How much is the free water deficit?
Enter the body weight, the patient group, and the serum sodium to estimate the free water deficit in liters. For information only. This is not medical advice or a diagnosis. Do not use it to make treatment decisions without a clinician. No licensed clinician has reviewed this page.
- Free water deficit (L)
- 3
The estimated free water deficit is 3 L (total body water 42 L).
- Total body water (L)
- 42
Free water deficit (L): 3. The estimated free water deficit is 3 L (total body water 42 L).
This calculator gives general information only. It is not medical advice and does not replace a doctor or other health care provider. Talk with a professional about your results. Terms of use
How to calculate
Estimates the free water deficit in hypernatremia from body weight, sex and age group, and serum sodium: total body water × (sodium ÷ 140 − 1).
Example with the default inputs (Patient Adult man (0.6), Weight 70 kg, Serum sodium (mmol/L) 150): The estimated free water deficit is 3 L (total body water 42 L).
Method: Total body water (L) = weight (kg) × fraction (0.6 men, 0.5 women, 0.55 older men, 0.45 older women). Free water deficit (L) = total body water × (serum sodium ÷ 140 − 1).
- The target sodium is 140 mmol/L, as in the source equation.
- The deficit is worked from the exact typed values and rounded once to 1 decimal, halves up.
- The estimate does not include ongoing water losses (urine, stool, sweat, breathing).
Worked examples
Each example is checked against the calculator on every build.
- Patient Adult man (0.6), Weight 70 kg, Serum sodium (mmol/L) 150 gives Free water deficit (L) 3, Total body water (L) 42.
- Patient Adult woman (0.5), Weight 60 kg, Serum sodium (mmol/L) 166 gives Free water deficit (L) 5.6, Total body water (L) 30.Source: Yun, Baek and Kim 2023, worked example after Eq. 5: 0.5 × 60 × (166 ÷ 140 − 1) = 5.6 L
- Patient Older woman (0.45), Weight 50 kg, Serum sodium (mmol/L) 160 gives Free water deficit (L) 3.2, Total body water (L) 22.5.
- Patient Older man (0.55), Weight 80 kg, Serum sodium (mmol/L) 155 gives Free water deficit (L) 4.7, Total body water (L) 44.
- Patient Adult man (0.6), Weight 69.85 kg, Serum sodium (mmol/L) 145 gives Free water deficit (L) 1.5, Total body water (L) 41.9.
Medical disclaimer
This calculator is for information and education only. It is not medical advice, and its result is not a diagnosis. Do not use it to start, stop, or change a treatment without a clinician who knows your health history. No licensed clinician has reviewed this page. This site's editors checked the formulas and worked examples against published sources. If you think you have a medical emergency, call your local emergency number.
When this does not apply. The equation is for adults with hypernatremia from water loss (serum sodium above 140 mmol/L). It is not for children or for a sodium of 140 mmol/L or less. When the high sodium comes from salt gain rather than water loss, the source treats it as a separate cause. In water-depleted patients the source notes that lower fractions are often used (50% for men and 40% for women, of lean body weight), so the page may overestimate the deficit then.
How it works
- Total body water (L) = weight (kg) × fraction. The fraction is 0.6 for adult men and 0.5 for adult women, and 5 points less for older adults: 0.55 for older men, 0.45 for older women (Yun, Baek and Kim 2023).
- Free water deficit (L) = total body water × (serum sodium ÷ 140 − 1) (Eq. 5 in the same paper). 140 mmol/L is the target sodium.
- Serum sodium must be above 140 and at most 200 mmol/L. Weight is 20 to 300 kg (44.1 to 661 lb); a weight in pounds is read back as the exact decimal typed (1 lb = 0.45359237 kg).
- Both results are worked from the exact typed values and rounded once to 1 decimal, halves up.
Worked examples by hand
Page default. Adult man, 70 kg, sodium 150. Total body water 0.6 × 70 = 42.0 L. Deficit 42 × (150 ÷ 140 − 1) = 42 × 10 ÷ 140 = 3.0 L.
The paper's example. Woman, 60 kg, sodium 166. 0.5 × 60 = 30.0 L; 30 × 26 ÷ 140 = 5.571, 5.6 L (Yun 2023 gives 5.6 L).
Older woman. 50 kg, sodium 160. 0.45 × 50 = 22.5 L; 22.5 × 20 ÷ 140 = 3.214, 3.2 L.
Older man. 80 kg, sodium 155. 0.55 × 80 = 44.0 L; 44 × 15 ÷ 140 = 4.714, 4.7 L.
Weight in pounds. Adult man, 154 lb = 69.853 kg, sodium 145. 0.6 × 69.853 = 41.912, 41.9 L; 41.912 × 5 ÷ 140 = 1.497, 1.5 L.
Other questions people ask
How is the free water deficit calculated?
Free water deficit = total body water × (serum sodium ÷ 140 − 1). Total body water is body weight in kg times 0.6 for men or 0.5 for women, 5 points less for older adults.
What does the free water deficit mean?
It estimates how much water, in liters, would bring a high serum sodium back to 140 mmol/L if no more water were lost. It is a starting estimate, not a full fluid plan.
Why does the page refuse a sodium of 140 or less?
The equation is for hypernatremia (a high serum sodium). At 140 or below, the deficit would be zero or negative.
Why are the fractions different for men, women, and older adults?
Water is a smaller share of body weight in women and in older adults. The source estimates 60% of body weight for men and 50% for women, and says 5% is deducted for older adults; the page reads this as 55% and 45%. It does not set an age for "older".
Does the deficit include ongoing water losses?
No. Urine, stool, sweat, and breathing keep losing water. Yun et al. list these separately from the deficit.
Is mmol/L the same as mEq/L for sodium?
Yes. Sodium carries one charge, so 150 mmol/L is 150 mEq/L.