Free Water Deficit Calculator
Find free water deficit for high sodium, with body water and safe daily rate.
What it does
Hypernatremia means too little water for the sodium present, and treatment means replacing water, not removing sodium. The free water deficit puts a number on that shortage: how many liters of pure water would drag sodium back to 140 if nothing else changed. Without it, clinicians guess drip rates blind.
The tool above computes the deficit from weight, sex, and current sodium. It returns the deficit, total body water, and the daily share over 48 hours. Defaults describe a 70 kg man at 160, so the page opens solved at 6 L total and 3 L per day.
The sex split reflects body composition. Men average about 60 percent water by weight and women about 50, because adipose holds little water. Age and obesity push both fractions down, so the page slightly overstates water in older or obese patients, which only makes slow correction safer.
Speed kills here, in a specific way. Dropping sodium faster than about 10 per day lets water flood into brain cells adapted to salty surroundings, causing cerebral edema and seizures. Spreading 6 L over two days lands exactly on the ceiling for the worked case, which is why the daily line exists.
Use the table to feel how weight, sex, and sodium move the answer, then run the patient. Severe dehydration with shock gets isotonic fluids first; free water follows once volume is back.
How to use
- Pick metric (kg) or imperial (lb).
- Pick male or female for the water fraction.
- Enter current serum sodium.
- Read deficit first, then body water.
- Give about half the deficit per day for 2 days.
- Recheck sodium every 6 to 12 hours and add ongoing losses.
Formula
- TBW
- Total body water in liters, from weight and sex.
- Weight
- Body weight: kg in metric mode, lb converted inside in imperial mode.
- Na
- Current serum sodium in mEq/L.
- 140
- Goal sodium, fixed at 140.
Sodium in mEq/L against a goal of 140. Correct no faster than 10 mEq/L per day, which is why the page spreads the deficit over 48 hours. The formula assumes stable total body sodium; volume depleted patients carry a larger true deficit and overloaded patients need diuretics alongside water.
Worked example
Example: 70 kg man, sodium 160
A 70 kg man has serum sodium 160 mEq/L. Find the free water deficit.
- Body water for a man is 0.6 x weight: 0.6 x 70 = 42 L.
- Excess ratio: 160 / 140 - 1 = 0.1429.
- Deficit: 42 x 0.1429 = 6 L.
- Over 48 hours that is 6 / 2 = 3 L per day.
- Sodium falls 20 / 2 = 10 per day, exactly at the safety ceiling.
- Resuscitate shock with isotonic fluids first, then replace this free water.
Reference table
| Patient | Sodium | Deficit | Daily over 48 h |
|---|---|---|---|
| 70 kg man | 160 | 6 L | 3 L/day |
| 60 kg woman | 150 | 2.1 L | 1.1 L/day |
| 80 kg man | 140 | 0 L | 0 L/day |
| 154 lb man | 160 | 6.3 qt | 3.2 qt/day |
Limits
- Assumes stable total body sodium; depletion and overload differ.
- Water fractions are averages; age and obesity lower them.
- Ignores ongoing urine, stool, and sweat losses.
- Hospital math: recheck sodium every few hours.
Common mistakes
- Correcting faster than 10 per day and risking brain swelling.
- Giving free water before fixing shock with isotonic fluids.
- Forgetting ongoing losses, then wondering why sodium stalls.
- Using actual weight in edema instead of a dry estimate.
- Treating the number without checking volume status.
Try it yourself
Quick checks. Answers sit tucked under each question.
60 kg woman, sodium 150?
TBW = 0.5 x 60 = 30 L. Deficit = 30 x (150 / 140 - 1) = 2.1 L, so 1.1 L per day.
80 kg man, sodium already 140?
TBW = 0.6 x 80 = 48 L. Ratio 140 / 140 - 1 = 0, so deficit 0 L.
Same man entered as 154 lb?
154 lb is 69.9 kg, TBW 41.9 L, deficit 6.0 L. In quarts that prints 6.3 qt with 3.2 qt per day.
Questions
Where do 0.6 and 0.5 come from?
The 0.6 and 0.5 are average water fractions of body weight. Older adults and obesity lower them, so the page underestimates there and clinics adjust down.
Is 48 hours mandatory?
Yes, by the same ratio: 6 L over 2 days lowers 160 toward 140 at 10 per day. Faster risks cerebral edema as water rushes into brain cells.
D5W or drinking water?
D5W intravenously or water by mouth or tube. Both deliver pure water; the deficit math is identical either way.
Why does 154 lb give 6.3 qt?
154 lb equals 69.9 kg, so body water is 41.9 L and the deficit is 6.0 L, shown as 6.3 qt. Same patient, same answer.
What about ongoing losses?
Ongoing urine, stool, sweat, and fever losses continue during correction. Measure them, add them to the daily rate, and recheck sodium every few hours.
What are the dangers of treatment?
Volume overload in sodium overload states, plus brain swelling from fast correction. Loop diuretics and slow rates manage both.
Sources
- StatPearls: Hypernatremia, free water deficit formulas (NCBI)
- UCSF Hospital Handbook: hypernatremia water deficit