Water Deficit Calculator

The classic Adrogue–Madias estimate is: free water deficit (L) = TBW × (serum Na ÷ 140 − 1), where TBW is total body water in liters and serum Na is in mEq/L. It estimates how much pure water loss would explain the rise in sodium. It is an approximation, not a prescription — actual fluid therapy must be directed by a clinician.

The classic bedside estimate is 0.6 × body weight (kg) for men and 0.5 × body weight (kg) for women. These fractions are less accurate in obesity, the elderly, children, and critical illness, because fat tissue holds little water. Treat the TBW — and everything derived from it — as a starting estimate only.

140 mEq/L is the conventional midpoint of the normal serum sodium range (135–145 mEq/L). The formula measures the water deficit relative to that reference point. You can adjust it in the advanced settings, but 140 is the standard used throughout the Adrogue–Madias literature.

Hyperglycemia draws water out of cells and dilutes serum sodium, a phenomenon called translocational hyponatremia. The classic Katz (1973) correction adds 1.6 mEq/L to the measured sodium for every 100 mg/dL of glucose above 100 mg/dL: corrected Na = measured Na + 1.6 × (glucose − 100) ÷ 100. When glucose is elevated, use the corrected sodium in deficit calculations.

Educational guidance only: most references advise lowering sodium by no more than about 10 mEq/L per 24 hours, because faster correction risks cerebral edema. This calculator spreads the replacement plan over enough days to respect that limit. The actual rate is a decision for the treating clinician.

Educational guidance only: guidelines generally advise raising sodium by no more than 8 mEq/L per 24 hours and less than 18 mEq/L per 48 hours, because overcorrection risks osmotic demyelination syndrome, a serious neurologic injury. Severely symptomatic hyponatremia is managed in hospital with small boluses of 3% saline under close monitoring.

It predicts the change in serum sodium from one liter of infusate: ΔNa = (infusate Na − serum Na) ÷ (TBW + 1). For 3% saline (513 mEq/L of sodium) the expected rise is (513 − serum Na) ÷ (TBW + 1) mEq/L per liter. Like every formula here it assumes a closed system and ignores ongoing losses, so it is a planning estimate only.

Apply the Adrogue–Madias equation: for example, at a serum sodium of 120 mEq/L and a TBW of 42 L, one liter raises sodium by (513 − 120) ÷ 43 ≈ 9.1 mEq/L. Enter specific values in the Sodium Deficit tab to compute it for a given case. This is educational arithmetic, not a dosing recommendation.

No. This tool is for education and study only — it is not medical advice, it does not diagnose any condition, and it must not guide real fluid or sodium therapy. Electrolyte disorders can be life-threatening and require a qualified clinician; severe symptoms need emergency care.

The formulas assume a closed system: no ongoing water or electrolyte losses, a stable TBW, and full retention of any infusate. Real patients have urine output, insensible losses, and shifting TBW, and the TBW estimate itself is rough. Guidelines therefore stress frequent sodium rechecks and adjusting therapy to the measured response rather than to the formula alone.

Water deficit (free water deficit) applies to hypernatremia — it estimates the missing pure water. Sodium deficit applies to hyponatremia — it estimates the missing sodium as TBW × (target Na − actual Na) in mEq, convertible to a volume of 3% saline. They answer opposite questions, so use the tab that matches the direction of the sodium abnormality.

The 0.6/0.5 fractions assume average adult body composition. They are less reliable in obesity, the elderly, children, pregnancy, and critical illness. Because any TBW error propagates directly into the deficit, treat results as rough planning estimates and confirm with clinical assessment.

Weight in kilograms or pounds, sodium in mEq/L (numerically identical to mmol/L), and glucose in mg/dL. Results are shown in liters, milliliters, and mL per hour.

No. This calculator runs 100% in your browser with zero network requests — your numbers never leave your device.