# How much is the free water deficit?

Estimates the free water deficit in hypernatremia from body weight, sex and age group, and serum sodium: total body water × (sodium ÷ 140 − 1).

- Page: https://www.acalculator.org/health/free-water-deficit-calculator
- JSON spec: https://www.acalculator.org/health/free-water-deficit-calculator.json
- Version: 79dc5d8407b3

## Default answer

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).

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| group | Patient | Sets total body water as a share of body weight: 60% men, 50% women, 5 points less for older adults. |
| weight | Weight | Body weight, from 20 to 300 kg. |
| na | Serum sodium (mmol/L) | Serum sodium in mmol/L (the same as mEq/L), above 140 and up to 200. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| deficit | Free water deficit (L) | Total body water × (sodium ÷ 140 − 1), in liters, to 1 decimal. |
| tbw | Total body water (L) | Body weight in kg × the fraction for the patient group, in liters, to 1 decimal. |

## 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).

## Assumptions

- 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

1. group = man, weight = 70, na = 150 gives deficit = 3, tbw = 42.
2. group = woman, weight = 60, na = 166 gives deficit = 5.6, tbw = 30. Source: Yun, Baek and Kim 2023, worked example after Eq. 5: 0.5 × 60 × (166 ÷ 140 − 1) = 5.6 L.
3. group = olderWoman, weight = 50, na = 160 gives deficit = 3.2, tbw = 22.5.
4. group = olderMan, weight = 80, na = 155 gives deficit = 4.7, tbw = 44.
5. group = man, weight = 69.853225, na = 145 gives deficit = 1.5, tbw = 41.9.

## FAQ

### 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.

## Sources

- Yun G, Baek SH, Kim S. Evaluation and management of hypernatremia in adults: clinical perspectives. Korean J Intern Med. 2023;38(3):290-302. https://doi.org/10.3904/kjim.2022.346 (open at https://pmc.ncbi.nlm.nih.gov/articles/PMC10175862/, retrieved 2026-10-05)