For healthcare professionals
Sodium Infusate Calculator (Adrogue-Madias)
The Adrogue-Madias equation estimates how much one litre of an intravenous fluid will change the serum sodium, from the sodium in the fluid, the patient's sodium and the total body water. This tool uses the equation as printed in open-access papers and also shows the version for other volumes. It is written for clinicians and is not a prescription or a fluid plan.
Patient and infusate
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For example, 3% sodium chloride contains 513 mmol/L, the value used in the published examples.
What you will see
The expected change in serum sodium after the chosen volume, with the working, the change per litre and the expected sodium.
Educational only, not medical advice. Not a diagnosis. Decisions belong to the treating team.
Source
The Adrogue-Madias equation and its volume-adjusted form as printed by Voets PJGM and colleagues, PLoS One 2021 (Appendix Eq 3.1 and Eq 2), and by Arzhan S and colleagues, Frontiers in Medicine 2021 (Eq 2); the total body water fractions as printed by Voets PJGM and Vogtlander NPJ, Clinical and Experimental Nephrology 2019. All are open-access (CC BY). The tests reproduce the worked examples in Arzhan 2021 and Voets 2022 and the Adrogue-Madias predictions in Voets 2021, Table 2.
Validated in
The equation comes from the physiology of body water and sodium, not from a cohort, so it has no validated population. In one small retrospective comparison (15 measurements in 12 patients with SIADH, a condition where the kidney keeps water), its predictions correlated weakly with the measured change (r = 0.49, p = 0.07).
Limits
The equation looks only at how the infusate mixes into body water. It ignores urine and other losses of water, sodium and potassium, so it is a short-term estimate whose accuracy falls as time passes. In SIADH it can predict a rise when the sodium actually falls. Total body water uses fixed fractions (0.6 men, 0.5 women) with no adjustment for age or body build. It does not set a safe correction rate; follow your local protocol.
The equation
Change in serum sodium after 1 L of infusate (mmol/L) = (infusate sodium - serum sodium) / (total body water + 1) (Voets 2021) (Arzhan 2021).
The original equation is for 1.0 L only. Voets and colleagues rewrote it for any infusate volume V (in litres): change = V x (infusate sodium - serum sodium) / (total body water + V) (Voets 2021). With V = 1 the two give the same answer.
Total body water = 0.6 x body weight for men and 0.5 x body weight for women (Voets 2019).
Worked examples
A serum sodium of 110 mmol/L and a total body water of 40 L: 1 L of 3% saline (513 mmol/L) gives (513 - 110) / (40 + 1) = 9.8 mmol/L. If the wanted rise is 6 mmol/L, the volume is 1 x 6 / 9.8 = 0.6 L (Arzhan 2021).
A serum sodium of 95 mmol/L and a total body water of 31 L: 0.5 L of 3% saline gives 0.5 x (513 - 95) / (31 + 0.5) = about 6.6 mmol/L (Voets 2022).
Why the real change can differ
Arzhan and colleagues note that the equation does not include urinary losses of water, sodium and potassium, and that these can vary a lot during treatment (Arzhan 2021). Voets and colleagues describe Adrogue-Madias results as short-term predictions whose accuracy breaks down over time, because the equation leaves out how the kidney handles the infusate (Voets 2022). In their SIADH comparison, the equation predicted a rise in sodium for every measurement, while the measured sodium fell in 7 of 15; they conclude that frequent sodium measurements and clinical judgment remain essential (Voets 2021).
Related tools
For water loss in a high sodium, see the free water deficit calculator. To correct sodium for high glucose first, see the corrected sodium calculator. For the blood's overall concentration, see the serum osmolality calculator. Other bedside scores are listed under For healthcare professionals.
Sources
- Voets PJGM, Vogtlander NPJ, Kaasjager KAH. Comparing the Voets equation and the Adrogue-Madias equation for predicting the plasma sodium response to intravenous fluid therapy in SIADH patients. PLoS One. 2021;16(1):e0245499. doi:10.1371/journal.pone.0245499. Open access (CC BY). Eq 2 and Appendix Eq 3.1 (Adrogue-Madias equation, per 1 L and for any volume); Tables 1-2 (15 measurements in 12 SIADH patients; r = 0.49 for Adrogue-Madias). pmc.ncbi.nlm.nih.gov/articles/PMC7810276/
- Arzhan S, Lew SQ, Ing TS, Tzamaloukas AH, Unruh ML. Dysnatremias in chronic kidney disease: pathophysiology, manifestations, and treatment. Front Med (Lausanne). 2021;8:769287. doi:10.3389/fmed.2021.769287. Open access (CC BY). Eq 2 (Adrogue-Madias formula) with the worked example; note that the formula leaves out urinary losses. pmc.ncbi.nlm.nih.gov/articles/PMC8687113/
- Voets PJGM, Vogtlander NPJ. A quantitative approach to intravenous fluid therapy in the syndrome of inappropriate antidiuretic hormone secretion. Clin Exp Nephrol. 2019;23(8):1039. doi:10.1007/s10157-019-01741-6. Open access (CC BY 4.0). Abbreviations list (total body water 0.6 x body weight for men, 0.5 x body weight for women). pmc.ncbi.nlm.nih.gov/articles/PMC6647532/
- Voets PJGM, Maas RPPWM, Vogtlander NPJ, Kaasjager KAH. Osmotic demyelination syndrome and thoughts on its prevention. J Nephrol. 2022;35(1):339. doi:10.1007/s40620-021-01081-3. Open access (CC BY 4.0). Eq 3 (modified Adrogue-Madias worked example) and the note that its predictions are short-term. pmc.ncbi.nlm.nih.gov/articles/PMC8803789/
Written and maintained by the uncovermyrisk.com editorial team. We do not have a medical reviewer; every claim links to its primary source above. Last reviewed: 2026-11-02. Spotted an error? See About.