Free Water Deficit Calculator (Hypernatremia)
Enter the patient weight, demographics, current serum sodium, and target sodium to calculate the free water deficit caused by hypernatremia. The calculator also gives the volume of electrolyte-free water (D5W) to administer and the hourly infusion rates for a safe 24-hour, 48-hour, or 72-hour correction window. Results update instantly as you type.
Formula
Worked example
A 70 kg adult male (TBW fraction 0.6) with serum sodium of 155 mEq/L, target 145 mEq/L: TBW = 0.6 x 70 = 42 L. FWD = 42 x (155/145 - 1) = 42 x 0.069 = 2.9 L. Over 48 hours: 2900 mL / 48 h = 60.4 mL/h of D5W.
What is the free water deficit?
The free water deficit (FWD) is the estimated volume of electrolyte-free water that must be replaced to lower an elevated serum sodium back to a target level. Hypernatremia (serum sodium above 145 mEq/L) almost always reflects a net loss of free water relative to sodium, not excess sodium intake. Common causes include inadequate fluid intake, diabetes insipidus, excessive sweating, diarrhea, and osmotic diuresis. The FWD formula quantifies only the existing deficit at a single point in time - ongoing losses must be estimated and added separately to the total replacement volume.
How to use this calculator
Select your patient type (which determines the TBW fraction), enter body weight in kilograms or pounds, enter the measured serum sodium, and set a target sodium (usually 140-145 mEq/L). Choose a correction window: 24 hours for acute/ICU hypernatremia, 48 hours for most patients, or 72 hours for chronic or elderly patients. The calculator returns the total free water deficit in liters, estimated total body water, the sodium correction needed, and the hourly infusion rate of D5W (or free water enterally). Recheck sodium every 4-6 hours and adjust the plan as values change.
Correction rate and safety limits
Correcting hypernatremia too quickly risks cerebral edema and seizures, because the brain adapts to high osmolality by accumulating osmolytes - a process that takes 24-48 hours to reverse. For chronic or unknown-onset hypernatremia (lasting more than 48 hours), the serum sodium should not fall faster than 10 mEq/L per 24 hours. For acute hypernatremia with a clear short onset (such as from a dialysis error or formula mistake in an infant), faster correction of up to 1-2 mEq/L per hour may be acceptable and sometimes necessary. Always monitor the patient closely and titrate the infusion based on serial sodium measurements rather than relying solely on the calculated rate.
Fluid selection and administration
The most commonly used free water replacement fluid is 5% dextrose in water (D5W), which provides essentially free water after the dextrose is metabolised. Half-normal saline (0.45% NaCl) provides about half free water per volume, so the volume given must be roughly doubled relative to the calculated FWD. For patients who can drink or receive tube feeds, oral or enteral free water is equivalent and is preferred where tolerated. In volume-depleted patients with hypernatremia, isotonic saline should first be used to restore perfusion before switching to hypotonic fluids for sodium correction. This calculator assumes a pure free-water replacement scenario.
Total body water fractions by patient type
| Patient type | TBW fraction | TBW as % of weight |
|---|---|---|
| Adult male | 0.60 | 60% |
| Adult female | 0.50 | 50% |
| Elderly male | 0.50 | 50% |
| Elderly female | 0.45 | 45% |
| Child | 0.60 | 60% |
These fractions are applied to actual body weight to estimate TBW. Use actual (not ideal) weight.
Frequently asked questions
What is a normal serum sodium level?
Normal serum sodium is 135-145 mEq/L. Hypernatremia is defined as sodium above 145 mEq/L and almost always reflects a deficit of free water relative to sodium. Severe hypernatremia is generally above 160 mEq/L and can cause altered consciousness, seizures, and death if not treated promptly.
Why does the formula use the sodium ratio rather than the difference?
The formula FWD = TBW x (Na_current/Na_target - 1) is derived from the principle that total body sodium is conserved in pure water loss. If TBW decreases while total body sodium stays fixed, serum sodium rises proportionally. Rearranging to find the water that must be added to dilute sodium back to target gives the ratio form. A simpler approximation (using the sodium difference rather than the ratio) is sometimes used but is slightly less accurate, especially at very high sodium levels.
Do I need to add ongoing losses to the calculated deficit?
Yes. The free water deficit formula only estimates the static deficit at the moment of calculation, not future losses. A patient with diabetes insipidus, ongoing fever, or diarrhea will continue to lose free water during the correction period. Ongoing losses should be estimated (typically 500-1000 mL/day for insensible losses, plus measured urine and GI output) and added to the replacement volume to determine total daily fluid requirements.
Can I use this calculator for hyponatremia?
No. The free water deficit formula applies to hypernatremia (sodium above normal). Hyponatremia management involves different considerations, including distinguishing between euvolemic, hypervolemic, and hypovolemic states, and uses different correction rate limits (typically 8-10 mEq/L per 24 hours to avoid osmotic demyelination syndrome). Use a dedicated hyponatremia correction calculator for low sodium cases.
How often should sodium be rechecked during correction?
Most guidelines recommend checking serum sodium every 4-6 hours during active correction of hypernatremia. This allows the infusion rate to be titrated as the actual sodium response is observed, because calculated rates are estimates based on idealized TBW fractions. Faster checking (every 2-4 hours) may be appropriate in severe cases or when the response is unexpected.
Why is the TBW fraction different for elderly women?
Total body water as a percentage of body weight decreases with age as muscle mass (which holds water) is replaced by adipose tissue (which holds much less water). Women also generally have a higher proportion of body fat than men of the same age. Elderly women therefore have the lowest TBW fraction (about 45%), while young adult males have the highest (about 60%). Using the wrong fraction overestimates TBW and leads to prescribing too much fluid.