocrinol 2019 (PubMed · Free full text · DOI)
FAQ
6 questions and answers
and 4 more answers
Questions
Free water deficit (L) = total body water × (serum sodium / 140 − 1), where total body water is body weight times a fraction: 0.6 for children and men under 65, 0.5 for women under 65 and men 65 or older, 0.45 for women 65 or older. A 70 kg man with a sodium of 160 mmol/L has a deficit of 70 × 0.6 × (160 / 140 − 1) = 6.0 L.
The usual fractions (Adrogué and Madias 2000) are 0.6 for children and men under 65, 0.5 for women under 65 and men 65 or older, and 0.45 for women 65 or older. Body water is a smaller share of weight in obesity and a larger share in lean, muscular people. Published case reports do not always follow these groups, which is why the calculator asks you to choose.
No. The deficit is the water missing at the moment of measurement. Urine, stool, sweat and breathing keep losing water during treatment, and in diabetes insipidus or an osmotic diuresis the urine losses can be large. Ongoing losses are not part of the deficit, and the sodium needs repeated checks during treatment. This page does not give an infusion rate.
It depends on how quickly it developed. When hypernatremia has built up over more than about 48 hours, or the timing is unknown, brain cells have adapted and fast correction risks cerebral edema, so guidance commonly cites no more than about 10 to 12 mmol/L in 24 hours. Hypernatremia that developed over hours, as in salt poisoning, can be corrected faster. Follow local protocols and specialist advice.
It assumes the patient lost pure water. Vomiting, diarrhea and an osmotic diuresis lose hypotonic fluid that contains sodium and potassium as well as water, so more fluid is missing than the sodium rise implies. These patients often have a low circulating volume that needs correcting first.
The formula uses 140 mmol/L by default, the middle of the normal range. You can enter a different target, for example an intermediate goal for the first day, and the calculator gives the deficit relative to that target.
Further reading
6 references with PubMed and DOI links
6
references
3
free full text
From Adrogué HJ et al., N Engl J Med 2000 to the newest case reports.
References
Contributed by Dr. Meng Zhao (MD · Former Neurosurgeon · Medical AI Researcher), from the original publications listed here. Last updated November 11, 2026. LinkedIn
The calculator code is tested against every worked example on this page before each release.
This calculator supports, and does not replace, clinical judgment. It is meant for healthcare professionals and is not medical advice for patients. Report an error through the contact page.
clinical grade of aneurysmal subarachnoid hemorrhage, I to V.
total calcium adjusted for albumin, in mg/dL or mmol/L.
stroke severity from 15 bedside items, 0 to 42.
MAP from systolic and diastolic pressure, against the 65 mm Hg target.
eye, verbal and motor scores for preverbal children, 3 to 15.
oxygenation ratio with the Berlin ARDS severity ranges.
serum sodium corrected for high glucose, Katz or Hillier factor.
sodium − (chloride + bicarbonate), with the albumin-corrected gap.
urea nitrogen to creatinine ratio, in US or SI units.
estimated creatinine clearance with actual, ideal or adjusted weight.
cardiac output and index from oxygen consumption and saturations.
ANC from the white cell count, neutrophils and bands.
insulin resistance from fasting glucose and insulin, in US or SI units.
FENa from plasma and urine sodium and creatinine: prerenal, indeterminate or tubular pattern.
three-item stroke severity screen for large vessel occlusion, 0 to 4.
expected PaCO2 in metabolic acidosis, 1.5 × HCO3 + 8 ± 2.
To adjust the measured sodium for a high glucose.
Another electrolyte calculation from the same blood test.
Which published the Adrogué and Madias review, with its current metrics.