Sodium Deficit Calculator

Methodology

Adrogué–Madias (2000)

deficit = TBW × (target − Na); ΔNa per litre = (infusate Na + infusate K − serum Na) ÷ (TBW + 1)

The formula predicts the effect of one litre of fluid, ignoring ongoing losses and urine output; measured sodium must guide therapy.

Who it is for

Adults with hyponatraemia under specialist care.

Version

1.1.0

How this calculator works

Where the formula comes from

• The formula for the change in serum sodium after one litre of fluid was published by Adrogué and Madias in 1997 in Intensive Care Medicine and restated in their 2000 review of hyponatraemia in the New England Journal of Medicine.^[1][2]
• The equation is based on body-water and electrolyte physiology; Edelman's 1958 relationship between serum sodium, exchangeable sodium plus potassium, and total body water is its physiological foundation.^[1][3]
• Adrogué and Madias presented the equation as a way to estimate the expected change in serum sodium after a fluid is given, to help clinicians prescribe fluids.^[1]
• The sodium deficit, total body water × (target sodium − current sodium), is a separate mass-balance estimate; it is not the one-litre equation of the 1997 Adrogué–Madias paper.^[4][5]

The inputs

• Total body water is estimated, not measured: body weight × 0.6 in younger men, 0.5 in younger women and older men, and 0.45 in older women.^[2]
• The "+ 1" in the denominator adds the one litre of infused fluid to total body water.^[1]
• When potassium is given in the fluid, the standard equation adds the infusate potassium concentration to the infusate sodium concentration: (infusate Na + infusate K − serum Na) ÷ (total body water + 1).^[1][5]

Versions and alternatives

• Nguyen and Kurtz (2003) proposed alternative equations that account for sodium, potassium and water balance, including changes in body water during treatment.^[4]
• A 2021 modification extends the calculation to infused volumes other than one litre.^[6]
• In a study of patients with SIADH, the Voets equation predicted the plasma sodium response better than the Adrogué–Madias equation; the finding applies to SIADH and should not be generalised to all hyponatraemia.^[7]
• Total body water can also be estimated with anthropometric equations, such as Watson's, that use age, height and weight instead of a fixed fraction.^[8]

Where accuracy falls (published evidence)

• The formula assumes a closed system: it ignores urine output and other ongoing losses of water, sodium and potassium, so the measured change often differs from the prediction.^[5][9]
• In a study of hypernatraemic and normonatraemic intensive-care patients, the formulae tested did not accurately predict the change in serum sodium in individual patients.^[10]
• A 2016 retrospective study of 31 patients with abnormal sodium found prediction errors of about 5–6 mmol/L (root mean square error 4.79–6.37 mmol/L) across four equations.^[11]
• In a study of patients treated with hypertonic saline, the observed rise in serum sodium exceeded the predicted rise in 74.2% of those with sodium below 120 mmol/L, and overcorrection occurred despite use of the formula.^[12]
• An inaccurate estimate of the patient's starting total body water is another source of error.^[5]

What guidelines say

• The 2014 European clinical practice guideline recommends limiting the rise in serum sodium to 10 mmol/L in the first 24 hours and 8 mmol/L in every following 24 hours.^[9]
• The European guideline recommends repeated measurement of serum sodium during treatment and discusses the limitations of formula-based predictions.^[9]
• A 2013 US expert panel recommended correction limits of 10–12 mmol/L in 24 hours, or 8 mmol/L in 24 hours in patients at high risk of osmotic demyelination.^[13]

Sources

1. Adrogué HJ, Madias NE. Aiding fluid prescription for the dysnatremias. Intensive Care Med. 1997;23(3):309–316. doi:10.1007/s001340050333
2. Adrogué HJ, Madias NE. Hyponatremia. N Engl J Med. 2000;342(21):1581–1589. doi:10.1056/NEJM200005253422107
3. Edelman IS, Leibman J, O'Meara MP, Birkenfeld LW. Interrelations between serum sodium concentration, serum osmolarity and total exchangeable sodium, total exchangeable potassium and total body water. J Clin Invest. 1958;37(9):1236–1256. doi:10.1172/JCI103712
4. Nguyen MK, Kurtz I. A new quantitative approach to the treatment of the dysnatremias. Clin Exp Nephrol. 2003;7(2):125–137. doi:10.1007/s10157-003-0233-3
5. Wagner B, et al. Hypertonic saline infusion for hyponatremia: limitations of the Adrogué-Madias and other formulas. Kidney360. 2023. doi:10.34067/KID.0000000000000075
6. Chen S, et al. Improving on the Adrogué–Madias formula. Kidney360. 2021. doi:10.34067/KID.0005882020
7. Voets PJGM, et al. 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. doi:10.1371/journal.pone.0245499
8. Watson PE, Watson ID, Batt RD. Total body water volumes for adult males and females estimated from simple anthropometric measurements. Am J Clin Nutr. 1980;33(1):27–39. doi:10.1093/ajcn/33.1.27
9. Spasovski G, Vanholder R, Allolio B, et al. Clinical practice guideline on diagnosis and treatment of hyponatraemia. Eur J Endocrinol. 2014;170(3):G1–G47. doi:10.1530/EJE-13-1020
10. Lindner G, Schwarz C, Kneidinger N, et al. Can we really predict the change in serum sodium levels? An analysis of currently proposed formulae in hypernatraemic patients. Nephrol Dial Transplant. 2008;23(11):3501–3508. doi:10.1093/ndt/gfn476
11. Hanna RM, Yang WT, Lopez EA, et al. The utility and accuracy of four equations in predicting sodium levels in dysnatremic patients. Clin Kidney J. 2016;9(4):530–539. doi:10.1093/ckj/sfw034
12. Mohmand HK, Issa D, Ahmad Z, Cappuccio JD, Kouides RW, Sterns RH. Hypertonic saline for hyponatremia: risk of inadvertent overcorrection. Clin J Am Soc Nephrol. 2007;2(6):1110–1117. doi:10.2215/CJN.00910207
13. Verbalis JG, Goldsmith SR, Greenberg A, et al. Diagnosis, evaluation, and treatment of hyponatremia: expert panel recommendations. Am J Med. 2013;126(10 Suppl 1):S1–S42. doi:10.1016/j.amjmed.2013.07.006

Compiled from the published sources above. Every statement was agreed independently by three AI research tools (Claude, ChatGPT, DeepSeek) and its source verified in PubMed or Crossref by the Hakeemly editorial team. Not reviewed by a doctor unless stated. Agreed on 2026-10-11

Worked example: how to calculate sodium deficit

Calculation:

42 × 8 = 336; (513 − 120)/43 = 9.14

An illustration with sample values, worked out with the same method the tool above uses.

Limitations

• Frequently over- or under-predicts the real change; frequent sodium monitoring is essential.

References

1. Adrogué HJ, Madias NE. Hyponatremia. N Engl J Med. 2000;342(21):1581–1589. doi:10.1056/NEJM200005253422107
2. Spasovski G, Vanholder R, Allolio B, et al. Clinical practice guideline on diagnosis and treatment of hyponatraemia. Eur J Endocrinol. 2014;170(3):G1–G47. doi:10.1530/EJE-13-1020