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NephrologyAdjusted Na⁺

Hyperglycemia-Adjusted Sodium Calculator (Katz & Hillier)

Compare Katz 1.6 and Hillier overall 2.4 hyperglycemia-adjusted sodium estimates from measured sodium and paired glucose in mg/dL or mmol/L, without selecting a primary model.

Content updated: View sources

QuickMedCalc is developed and maintained by an independent developer. Medical content is not independently reviewed by a physician.

Formula and medical content are based on the references listed on this page. See sources, About, and Sources and Review Process.

Before calculating

Enter measured sodium in mmol/L and paired glucose in mg/dL or mmol/L. The page returns two unit-preserving arithmetic estimates. It does not calculate osmolality, diagnose a hyperglycemic crisis, select a primary coefficient, or recommend treatment.

mmol/L; for monovalent sodium, mmol/L and mEq/L have the same numeric value.

Changing glucose clears the paired-sample confirmation and any previous result.

A real unit change clears glucose, paired confirmation, and any previous result.

I confirm the paired measurement context.

Sodium and glucose are from the same specimen or a reasonably paired clinical time point.

About

This calculator compares two coefficient-based estimates of sodium at the fixed glucose anchor of 100 mg/dL: Katz 1.6 and Hillier’s overall 2.4. It requires measured sodium and glucose from the same specimen or a reasonably paired clinical time point. Both results are displayed; neither is designated as the primary or universally correct estimate. [1, 2]

Katz derived the 1.6 relationship from a theoretical closed-system model of glucose-related water movement. Hillier experimentally studied six healthy participants, observed an overall average relationship of 2.4 mmol/L sodium per 100 mg/dL glucose, and reported nonlinearity at higher glucose concentrations. This page reproduces the overall published coefficients but does not convert Hillier’s exploratory high-glucose observation into an automatic 4.0 or piecewise formula. [1, 2, 4]

An adjusted sodium value is an arithmetic estimate, not a future measured sodium concentration, measured osmolality, effective osmolality, a diagnosis of DKA or HHS, or a fluid, insulin, potassium, or electrolyte prescription. Hyperglycemic crises are dynamic open systems in which osmotic diuresis, renal function, dialysis, external fluids, and continuing losses can change interpretation. [3, 4]

Formula

Katz: adjusted sodium = measured sodium + 1.6 × [(glucose mg/dL − 100) ÷ 100]. [1, 4]
Hillier overall: adjusted sodium = measured sodium + 2.4 × [(glucose mg/dL − 100) ÷ 100]. [2]
Software conversion: glucose mmol/L = glucose mg/dL × 0.05551; glucose mg/dL = glucose mmol/L ÷ 0.05551. Conversion occurs before either formula is applied. The 100 mg/dL term is the fixed formula anchor, not a diabetes diagnostic threshold; this implementation calculates only when glucose is at least 100 mg/dL.

Interpretation

QuantityWhat it representsCalculated here
Measured sodiumLaboratory sodium at the submitted glucose concentrationInput only
Katz adjusted sodiumProjection to the 100 mg/dL glucose anchor using coefficient 1.6Yes
Hillier adjusted sodiumProjection to the 100 mg/dL glucose anchor using overall coefficient 2.4Yes
Effective osmolality / tonicityDifferent calculation incorporating effective osmolesNo
Measured osmolalityDirect laboratory measurementNo

These quantities are not interchangeable. Neither adjusted-sodium estimate is a future direct measurement, and neither result alone diagnoses true hyponatremia, hypernatremia, DKA, or HHS. The output cannot automatically determine fluid type or rate, insulin, potassium, or another electrolyte treatment. [3, 4]

How the two estimates are calculated

For each model, the calculator subtracts the fixed 100 mg/dL anchor from normalized glucose, divides by 100, multiplies by that model’s coefficient, and adds the resulting increment to measured sodium. It displays Katz and Hillier side by side; it does not choose a primary estimate, average them, feed one result into the other formula, or relabel either projection as measured sodium.

Why this page shows both coefficients

Katz is a theoretical closed-system model, whereas Hillier’s overall 2.4 relationship came from an experiment involving six healthy participants. Their evidence bases and assumptions differ, and Hillier reported nonlinearity at higher glucose. No single coefficient is a universal measured truth across every glucose concentration, fluid state, renal context, and patient population. Showing both estimates makes that model difference visible rather than hiding it. [1, 2, 4]

Why the calculator does not implement an automatic 4.0 model

Hillier observed a steeper relationship in the higher-glucose range, but that exploratory observation came from a small, short-term six-person experiment. This page does not transform it into a universally applicable piecewise clinical rule, and it does not claim that the overall 2.4 coefficient is exact at every extreme glucose concentration. Users see a transparent fixed comparison of Katz 1.6 and Hillier overall 2.4. [2, 4]

Units, pairing, precision, and display

  • Measured sodium is entered in mmol/L; for monovalent sodium, mmol/L and mEq/L have the same numeric value.
  • Glucose accepts mg/dL or mmol/L. The mmol/L path divides by 0.05551 before calculation.
  • Sodium and glucose must come from the same specimen or a reasonably paired clinical time point.
  • Unit normalization and model arithmetic use unrounded intermediate values. Final increments and sodium estimates display one decimal place.
  • A true zero increment displays as 0.0; a positive increment below the one-decimal boundary displays as <0.1.
  • Changing sodium, glucose, or glucose unit clears paired confirmation and any previous result. Software input limits are not health ranges or laboratory reference intervals.

Worked examples

130 mmol/L and 400 mg/dL

Katz increment 4.8 and adjusted sodium 134.8 mmol/L; Hillier increment 7.2 and adjusted sodium 137.2 mmol/L.

120 mmol/L and 600 mg/dL

Katz adjusted sodium 128.0 mmol/L; Hillier adjusted sodium 132.0 mmol/L.

The 100 mg/dL anchor

At sodium 130 mmol/L and glucose 100 mg/dL, both increments are 0.0 and both estimates are 130.0 mmol/L. The anchor is not a diabetes diagnostic threshold.

Equivalent glucose units

400 mg/dL and 22.204 mmol/L follow equivalent normalized arithmetic and produce the same unrounded and displayed results.

These examples audit this implementation’s formula, unit, and display paths. They are not patient interpretation or treatment advice.

Adjusted sodium is not osmolality

Adjusted sodium and effective osmolality (tonicity) are different calculations, while measured osmolality is a laboratory measurement. Adjusted sodium cannot replace either quantity. DKA/HHS assessment uses glucose, ketones, acid–base status, osmolality, fluid balance, and clinical context; this page does not run a DKA or HHS diagnostic algorithm. [3, 4]

Closed-system arithmetic versus real hyperglycemic crises

Katz models glucose-related water movement in a closed system. DKA and HHS can involve osmotic diuresis with continuing water and electrolyte losses; residual renal function, oliguria or anuria, end-stage kidney disease or dialysis, external fluid input, and ongoing urine losses can all alter interpretation. The same adjusted-sodium number does not imply the same water or sodium balance in every person. [3, 4]

Current consensus context

The 2024 adult hyperglycemic-crisis consensus describes that sodium may rise by about 1.6 mmol/L for each 100 mg/dL fall in glucose. That relationship belongs within dynamic monitoring; sodium change cannot be separated from osmolality, fluid balance, renal status, and the treatment course. This calculator does not turn it into a fluid, insulin, potassium, or electrolyte regimen. [3]

When the estimate may be less reliable

  • Sodium and glucose were not collected from the same specimen or a reasonably paired time point.
  • Values are changing rapidly during fluid administration, diuresis, or another intervention.
  • DKA or HHS includes continuing osmotic diuresis and electrolyte loss.
  • Oliguria, anuria, end-stage kidney disease, or dialysis changes the open-system context.
  • Severe hyperglycemia extends beyond what a fixed coefficient can represent uniformly.
  • Marked volume depletion, volume excess, or another factor affects sodium or its laboratory measurement.
  • A static projection is mistaken for the sodium that will be measured after treatment.

These are static limitations, not individualized management instructions. [3, 4]

References

  1. Katz MA. Hyperglycemia-induced hyponatremia—calculation of expected serum sodium depression. N Engl J Med. 1973;289:843–844. PMID 4763428. DOI 10.1056/NEJM197310182891607.
  2. Hillier TA, Abbott RD, Barrett EJ. Hyponatremia: evaluating the correction factor for hyperglycemia. Am J Med. 1999;106:399–403. PMID 10225241. DOI 10.1016/S0002-9343(99)00055-8.
  3. Umpierrez GE, et al. Hyperglycemic Crises in Adults With Diabetes: A Consensus Report. Diabetes Care. 2024;47:1257–1275. PMID 39052901. DOI 10.2337/dci24-0032.
  4. Ing TS, et al. The Corrected Serum Sodium Concentration in Hyperglycemic Crises: Computation and Clinical Applications. Front Med. 2020;7:477. PMID 32984372. DOI 10.3389/fmed.2020.00477.

FAQ

Related Calculators

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Calculate serum osmolality and effective osmolality (tonicity), with optional measured osmolality, osmolal gap, and separate ethanol assumptions; no toxic-alcohol or HHS diagnosis.

Anion Gap

Calculate serum anion gap from sodium, chloride, and bicarbonate or total CO₂ using the formula without potassium, with an input-specific calculation audit.

Free Water Deficit

Estimate a static positive free water deficit for hypernatremia when current sodium is >145 mmol/L or mEq/L, using an explicitly selected lower target, kg or lb weight, and an explicit TBW coefficient, with estimated TBW and results in L and mL—not an infusion volume or treatment output.

Disclaimer

Educational and informational reference only. Not intended to replace professional medical advice, diagnosis, treatment, or independent verification.