Sodium Correction Rate Calculator (Adrogué–Madias)
Plan a safe rate of sodium correction in hyponatraemia or hypernatraemia using the Adrogué–Madias formula. Enter the serum sodium, body weight and total-body-water fraction, choose an intravenous fluid, and the calculator predicts how much one litre changes the serum sodium and the infusion rate needed to hit a chosen 24-hour target — without overcorrecting.
About the Adrogué–Madias formula
The Adrogué–Madias formula estimates the change in serum sodium from one litre of a given fluid, so an infusion rate can be planned to stay within safe limits. Source: Adrogué HJ, Madias NE, “Hyponatremia,” New England Journal of Medicine 2000;342(21):1581–1589. Pairs with the free water deficit and corrected sodium calculators.
How this is calculated
Equation. ΔNa per litre = (infusate[Na + K] − serum Na) ÷ (TBW + 1), where TBW = weight(kg) × fraction (0.6 / 0.5 / 0.45).
| Term | Meaning |
|---|---|
| infusate[Na + K] | Sodium + potassium of the fluid (855 / 513 / 154 / 130 / 77 / 34 / 0 mmol/L) |
| serum Na | Current serum sodium (mmol/L) |
| TBW | Total body water = weight × 0.6 / 0.5 / 0.45 |
Volume for the 24-hour target = target ÷ ΔNa-per-litre; rate = that volume over 24 hours. Limit a rise to ≈ 8 mmol/L per 24 h. Source: Adrogué HJ, Madias NE, N Engl J Med 2000;342(21):1581–1589.
Frequently asked questions
What is the Adrogué–Madias formula?
The Adrogué–Madias formula predicts how much one litre of a chosen intravenous fluid will change the serum sodium: change in Na = (infusate [Na + K] − serum Na) ÷ (total body water + 1), where total body water is body weight in kg times a fraction (0.6 for a non-elderly man or a child, 0.5 for a non-elderly woman or elderly man, 0.45 for an elderly woman). The result is per litre of that fluid, in mmol/L. Adrogué and Madias published the formula in 2000 as part of a two-part review on the diagnosis and treatment of hyponatraemia and hypernatraemia in the New England Journal of Medicine.
How fast can sodium be corrected safely?
For chronic hyponatraemia the usual limit is a rise of no more than 8 mmol/L in 24 hours (many guidelines cap it at 10–12 mmol/L per 24 hours and 18 per 48 hours) to avoid osmotic demyelination syndrome. For hypernatraemia the serum sodium is usually lowered by no more than 10 mmol/L per 24 hours to avoid cerebral oedema. The default target here is 8 mmol/L; adjust it to your clinical situation.
How is the infusion rate calculated?
Once you know how much one litre changes the sodium, the volume needed for the target 24-hour change is target ÷ change-per-litre, and the rate is that volume spread over 24 hours (in mL/hour). If the chosen fluid would move the sodium in the wrong direction — for example 5% dextrose in hyponatraemia — the calculator flags it, because you would need a more concentrated (for a rise) or more dilute (for a fall) fluid. The calculation assumes the volume is delivered as a steady continuous infusion spread evenly across the full 24-hour target rather than as a bolus, consistent with the gradual correction the formula is meant to guide.
What are the sodium contents of common fluids?
In mmol/L of sodium plus potassium: 5% saline 855, 3% saline 513, 0.9% (“normal”) saline 154, Ringer’s lactate 130, 0.45% (half-normal) saline 77, 0.2% saline in 5% dextrose 34, and 5% dextrose in water 0. Hypertonic (3% or 5%) saline is used to raise a dangerously low sodium; dextrose or half-normal saline is used to bring a high sodium down. Ringer’s lactate, for example, also contains about 4 mmol/L of potassium in addition to its 130 mmol/L of sodium, which is why its combined [Na + K] value differs slightly from plain saline of a similar strength.
What are the limits of this estimate?
The Adrogué–Madias formula is a single-point prediction that assumes a closed system and ignores ongoing urinary and other losses, so the real change can differ — it is known to under-predict the rise with hypertonic saline. Serum sodium must be rechecked frequently (for example every 2–4 hours during active correction). This is an educational reference, not medical advice.
This is a reference tool, not a diagnosis or medical advice. Results depend on the laboratory, assay and clinical context, and reference intervals vary between labs and by age and sex — always read your result against the range printed on your own report and discuss it with a qualified healthcare professional.
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