Hyponatremia Treatment – 3% Saline Infusion Rate Calculator (Adrogue-Madias Formula)

This calculator uses the Adrogue-Madias formula to determine the infusion rate of 3% saline during the initial treatment of Hyponatremia.
Infusion rate of 3% Saline[mL/hr] = ( (Target Na-Serum Na) / ((513-Serum Na) / (TBW+1)) / Target period[hr] )×1000
※ TBW (Total Body Water) = Body weight × 0.6 (0.5, if female)
※ Sodium concentration in 3% saline: 513 mEq/L

Example: 46 kg female, current serum Na 112, aiming to increase serum Na by 3 mEq/L over 3 hours
Formula: [((115-112) / ((513-112) / ((46×0.5) + 1))) / 3] × 1000 = 59.9
Result: Infusing 3% saline at 60 mL/hr for 3 hours is expected to raise serum Na by about 3.

Normal saline(1L) : 154 mEq Na
0.45% saline(1L) : 77 mEq Na
3% saline(1L) : 513 mEq Na
5% DW(1L) : 0 mEq Na
Hartmann’s(1L) : 130 mEq Na + 4 mEq K

⚠ To reduce the risk of osmotic demyelination, avoid excessive correction of serum Na. A correction rate not exceeding 8 mEq/L per day is recommended.
⚠ Pitfall of the Adrogue-Madias formula
This formula is suitable for predicting changes with bolus infusion or over a short period, but not for long-term (steady-state) prediction.
– Applicable only under the assumption that there is no fluid loss (urine, diarrhea, etc.)
– In volume depletion (but not dehydration), serum Na is often normal; therefore, the formula is not applicable

Reference :
Adrogué HJ, Madias NE. Aiding fluid prescription for the dysnatremias. Intensive Care Med. 1997 Mar;23(3):309-16. doi: 10.1007/s001340050333. PMID: 9083234.
Adrogué HJ, Madias NE. Hyponatremia. N Engl J Med. 2000 May 25;342(21):1581-9. doi: 10.1056/NEJM200005253422107. PMID: 10824078.