What is the formula to calculate free water loss?

Calculating Free Water Loss in Hypernatremia

Free water loss is calculated using the formula: Free Water Deficit = 0.6 × Body Weight (kg) × [1 - (140 ÷ Current Serum Sodium)], though this traditional formula significantly underestimates actual losses and requires important modifications for clinical accuracy 1.

The Standard Formula and Its Limitations

• The conventional water deficit equation assumes total body water (TBW) is 60% of body weight in men and 50-55% in women 1
• This formula systematically underestimates both total body water loss and free water loss by 1.5-2.5 liters for TBW and 0.5-1.0 liters for free water 1
• The equation assumes a normal baseline sodium of 140 mmol/L, which may not reflect the patient's actual premorbid state 1

Improved Formula Using Osmolality

For more accurate estimation of free water loss, use plasma osmolality instead of sodium: Free Water Deficit = 0.6 × Body Weight (kg) × [1 - (290 ÷ Current Plasma Osmolality)] 1

• This osmolality-based formula (using 290 mOsm/kg as the normal baseline) estimates free water loss to within 0.06-0.16 liters of actual loss 1
• The osmolality approach accounts for all effective osmoles, not just sodium 2
• This modification still underestimates total body water losses by more than 40%, but accurately reflects the free water component that needs replacement 1

Critical Adjustments for Specific Clinical Scenarios

Hyperglycemia Correction

• In hyperglycemic patients, you must use corrected sodium concentration in the formula, not the measured value 3
• For every 100 mg/dL glucose elevation above 100 mg/dL, add 1.6-2.4 mmol/L to the measured sodium to get the corrected value 3
• Failure to correct for hyperglycemia will lead to inappropriate fluid replacement calculations 3

Body Weight Considerations

• Use actual body weight for non-obese patients 4
• For obese patients, use ideal body weight calculated from height (BMI = 25 kg/m²) to avoid over-resuscitation 4
• If actual weight is unknown, estimate from body length using length-based methods rather than age-based estimates 4

Understanding Electrolyte-Free Water Clearance

• Electrolyte-free water clearance (EFWC) quantifies ongoing renal free water losses and helps guide replacement therapy 5, 6
• EFWC = Urine Volume × [1 - (Urine Na + Urine K) ÷ Plasma Na] 2
• A negative EFWC indicates the kidney is retaining free water (appropriate response to hypernatremia) 6
• A positive EFWC during hypernatremia indicates inappropriate free water excretion and confirms ADH-renal axis dysfunction 6

Practical Application Algorithm

Step 1: Calculate Initial Deficit

• Use the osmolality-based formula: 0.6 × Body Weight × [1 - (290 ÷ Posm)] 1
• Adjust body weight for obesity if applicable 4
• Correct sodium for hyperglycemia before calculating if glucose >100 mg/dL 3

Step 2: Account for Ongoing Losses

• Calculate EFWC from urine sodium, potassium, and volume measurements 3
• During active osmotic diuresis, replacement should be based directly on measured urine volume and electrolyte concentrations, not predictive formulas 3
• Monitor urine output and composition every 4-6 hours during active treatment 3

Step 3: Determine Replacement Composition

• The composition of replacement fluid should reflect the ratio of water to electrolytes being lost 3
• Use measured urine sodium and potassium concentrations at presentation to guide initial replacement solution composition 3
• For ongoing losses, adjust replacement solutions based on serial urine measurements 3

Common Pitfalls to Avoid

• Do not rely solely on the traditional water deficit formula without recognizing it underestimates actual losses by 40-70% 1
• Never use actual body weight for obese patients in initial calculations, as this leads to excessive fluid administration 4
• Do not ignore urea as a urinary solute when calculating free water clearance—urea is an ineffective osmole that does not contribute to plasma sodium regulation 2
• Avoid using age-based weight estimates; length-based methods are significantly more accurate 4
• Do not calculate replacement needs for ongoing osmotic diuresis using predictive formulas—always use direct measurements of urine volume and electrolyte concentrations 3

Monitoring During Correction

• Subsequent fluid doses should be titrated based on observed clinical effects rather than continuing with initial weight-based calculations 4
• Monitor serum sodium, potassium, glucose, urine volume, and urine electrolytes during treatment of severe dehydration 3
• Reassess EFWC periodically to confirm appropriate ADH-renal axis response 6
• The absolute difference between standard EFWC and modified EFWC is largest in hyponatremia (437 ml vs 256 ml in normonatremia), so the more complex modified formula may be justified in severe dysnatremias 5