Calculates serum osmolality from sodium, glucose and urea, and the osmolal gap when a measured osmolality is available.
Result
Enter the sodium, glucose and BUN (or urea).
Sources
4 studies
4
studies
135
citations
421
PubMed papers
Evidence
Known limitations
In 305 emergency department adults with known ethanol levels, the osmolal gap (2Na + glucose/18 + BUN/2.8 + ethanol/4.6) averaged −2 mOsm with a standard deviation of 6, and the gap ranged from −5 to +15 depending on the formula used. The authors warn that small gaps should not be used to exclude a toxic alcohol.
J Toxicol Clin Toxicol: Journal Metrics Score 2.1, Q1 · cited 152 times
In 98 emergency patients, the osmolal gap rose in a straight line with the ethanol level (r = 0.99), giving the factor ethanol (mg/dL) ÷ 3.7, or 1.25 × ethanol in mmol/L. In a validation group of 128 patients, the gap left after this correction averaged 0.84.
Ann Emerg Med: Journal Metrics Score 0.8, Q3 · cited 99 times
In 131 patients tested for toxic alcohols, 20 had levels above the threshold for antidote therapy. A gap above 10 found 85% to 90% of them, depending on the ethanol factor, but its specificity was low; it found every patient who needed dialysis.
BMC Emerg Med: Journal Metrics Score 2.9, Q1 · cited 68 times
PubMed · Free full text · DOI
A review of methanol, ethylene glycol, diethylene glycol, propylene glycol and isopropanol poisoning and alcoholic ketoacidosis: most raise both the anion gap and the osmolal gap, while isopropanol raises the osmolality without an acidosis.
Clin J Am Soc Nephrol: Journal Metrics Score 2.8, Q1 · cited 413 times
The original paper has been cited 135 times, and 421 PubMed articles mention the osmolal gap or calculated osmolality in their title or abstract. Citation counts from OpenAlex and article counts from PubMed, retrieved November 13, 2026. Journal Metrics Scores and quartiles are from this site’s current release; follow the journal name for details.
After the result
Raised osmolal gap · Gap not raised · Abnormal calculated osmolality
Look for a toxic alcohol. Does not exclude a toxic alcohol. Find which term drives it.
Next steps
Avoid common errors
5 common errors to avoid
and 3 more
When the gap misleads
1Same sample, same time
The sodium, glucose, urea and measured osmolality must come from the same blood sample. Values hours apart give a meaningless gap.
2Freezing point, not vapor pressure
Vapor pressure osmometers do not detect volatile substances such as methanol and ethanol. The measured value needs a freezing point depression osmometer.
3Late presentation
As methanol and ethylene glycol are metabolized, the osmolal gap falls and the anion gap rises. A patient seen late can have a normal osmolal gap and a severe acidosis.
4Wide normal range
Because a person’s baseline gap can be well below zero, a toxic alcohol can raise the gap substantially and still leave it under 10.
5Formula and units
Different formulas give different gaps; compare like with like. The formula here gives an osmolarity in mOsm/L, shown in mOsm/kg by convention and compared with the measured osmolality, as is usual.
Formula
2 × sodium + glucose/18 + BUN/2.8 (mg/dL); osmolal gap = measured − calculated, raised above 10.
2Na + Glu/18 + BUN/2.8
2 × sodium + glucose/18 + BUN/2.8 (mg/dL); osmolal gap = measured − calculated, raised above 10.
Formula and ranges
| Value | Formula |
|---|---|
| Calculated osmolality | 2 × Na + glucose (mg/dL) ÷ 18 + BUN (mg/dL) ÷ 2.8; in SI, 2 × Na + glucose + urea (mmol/L) |
| With ethanol | add ethanol (mg/dL) ÷ 3.7, or 1.25 × ethanol (mmol/L) |
| Effective osmolality | 2 × Na + glucose (mg/dL) ÷ 18, leaving out urea |
| Osmolal gap | measured osmolality − calculated osmolality |
| Result | Range | Meaning |
|---|---|---|
| Low calculated osmolality | below 275 | Below about 275: usually reflects a low sodium (hypotonic hyponatremia). Measure the serum osmolality to confirm, since unmeasured osmoles can raise the true value. |
| Within the usual range | 275 to 295 | Within the usual reference range of about 275 to 295. A normal calculated value cannot show an unmeasured osmole; for that, measure the osmolality and look at the gap. |
| High calculated osmolality | above 295 | Above about 295: from a high sodium, glucose or urea. Urea crosses cell membranes freely, so check the effective osmolality (tonicity) in the working. |
| Result | Gap | Meaning |
|---|---|---|
| Osmolal gap not raised | 10 or less | A gap of 10 or less is in the commonly used normal range. It does not rule out a toxic alcohol: the normal gap has a standard deviation of about 6, so it ranges from about −14 to +10, and once the alcohol has been metabolized to its acids the gap closes while the anion gap rises. |
| Raised osmolal gap | above 10 | A gap above 10 points to unmeasured osmoles: most often ethanol, but also methanol, ethylene glycol, isopropanol or acetone, propylene glycol, mannitol or glycine, ketoacidosis, lactic acidosis, advanced kidney failure, or a very high lipid or protein level (pseudohyponatremia). |
Smithline and Gardner 1976
Dorwart and Chalmers 1975
Purssell 2001
Units
Test cases
3 published cases, each also a test case
3 published cases; the calculator reproduces every result.
Worked examples
A 69-year-old man found unresponsive had a high anion gap acidosis. Sodium was 149 mmol/L, glucose 138 mg/dL and BUN 113 mg/dL, with a measured osmolality of 362 mOsm/kg. Ethanol, methanol and isopropanol were not detected, but serum acetone was high. The report gives a calculated osmolality of 346 and a gap of 16.
“Serum osmolality was 362 mOsm/kg, and calculated osmolality was 346 mOsm/kg, with an elevated osmolar gap of 16 mOsm/kg.”
The high BUN (113 mg/dL, acute kidney injury) adds 40 to the calculated value; because urea is in the formula it does not itself widen the gap. The acetone level of 50 mg/dL accounts for about 9 of the 16 (50 ÷ 5.8). Ethylene glycol was not measured, and ketoacidosis or the kidney injury may explain the rest. After 48 hours of continuous renal replacement therapy both gaps closed.
Entered as: Sodium: 149 mmol/L (mEq/L); Glucose: 138 mg/dL; BUN or urea: 113 mg/dL (BUN); Measured osmolality: 362 mOsm/kg.
Source: Basuli D et al., Cureus 2022 (PubMed · Free full text · DOI)
A 28-year-old man drank antifreeze about 5 hours before arrival. Sodium was 136.4 mmol/L, glucose 125 mg/dL, BUN 11 mg/dL and the measured osmolality 375 mOsm/kg, with a venous pH of 6.90 and an anion gap of 19.7. The report gives an osmolar gap of 91.34. He recovered with fomepizole and renal replacement therapy.
“an anion gap of 19.7 mmol/L and osmolar gap of 91.34 mOsm/kg H20”
The calculated osmolality is normal; only the measured value shows the alcohol. 375 − 283.7 = 91.3, as in the report.
Entered as: Sodium: 136.4 mmol/L (mEq/L); Glucose: 125 mg/dL; BUN or urea: 11 mg/dL (BUN); Measured osmolality: 375 mOsm/kg.
Source: Song CH et al., Electrolyte Blood Press 2017 (PubMed · Free full text · DOI)
A 70-year-old woman with dementia was unresponsive after accidentally drinking an entire bottle of rubbing alcohol. Sodium was 145 mmol/L, glucose 162 mg/dL, BUN 23 mg/dL, bicarbonate 22 mmol/L and lactate normal; the measured osmolality was 359 mOsm/kg and the isopropanol level 82 mg/dL. She was treated with hemodialysis.
“IPA toxicities exhibit a distinctive laboratory pattern of an increased osmolar gap without metabolic acidosis”
The report gives the values but not the gap; the calculator gives 359 − 307.2 = 51.8. Isopropanol is metabolized to acetone, a ketone, not an acid, so the gap rises without an anion gap acidosis. The isopropanol level of 82 mg/dL accounts for only about 14 of the gap (82 ÷ 6.0); the report does not explain the rest.
Entered as: Sodium: 145 mmol/L (mEq/L); Glucose: 162 mg/dL; BUN or urea: 23 mg/dL (BUN); Measured osmolality: 359 mOsm/kg.
Source: Kumar S et al., Cureus 2024 (PubMed · Free full text · DOI)
FAQ
6 questions and answers
and 4 more answers
Questions
2 × sodium + glucose/18 + BUN/2.8, with sodium in mmol/L and glucose and BUN in mg/dL. In SI units it is simply 2 × sodium + glucose + urea, all in mmol/L. A sodium of 140, glucose of 90 mg/dL and BUN of 14 mg/dL give 280 + 5 + 5 = 290.
Osmolal gap = measured osmolality − calculated osmolality. The measured value comes from the laboratory’s osmometer (freezing point depression); the calculated value comes from the formula. A gap above about 10 suggests an unmeasured osmotically active substance.
Commonly taken as 10 or less, but the normal gap varies widely between people and depends on the formula used. Hoffman and colleagues found a mean of −2 with a standard deviation of 6, using this formula with ethanol divided by 4.6, so in about 95% of people the baseline gap lies between about −14 and +10.
No. A small toxic alcohol load can sit within the normal range, and late after ingestion the parent alcohol has been metabolized to acids that do not raise the gap. Then the anion gap rises instead. Hoffman 1993 concluded that small gaps should not be used to exclude a toxic alcohol.
Enter the ethanol level: the calculator adds ethanol (mg/dL) ÷ 3.7, the factor Purssell and colleagues derived, or 1.25 × ethanol in mmol/L. Any gap left over is not explained by ethanol. Older sources divide by 4.6, which assumes ethanol behaves ideally and leaves a larger apparent gap.
Effective osmolality, or tonicity, leaves out urea because urea crosses cell membranes and does not move water between cells and the blood: 2 × sodium + glucose/18. Definitions of hyperosmolar hyperglycemic state use an effective osmolality above 300 or 320, or a total osmolality above 320, depending on the guideline.
Further reading
9 references with PubMed and DOI links
9
references
4
free full text
From Smithline N et al., JAMA 1976 to the newest case reports.
References
clinical grade of aneurysmal subarachnoid hemorrhage, I to V.
total calcium adjusted for albumin, in mg/dL or mmol/L.
stroke severity from 15 bedside items, 0 to 42.
MAP from systolic and diastolic pressure, against the 65 mm Hg target.
eye, verbal and motor scores for preverbal children, 3 to 15.
oxygenation ratio with the Berlin ARDS severity ranges.
serum sodium corrected for high glucose, Katz or Hillier factor.
sodium − (chloride + bicarbonate), with the albumin-corrected gap.
urea nitrogen to creatinine ratio, in US or SI units.
estimated creatinine clearance with actual, ideal or adjusted weight.
cardiac output and index from oxygen consumption and saturations.
ANC from the white cell count, neutrophils and bands.
insulin resistance from fasting glucose and insulin, in US or SI units.
FENa from plasma and urine sodium and creatinine: prerenal, indeterminate or tubular pattern.
three-item stroke severity screen for large vessel occlusion, 0 to 4.
water deficit in hypernatremia from sodium, weight and body water.
expected PaCO2 in metabolic acidosis, 1.5 × HCO3 + 8 ± 2.
corrected QT interval by Bazett, Fridericia, Framingham or Hodges.
head CT decision rule for children with minor head trauma.
blood loss before hemoglobin or hematocrit reaches a chosen lowest value.
eye, verbal and motor response, 3 to 15, with GCS-Pupils.
Devine ideal body weight and adjusted weight from height and sex.
cuffed and uncuffed tube size and oral depth by age.
severity of alcohol-associated hepatitis from prothrombin time and bilirubin.
MELD, MELD-Na and MELD 3.0 for chronic liver disease.
early stroke risk after a transient ischemic attack.
Which, as Journal of Toxicology: Clinical Toxicology, published the Hoffman study of normal gaps, with its current metrics.
Contributed by Dr. Meng Zhao (MD · Former Neurosurgeon · Medical AI Researcher), from the original publications listed here. Last updated November 13, 2026. LinkedIn
The calculator code is tested against every worked example on this page before each release.
This calculator supports, and does not replace, clinical judgment. It is meant for healthcare professionals and is not medical advice for patients. Report an error through the contact page.