How this instrument works
The Adrogué-Madias equation predicts how much serum sodium will move after infusing one liter of a chosen fluid, given the fluid's own sodium and potassium content and an estimate of the patient's total body water. Total body water is approximated as a fraction of weight that depends on sex and age — men typically estimate higher than women, and older adults lower than younger ones, because lean tissue holds more water than fat and both muscle mass and water content decline with age.
The equation comes from a widely cited 2000 review by Adrogué and Madias in the New England Journal of Medicine, written specifically to guide the treatment of low serum sodium, hyponatremia. It reframes a fluid choice as arithmetic: the gap between what the fluid brings and what the serum already contains, spread across the estimated body-water volume, gives the predicted change for that single liter — larger for concentrated fluids like hypertonic saline, small for something close to isotonic.
The same arithmetic runs in reverse without any change to the formula. Give a sodium-poor, potassium-containing fluid to someone whose level is already high, and the equation correctly predicts a fall rather than a rise — it has no built-in assumption about which direction treatment is going, only the composition of the fluid relative to the serum reading in front of it.
- Set Sex and Age (years) — together they select the total body water fraction the formula uses.
- Enter Weight (kg), the body weight the water estimate is scaled against.
- Enter Infusate sodium (mEq/L) and Infusate potassium (mEq/L) for the fluid under consideration.
- Enter Serum sodium (mEq/L), the patient's current reading.
- Read the predicted change in serum sodium per liter of that fluid, and recheck the level before assuming it holds for a second liter.
Worked example — 70 kg man, serum sodium 128, normal saline
A 45-year-old man weighing 70 kg has a serum sodium of 128 mEq/L, mild hyponatremia. Given normal saline, 154 mEq/L sodium with no potassium, the total body water fraction for a man under 65 is 0.6. Plugging in: (154 + 0 − 128) divided by (0.6 × 70 + 1), which is 26 divided by 43, giving a predicted rise of about 0.60 mEq/L for that liter.
Compare that to a 70-year-old woman at 60 kg with a much lower reading of 118 mEq/L, given 3% hypertonic saline at 513 mEq/L sodium. Her body-water fraction drops to 0.45 for an older woman, and the formula returns roughly 14.1 mEq/L for a full liter — which is precisely why hypertonic saline is dosed in small measured volumes rather than a whole liter at once.
Questions
Why does this matter so much — can't sodium just be corrected as fast as possible?
No — correcting chronic low sodium too quickly is a genuine safety hazard, not a theoretical one. Raising the level faster than the brain can adjust risks osmotic demyelination syndrome, a serious and sometimes irreversible neurological injury. Standard practice limits the rise to roughly 8-10 mEq/L in 24 hours, tighter still for patients already at higher risk, which is exactly why correction is done in small steps with frequent blood draws rather than one calculated liter run in unchecked.
Does the predicted change apply the same way to a second or third liter?
Not reliably. The equation is most accurate for the first liter infused; body water and ongoing losses shift as fluid is given, so the relationship isn't perfectly linear across larger volumes. Rechecking the actual serum sodium after each liter, rather than multiplying one prediction by the number of liters planned, is how the formula is meant to be used in practice.
Why do age and sex change the total body water fraction?
Total body water tracks lean tissue, and lean mass differs by sex and declines with age, so the standard estimate uses roughly 0.6 of weight for younger men, 0.5 for younger women, and 0.5 and 0.45 respectively past age 65. It is a population average rather than a direct measurement of any one person's body composition, which is a known source of imprecision in the prediction.
Can this formula predict a fall in sodium instead of a rise?
Yes. Give a fluid whose combined sodium and potassium content is lower than the current serum reading — a potassium-containing, sodium-free solution given to someone with an elevated level, for instance — and the same arithmetic returns a negative number, correctly predicting a drop. The formula has no built-in direction; it only compares what the fluid contains against what the serum already holds.
Is this the same calculation as the water deficit tool for high sodium?
No, they solve different problems with different starting papers. This one predicts the per-liter effect of a specific fluid on low sodium, from the 2000 Adrogué-Madias hyponatremia paper. The free water deficit calculation instead estimates fluid needed to lower an elevated reading, from a separate companion paper on hypernatremia by the same authors — related arithmetic, not interchangeable formulas.
References
- Adrogué HJ, Madias NE. Hyponatremia. N Engl J Med. 2000 (PubMed)
- Spasovski et al. Clinical practice guideline on hyponatraemia, 2014
Read this first: This instrument computes a screening figure from population formulas — it is not a diagnosis, and it cannot see the whole picture a clinician can. Use it to inform a conversation, not to replace one.