Calculator for Serum Na Change After Infusion (Adrogue-Madias Formula)

Adrogue-Madias formula
Δ[serum Na](mEq/L) = ([Infusion Na] + [Infusion K] – [Serum Na]) ÷ (TBW(L) + V(L))
※ TBW (Total Body Water) = Body weight × 0.6 (0.5, if female)
※ V : volume of infusion (L)
※ For Na and K, mmol/L = mEq/L

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.