Water Deficit Calculator

What Is Free Water Deficit in Hypernatremia?

Free water deficit (FWD) is the volume of pure water that must be replaced in a hypernatremic patient to restore their serum sodium concentration ($[\text{Na}^+]$) to a normal physiological target (typically $140\text{ mEq/L}$). Hypernatremia (defined as serum $[\text{Na}^+] > 145\text{ mEq/L}$) represents a hyperosmolar state where total body water is depleted relative to total body solute.

To evaluate related fluid dynamics and plasma osmolality, try our Plasma Osmolality Calculator, Sodium Correction Rate Calculator, or Sodium Deficit Calculator.

The Free Water Deficit Formula

The standard clinical formula relates water deficit to Estimated Total Body Water ($\text{TBW}$):

$$\text{Free Water Deficit (L)} = \text{TBW} \times \left( \frac{\text{Current } [\text{Na}^+]}{\text{Target } [\text{Na}^+]} - 1 \right)$$

Where $\text{TBW}$ is calculated based on body weight and patient demographics:

• Adult Men: $\text{TBW} = 0.60 \times \text{Weight (kg)}$
• Adult Women: $\text{TBW} = 0.50 \times \text{Weight (kg)}$
• Elderly Men: $\text{TBW} = 0.50 \times \text{Weight (kg)}$
• Elderly Women: $\text{TBW} = 0.45 \times \text{Weight (kg)}$
• Children: $\text{TBW} = 0.60 \times \text{Weight (kg)}$

IV Infusion Calculations using Adrogué-Madias Equation

When replacing fluid using hypotonic IV solutions (such as 5% Dextrose in Water or 0.45% Normal Saline), the expected change in serum sodium per liter of infusate is calculated by:

$$\Delta [\text{Na}^+] \text{ per Liter} = \frac{[\text{Na}^+]_{\text{infusate}} - [\text{Na}^+]_{\text{serum}}}{\text{TBW} + 1}$$

The total infusate volume needed is then given by:

$$\text{Infusate Volume (L)} = \frac{\text{Target } [\text{Na}^+] - \text{Current } [\text{Na}^+]}{\Delta [\text{Na}^+] \text{ per Liter}}$$

Critical Safety Rules for Correcting Hypernatremia

• Chronic Hypernatremia (> 48 hours): Never lower serum sodium faster than $0.5\text{ mEq/L/hour}$ (maximum $10\text{ to }12\text{ mEq/L}$ drop in 24 hours). Rapid overcorrection causes water to rush into brain cells, leading to cerebral edema, seizures, permanent neurological damage, and death.
• Ongoing Fluid Losses: In addition to the calculated deficit, clinicians must replace ongoing daily maintenance fluid requirements and insensible losses (sweat, respiratory evaporation, and urine).