Free Water Deficit – Hypernatremia Calculator
This calculator estimates the free water deficit in patients with hypernatremia. Select the patient type and enter weight, current serum sodium, and target sodium to find how much free water is needed to correct the sodium level.
Free Water Deficit – Hypernatremia
Free Water Deficit Formula
Where:
- \(TBW\) — total body water in liters, estimated as body weight multiplied by a factor based on patient type: 0.6 for adult males and children, 0.5 for adult females and elderly males, 0.45 for elderly females
- \(\text{Na}_{\text{current}}\) — current serum sodium concentration (mEq/L)
- \(\text{Na}_{\text{desired}}\) — target serum sodium concentration, usually around 140 mEq/L
The formula estimates the volume of free water (pure water, without electrolytes) that must be replaced to bring the serum sodium concentration down to the desired value.
Free Water Deficit – Calculation Example
Example: an adult male weighing 70 kg has a serum sodium of 160 mEq/L, and the treatment goal is to lower it to 140 mEq/L.
\[ TBW = 0.6 \times 70 = 42 \text{ L} \]
\[ \text{Free Water Deficit} = 42 \times \left( \frac{160}{140} - 1 \right) = 42 \times 0.1429 \approx 6.0 \text{ L} \]
Result: the free water deficit is approximately 6.0 liters.
How to use the calculator
- Open the Patient type dropdown and select Adult Male, Adult Female, Elderly Male, Elderly Female, or Child. This sets the total body water fraction used in the formula.
- Enter the patient's Weight in kilograms.
- Enter the Current sodium level in mEq/L from the most recent laboratory result.
- Enter the Desired sodium target in mEq/L — typically 140 mEq/L, or a safe intermediate goal.
- Read the Free water deficit result, shown in liters.
What is free water deficit?
Free water deficit is the amount of water the body is missing relative to its electrolyte content. Hypernatremia — a serum sodium above roughly 145 mEq/L — almost always reflects a deficit of water rather than an excess of sodium. Because sodium is dissolved in body water, the ratio between sodium and water determines the measured concentration. When water is lost faster than sodium (through inadequate intake, diabetes insipidus, osmotic diuresis, or excessive losses from skin and gut), the sodium concentration rises even though total body sodium may be normal.
The free water deficit formula works backwards from that ratio. Total body water (TBW) is estimated from weight using population averages: about 60% of body weight in adult men and children, 50% in adult women and elderly men, and 45% in elderly women, since body water content falls with age and varies with body composition. The formula then asks how much pure water must be added so that the current amount of sodium is diluted to the target concentration.
The result should be interpreted as a total correction volume, not a dose to give all at once. Serum sodium must be lowered slowly — typically no faster than 10–12 mEq/L in 24 hours — because rapid correction can cause cerebral edema and seizures. In practice, clinicians divide the deficit over 48–72 hours and reassess sodium levels frequently, adjusting fluids to ongoing losses. The choice of fluid (usually hypotonic saline or dextrose-containing solutions rather than sterile water) also affects how quickly the deficit is corrected, and ongoing water losses must be replaced in addition to the calculated deficit.
Assumptions and limitations
- TBW estimates are approximations. The fraction of body weight that is water varies with obesity, muscle mass, and hydration status. In obese patients, using actual weight may overestimate TBW; some clinicians use adjusted body weight.
- The formula assumes a steady state. It does not account for ongoing free water losses (urine output, fever, ventilator losses), which must be measured and added separately.
- It ignores sodium and potassium changes. The classic Adrogué–Madias approach, which factors in the sodium and potassium content of the replacement fluid, may predict correction rates more accurately than the simple deficit formula.
- Not all hypernatremia is treated the same way. In hypovolemic patients, volume must be restored with isotonic fluids before free water deficit is corrected; in diabetes insipidus, the underlying cause must be addressed.
- This tool is for education and reference. It does not replace clinical judgment, and any fluid plan for hypernatremia should be managed by a physician with serial sodium monitoring.
Related calculators
For related assessments, you may also find these useful: the Corrected Sodium (Hyperglycemia) Calculator adjusts sodium readings when glucose is elevated, the Clinical Dehydration Scale grades the severity of dehydration in children, and the Dosage Infusion Calculator helps set up the intravenous fluid rates needed to deliver the calculated replacement volume.
Frequently Asked Questions
Can I calculate free water deficit by hand without a calculator?
Yes. Multiply body weight by the water fraction (e.g., \(0.6 \times 70 = 42\) L for an adult male), then apply \(42 \times (160/140 - 1) \approx 6\) L. A quick bedside shortcut is \(\text{deficit} \approx 0.6 \times \text{weight} \times \frac{\text{Na} - 140}{140}\) for men. The calculation takes seconds once you have the weight and both sodium values.
What sodium level is considered normal, and what counts as hypernatremia?
A normal serum sodium concentration is roughly 135–145 mEq/L (mmol/L). Hypernatremia is defined as a sodium above 145 mEq/L. Mild elevations (145–150) often need only oral or enteral water, while values above 160 mEq/L represent a significant deficit and usually require a structured intravenous plan with close monitoring.
Are mEq/L and mmol/L the same for sodium?
Yes. For sodium, 1 mEq/L equals 1 mmol/L because it is a monovalent ion, so no conversion is needed. If your lab reports results in mmol/L, you can enter them directly into the calculator. Only polyvalent ions like calcium or magnesium require conversion between these units.
Why is my result zero or negative?
The result is zero when the current sodium equals the target, meaning no deficit exists. A negative number appears when sodium is already below the target — for example in hyponatremia. The free water deficit formula is only valid for high sodium; a low sodium requires a completely different evaluation and treatment approach.
Why can't the deficit be corrected quickly with sterile water?
Rapidly lowering sodium causes water to shift into brain cells, leading to cerebral edema, seizures, and permanent brain damage. Sterile water given intravenously is also dangerous because it destroys red blood cells. In practice, the deficit is replaced over 48–72 hours with hypotonic saline or dextrose solutions, limiting the drop to about 10–12 mEq/L per day. This dosing decision belongs to a physician.
Does the result tell me how much fluid to infuse per hour?
No — the result is the total volume of pure water needed, not an infusion order. To get an hourly rate, clinicians divide the deficit over the planned correction period (usually 48–72 hours), factor in ongoing losses and the sodium content of the chosen fluid, then reassess with frequent lab draws. The Adrogué–Madias equation is often used to estimate the expected change per liter infused.
How do I handle the calculation in obese patients?
In obesity, using actual body weight overestimates total body water because fat tissue contains little water. Many clinicians use an adjusted body weight instead: for men, \(\text{ABW} = \text{IBW} + 0.4 \times (\text{actual weight} - \text{IBW})\). Enter the adjusted weight into the calculator to get a more realistic deficit estimate, and expect the correction to proceed faster than the simple formula predicts.