π§ Free Water Deficit Calculator
How much water is missing when sodium runs high?
Estimated free water deficit
For informational purposes only, not medical advice.
Free water deficit equals total body water times (sodium divided by 140, minus 1). A 70 kg man with sodium of 160 has about 42 liters of body water, and the deficit is 42 times (160/140 minus 1), which is 6.0 liters of pure water missing. High sodium almost always means low water, not high salt, and this formula sizes the shortfall.
The 140 is the target: the math asks how much water would dilute the current sodium back to 140. Like its low-sodium cousin, this is an educational estimate. Ongoing losses, kidney function, and the cause all shape the real replacement plan.
How to Use This Calculator
Enter weight, sex, and the current sodium above 140. The tool estimates total body water and returns the liters of free water needed to normalize the concentration.
Enter weight in kilograms and select sex for the 0.6 or 0.5 body-water fraction.
Enter the current sodium. The tool only accepts values above 140, since deficit math needs hypernatremia.
Read the deficit in liters. Replacement uses hypotonic fluids or oral water, given slowly, not all at once.
The Formula
Concentration is amount divided by volume. Sodium amount is roughly fixed in the short term, so the high concentration must come from low volume. The formula solves for the missing volume: how many liters of water, added to the current pool, bring the ratio back to 140. Elegant, and it usually matches clinical reality because hypernatremia is a water problem first.
The same caveats apply as everywhere in body-water math: the fractions are averages, the elderly and obese carry less water per kilo, and the formula ignores water the patient is still losing. It sizes the hole; it does not fill it.
Worked Example
A 70 kg man presents with sodium of 160 mEq/L. Total body water is 0.6 times 70, or 42 liters. Divide 160 by 140 to get 1.143, subtract 1 to get 0.143, and multiply by 42: the free water deficit is 6.0 liters.
Six liters is a large deficit, consistent with days of poor intake or heavy water losses, and it explains why hypernatremia often develops gradually in people who cannot drink freely. Replacement would run over days: lowering sodium faster than about 8 to 12 mEq/L per day risks cerebral edema as water rushes back into brain cells.
Reading Your Result
| Deficit | What it suggests |
|---|---|
| Under 2 liters | Mild. Often correctable with increased oral intake if the patient can drink. |
| 2 to 4 liters | Moderate. Usually needs planned hypotonic fluid replacement. |
| Over 4 liters | Severe. Days of deficit; replace slowly with close monitoring. |
My rule: hypernatremia with a big deficit and a patient who cannot drink is a setup for recurrence. Fixing the number without fixing access to water just schedules the next admission. The deficit tells you the liters; the history tells you why they went missing.
Limits
The formula targets 140 exactly, but many clinicians accept a landing zone rather than a point. It also assumes the sodium is real and current, and it cannot account for concurrent sodium losses, as in diarrhea, where both water and salt are missing and the math gets more complex. As always, volume status and cause drive the plan more than the liters do.
Related Tools
For everyday hydration, the daily water intake calculator sets your baseline before deficits happen. The sodium deficit calculator covers the mirror-image low-sodium problem, and the blood pressure checker tracks the pressure that fluid balance moves.
For informational purposes only, not medical advice. Consult a healthcare professional.
Frequently Asked Questions
What is free water deficit?
The liters of pure water missing from the body when sodium is high. It is calculated as total body water times (current sodium/140 minus 1). A 70 kg man at sodium 160 is missing about 6 liters. Hypernatremia is usually a water deficit, not a salt excess.
Why is 140 the target in the formula?
140 mEq/L sits in the middle of the normal 135 to 145 range and is the conventional reference point. The formula asks how much water would dilute the current sodium back to that midpoint. Clinicians may accept a nearby landing zone rather than exactly 140.
How fast should hypernatremia be corrected?
Roughly 8 to 12 mEq/L per day downward. Correcting too fast risks cerebral edema as water shifts rapidly into brain cells. Severe chronic hypernatremia is typically corrected over several days with frequent lab checks.
What fluid replaces free water deficit?
Hypotonic fluids such as half-normal saline or 5% dextrose in water, or plain oral water when the patient can drink safely. Isotonic saline would not fix the concentration problem. The choice depends on volume status and the clinical setting.
What causes hypernatremia?
Most often inadequate water intake relative to losses: people who cannot drink freely, fever, diarrhea, diabetes insipidus, or osmotic diuresis from high glucose. Because the thirst mechanism is strong, hypernatremia in an alert adult usually signals impaired access to water.
Can I just drink the deficit?
Only for mild cases in people who can drink safely and whose cause is simple under-drinking. Moderate to severe hypernatremia, altered mental status, or ongoing losses need medical management. Do not try to drink 6 liters at once; that pace is dangerous.
Does the formula work for children?
The body-water fractions differ in children, roughly 0.6 to 0.7 depending on age, and pediatric hypernatremia management is specialized. This tool uses adult fractions; children need clinician-directed calculation.
Why do men and women use different fractions?
Average body composition: women typically carry more adipose tissue, which contains little water, so total body water is about 50 percent of weight versus 60 percent for men. Age and obesity shift individual values away from these averages.
What if sodium is high and the patient is also volume depleted?
Then both water and some sodium are missing, and isotonic fluids may come first to restore perfusion before the free-water math applies. The deficit formula isolates the water component; resuscitation order is a clinical decision.
Who should not use this calculator?
Anyone managing real hypernatremia without medical supervision. The deficit is an estimate that starts a clinical conversation, not a fluid order. Severe hypernatremia, confusion, or inability to drink all warrant prompt medical care.