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Sodium Change per Litre of Infusate (Adrogué–Madias)

The Adrogué–Madias formula estimates the change in serum sodium after 1 L of a fluid: (infusate Na + K − serum Na) ÷ (total body water + 1). In chronic hyponatraemia limit correction to ~8 mmol/L in 24 h in high-risk patients and never exceed 10–12 mmol/L, to avoid osmotic demyelination.

Serum sodium (mmol/L or mEq/L)
Weight (kg or lb)
Age (years)
Sex: Male; Female
Infusate: 5% NaCl (Na 855); 3% NaCl (Na 513); 0.9% NaCl (Na 154); Plasma-Lyte 148 (Na 140, K 5); Ringer's lactate (Na 130, K 4); 0.45% NaCl (Na 77); 0.2% NaCl in D5W (Na 34); D5W / free water (Na 0)
Added potassium in infusate (mmol/L or mEq/L)

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Interpretation

Result	Meaning
> 0	Fluid raises serum sodium
< 0	Fluid lowers serum sodium

Formula

ΔNa (per 1 L) = (infusate Na⁺ + infusate K⁺ − serum Na⁺) ÷ (TBW + 1). TBW = weight × 0.6 (children, men <65), 0.5 (women <65, men ≥65), 0.45 (women ≥65).

Clinical pearls

The formula assumes a closed system; ongoing urine output (especially a water diuresis once ADH falls) can cause overcorrection. Check sodium every 2–4 h.
Isotonic saline can worsen hyponatraemia in SIADH when urine osmolality exceeds that of the infusate.
High-risk for osmotic demyelination: Na ≤105, hypokalaemia, alcohol use disorder, malnutrition, advanced liver disease: aim ≤8 mmol/L per 24 h.

Examples

adrogue madias na 115 70 kg 40M 3% saline how much will 1 litre of normal saline raise sodium of 120 in a 60 kg 75 year old woman sodium 160, 80 kg man age 50, D5W change per litre

FAQ

How much will 1 L of 3% saline raise the sodium?

Roughly (513 − serum Na) ÷ (TBW + 1); for a 70 kg man with Na 115 that is about 9 mmol/L per litre.

What is the maximum safe rate of sodium correction?

In chronic hyponatraemia, generally ≤10–12 mmol/L in 24 h, and ≤8 mmol/L in patients at high risk of osmotic demyelination.

Evidence

Nephrology & Electrolytes · Reviewed 2026-10-14 · Methodology