Sodium Change Calculator — Adrogue-Madias Equation
The Adrogue-Madias equation predicts how much an intravenous infusion will raise or lower a patient's serum sodium concentration. Enter the current sodium, patient weight and type, the chosen fluid, and the volume to infuse.
mEq/L
kg
Patient type
Infusate / IV fluid
mL
Infusate raises serum sodium — monitor closely for osmotic demyelination if rate is too fast
- 1
Total body water (TBW)
70 × 0.6 = 42TBW factor varies by sex and age (0.45–0.60). - 2
ΔNa per litre of infusate
(154 − 125) ÷ (42 + 1) = 0.674 - 3
Volume infused
1,000 ÷ 1000 = 1 - 4
Serum sodium change
0.674 × 1 = 0.67
How does this calculator work?
ΔNa = (Na_infusate − Na_serum) / (TBW + 1) per litre infused, where TBW = weight × 0.6 (adult males), 0.5 (adult females), 0.45 (elderly females). Multiply by litres infused for total predicted change. Limit correction to 10–12 mEq/L per 24 h in hyponatraemia to avoid osmotic demyelination. Monitor serum sodium frequently — the equation is a guide, not a guarantee.
Formula
How this is calculated
Serum sodium concentration is determined by the ratio of total body solutes to total body water (TBW). When you add one litre of intravenous fluid, you simultaneously add sodium (at the infusate concentration) and water. The Adrogue-Madias equation (NEJM 2000) captures this precisely: ΔNa per litre = (Na_infusate − Na_serum) / (TBW + 1). The "+1" in the denominator accounts for the litre being added to the existing TBW. Multiplying by the volume infused gives the total predicted change.
TBW is estimated from body weight using population-derived factors: 60% for adult males and children, 50% for adult females and elderly males, 45% for elderly females. These reflect average body composition differences. Obesity, malnutrition and oedema all alter actual TBW, so clinical monitoring is essential.
The equation is a valuable planning tool but has several limitations. It assumes no ongoing losses (urine, insensible losses) or gains other than the infusate, and it treats TBW as a static compartment. In practice, the kidney's response to volume loading (via ADH suppression) can increase free-water excretion and amplify the rise in sodium, making the actual change larger than predicted — particularly when infusing hypotonic fluids. Always monitor serum sodium frequently during treatment and adjust rates accordingly. For hyponatraemia, do not exceed 10–12 mEq/L in 24 hours to avoid osmotic demyelination syndrome.
Frequently asked questions
It predicts how much any intravenous fluid will change the serum sodium concentration. It is used in clinical practice to select the appropriate fluid and infusion rate when treating hyponatraemia or hypernatraemia, allowing the clinician to estimate the effect before starting treatment.
Because infusing one litre of fluid adds that litre to the existing body water pool. The denominator (TBW + 1) represents the new total body water after the infusion, giving the diluted or concentrated sodium concentration.
Guidelines recommend raising serum sodium by no more than 10–12 mEq/L in the first 24 hours and 18 mEq/L in 48 hours for chronic hyponatraemia. Faster correction risks osmotic demyelination syndrome (central pontine myelinolysis), a potentially devastating neurological complication. Acute symptomatic hyponatraemia (seizures, coma) may warrant a rapid initial 1–2 mEq/L/hr rise for the first 2–3 hours only.
Also known as
TG we-Calculate Editorial Team. (2026). Sodium Change Calculator — Adrogue-Madias Equation [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/sodium-change-calculator
TG we-Calculate Editorial Team. "Sodium Change Calculator — Adrogue-Madias Equation." TG we-Calculate. 2026. https://we-calculate.com/calculator/sodium-change-calculator.
TG we-Calculate Editorial Team, "Sodium Change Calculator — Adrogue-Madias Equation," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/sodium-change-calculator
@misc{wecalculate_sodium_change_calculator, title = {Sodium Change Calculator — Adrogue-Madias Equation}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/sodium-change-calculator}}, year = {2026}, note = {TG we-Calculate} }
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