Adrogué-Madias Formula Calculator
Adrogué-Madias Formula Calculator
Predict the change in serum sodium from one litre of a chosen infusate, using the Adrogué-Madias formula.
Adrogué-Madias Formula
Predicted ΔNa per litreSodium 118 mmol/L, 3% saline (513 mmol/L), weight 70 kg, adult male total body water fraction 0.6
Formula
- infusate Na
- mmol/L of sodium in the chosen fluid
- TBW + 1
- the volume of distribution — total body water plus the one litre being infused
- result
- predicted change in serum sodium per litre infused, before accounting for ongoing losses
Worked example
Sodium 118 mmol/L, 3% saline (513 mmol/L), weight 70 kg, adult male total body water fraction 0.6
TBW = 70 × 0.6 = 42 L
513 − 118 = 395
395 ÷ (42 + 1) = 395 ÷ 43 = 9.19 mmol/L per litre
Common infusates
| Infusate | Sodium (mmol/L) |
|---|---|
| 3% saline | 513 |
| 0.9% saline | 154 |
| Lactated Ringer’s | 130 |
| 0.45% saline | 77 |
| 5% dextrose | 0 |
A starting estimate, not a substitute for measurement
The Adrogué-Madias formula predicts the change in serum sodium produced by one litre of a chosen infusate, using total body water as the volume of distribution. It is widely used to plan the choice and rate of fluid when correcting dysnatraemias, because it converts an infusate choice directly into an expected change in the number that matters.
Its well-documented weakness is that it accounts only for the infusate given — it ignores ongoing urinary and insensible losses entirely. This means it systematically underestimates the true rise in sodium in patients who begin a water diuresis during treatment, which is exactly what happens when the stimulus to antidiuretic hormone is removed, as in resolving hypovolaemia, correction of hyperglycaemia, or after stopping a thiazide diuretic. In these patients, free water is being lost through the kidneys in addition to whatever the infusate contributes, and sodium can rise considerably faster than the formula predicts.
Treat the result as a starting point for planning an infusion rate, never as a substitute for measuring sodium directly. During active correction of hyponatraemia or hypernatraemia, recheck sodium every 2–4 hours, and be prepared to slow or stop the infusion if the observed rate of change is running ahead of the correction limit, regardless of what the formula predicted.
Frequently asked questions
What does the Adrogué-Madias formula predict?
The expected change in serum sodium from infusing one litre of a chosen fluid, based on the sodium content of that fluid and the patient’s total body water.
Why can it underestimate the rise in sodium?
It accounts only for the infusate, not for ongoing urinary and insensible losses. In patients developing a water diuresis — for example as ADH stimulus resolves — sodium rises faster than predicted because free water is also being lost through the kidneys.
Which infusate should I choose to correct hyponatraemia?
3% saline for controlled correction of symptomatic hyponatraemia; 0.9% saline more cautiously, since it can still raise sodium too quickly in severe hyponatraemia. The right choice depends on severity, symptoms and correction limits, not the formula alone.
How often should sodium be rechecked during active correction?
Every 2–4 hours while actively correcting either hyponatraemia or hypernatraemia, since the formula does not capture ongoing losses and the actual rate of change can differ substantially from the prediction.
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References
- Adrogué HJ, Madias NE. Aiding fluid prescription for the dysnatremias. Intensive Care Med. 1997;23(3):309–316.
- Adrogué HJ, Madias NE. Hyponatremia. N Engl J Med. 2000;342(21):1581–1589.
Medical Disclaimer: The tools and content provided here are for educational and reference purposes only. They are not intended to substitute for professional medical advice, diagnosis, or treatment. Clinical decisions should always be based on the comprehensive assessment of a qualified healthcare professional.