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Free Water Deficit Calculator

Estimated free water deficit in hypernatraemia from sodium and total body water.

For healthcare professionalsIV, fluids & infusionv1.0.0

For healthcare professionals / clinical use. Not a self-diagnosis tool.

Your measurements

mmol/L
Sex
years

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Enter your measurements, then press Calculate.

Methodology

Adrogué & Madias (2000)

deficit = TBW × (Na/140 − 1); TBW = weight × 0.6 (men), 0.5 (women), 0.5/0.45 (older men/women)

Estimates the water needed to return sodium to 140 mmol/L, not counting ongoing losses.

Who it is for
Adults with hypernatraemia (sodium above 145 mmol/L).
Version
1.0.0

How this calculator works

Where the formula comes from

  • The free water deficit formula, total body water × (sodium ÷ 140 − 1), appears in Adrogué and Madias's 2000 review of hypernatraemia, a narrative review rather than a validation study.[1]
  • Hypernatraemia is generally defined as a serum sodium above 145 mmol/L; the equation estimates the water deficit relative to a target sodium of 140 mmol/L, under simplifying assumptions.[1]

The inputs

  • A commonly used approximation estimates total body water as body weight × 0.6 in younger men, 0.5 in younger women and older men, and 0.45 in older women.[1][2]

Versions and alternatives

  • An alternative water-deficit equation based on plasma osmolality was tested in 36 dehydrated volunteers.[3]

Where accuracy falls (published evidence)

  • The estimate does not include ongoing losses (urine, stool, fever, rapid breathing), which must be added.[1]
  • In a controlled study of 36 volunteers dehydrated by sweating, the standard sodium-based equation underestimated total body water loss by 1.5–2.5 L.[3]
  • The result depends on the assumed total body water fraction and does not by itself set the fluid regimen or the rate of correction.[1]

Sources

  1. Adrogué HJ, Madias NE. Hypernatremia. N Engl J Med. 2000;342(20):1493–1499. doi:10.1056/NEJM200005183422006
  2. Shah MK, Workeneh B, Taffet GE. Hypernatremia in the geriatric population. Clin Interv Aging. 2014;9:1987–1992. PMID 25429210
  3. Cheuvront SN, Kenefick RW, Sollanek KJ, Ely BR, Sawka MN. Water-deficit equation: systematic analysis and improvement. Am J Clin Nutr. 2013;97(1):79–85. doi:10.3945/ajcn.112.046839

Compiled from the published sources above. Every statement was agreed independently by three AI research tools (Claude, ChatGPT, DeepSeek) and its source verified in PubMed or Crossref by the Hakeemly editorial team. Not reviewed by a doctor unless stated. Agreed on

Worked example: how to calculate free water deficit

Inputs

Sodium
160 mmol/L
Weight
70 kg
Sex
Male
Age
50 years

Result

Free water deficit
6 L
Total body water
42 L

Calculation:

42 × (160/140 − 1) = 6.0 L

An illustration with sample values, worked out with the same method the tool above uses.

Limitations

  • Ongoing losses must be added; rate of correction is a clinical decision (rapid correction of chronic hypernatraemia risks cerebral oedema).

References

  1. Adrogué HJ, Madias NE. Hypernatremia. N Engl J Med. 2000;342(20):1493–1499. doi:10.1056/NEJM200005183422006

Continue with your measurements

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For healthcare professionals

Sodium Deficit Calculator

Weight, Sex, Age

Estimated sodium deficit in hyponatraemia, and the expected change in sodium per litre of a chosen fluid (Adrogué–Madias).

Professional~3 min

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