Free Water Deficit Calculator
Calculate free water deficit for hypernatremia correction from current and target sodium. Enter values for instant results with step-by-step formulas.
Formula
Free Water Deficit = TBW x ((Current Na / Target Na) - 1)
Where TBW = Total Body Water (body weight x TBW fraction based on age and sex), Current Na = measured serum sodium in mEq/L, and Target Na = desired serum sodium, typically 140 mEq/L. The TBW fraction is 0.60 for adult males, 0.50 for adult females, 0.50 for elderly males, and 0.45 for elderly females.
Worked Examples
Example 1: Elderly Patient with Hypernatremia
Problem: A 75-year-old female weighing 60 kg presents with sodium of 158 mEq/L. Calculate the free water deficit targeting a sodium of 140 mEq/L.
Solution: TBW fraction for elderly female = 0.45\nTBW = 60 kg x 0.45 = 27 liters\nFree Water Deficit = 27 x ((158/140) - 1)\n= 27 x (1.129 - 1)\n= 27 x 0.129 = 3.5 liters\nSodium difference = 18 mEq/L\nCorrection over at least 2 days (max 10 mEq/L per day)\nRate = 3.5 L / 48 hours = ~73 mL/hour of D5W
Result: Free Water Deficit: 3.5 L | Correct over 2+ days | ~73 mL/hr D5W
Example 2: Post-Surgical Hypernatremia
Problem: A 70 kg adult male develops sodium of 152 mEq/L after neurosurgery with suspected central diabetes insipidus. Calculate free water deficit targeting 140 mEq/L.
Solution: TBW fraction for adult male = 0.60\nTBW = 70 kg x 0.60 = 42 liters\nFree Water Deficit = 42 x ((152/140) - 1)\n= 42 x (1.086 - 1)\n= 42 x 0.086 = 3.6 liters\nSodium difference = 12 mEq/L\nCorrection over at least 2 days\nAdditional ongoing losses from DI must be added to replacement volume
Result: Free Water Deficit: 3.6 L | Correct over 2+ days | Add ongoing DI losses
Frequently Asked Questions
What is free water deficit and when is it calculated?
Free water deficit is the volume of electrolyte-free water that a patient needs to correct hypernatremia, which is a serum sodium level above 145 mEq/L. Hypernatremia occurs when there is a relative excess of sodium compared to body water, most commonly due to inadequate water intake or excessive water losses from the body. The free water deficit calculation estimates how much pure water is needed to dilute the serum sodium back to a normal target concentration. This calculation is essential in clinical settings for planning fluid replacement in hospitalized patients, particularly those who are unable to drink water independently.
How is free water deficit calculated?
The free water deficit formula is: Free Water Deficit (liters) = Total Body Water x ((Current Sodium / Target Sodium) - 1). Total body water (TBW) is estimated as a fraction of body weight, typically 60% for adult males, 50% for adult females, 50% for elderly males, and 45% for elderly females. For example, a 70 kg adult male with a sodium of 160 mEq/L targeting 140 mEq/L would have TBW of 42 liters and a free water deficit of 42 x (160/140 - 1) = 42 x 0.143 = 6.0 liters. This volume represents the theoretical amount of pure water needed to normalize the sodium concentration.
What fluids are used to replace free water deficit?
Several intravenous fluids can be used to replace free water, each contributing different amounts of electrolyte-free water per liter. Dextrose 5% in water (D5W) provides 1 liter of free water per liter administered, making it the most efficient choice. Half-normal saline (0.45% NaCl) provides approximately 500 mL of free water per liter. Quarter-normal saline (0.225% NaCl) provides about 750 mL of free water per liter. Normal saline (0.9% NaCl) provides zero free water and should not be used for free water replacement. Oral or enteral water is preferred when the patient can tolerate it, as it is the safest and most physiologic replacement route.
Can free water deficit calculations be used in pediatric patients?
Yes, the free water deficit formula can be applied to pediatric patients, but the total body water fraction must be adjusted for the child age and development. Neonates and infants have significantly higher body water content, with TBW approximately 75 to 80% of body weight in premature infants and 70 to 75% in term neonates. By age 1 year, TBW decreases to approximately 60%, and by puberty, adult values of 60% for males and 50% for females are reached. Pediatric patients are more vulnerable to both hypernatremia and its complications, and correction rates should generally be even more conservative. Frequent electrolyte monitoring every 2 to 4 hours is recommended in critically ill children during active correction.
Is my data stored or sent to a server?
No. All calculations run entirely in your browser using JavaScript. No data you enter is ever transmitted to any server or stored anywhere. Your inputs remain completely private.
Can I share or bookmark my calculation?
You can bookmark the calculator page in your browser. Many calculators also display a shareable result summary you can copy. The page URL stays the same so returning to it will bring you back to the same tool.