Serum osmolality calculator

The calculator above returns up to four numbers: calculated osmolality, effective osmolality (tonicity), an ethanol-adjusted value if you enter ethanol, and the osmolal gap if you enter a measured osmolality. This article sets out each formula in both unit systems, works through the arithmetic, and explains what the numbers can and cannot tell you. For gap interpretation and toxic alcohols, see the osmolar gap guide.

Units. US: glucose and BUN in mg/dL. SI: glucose and urea in mmol/L. Sodium mEq/L = mmol/L. BUN and urea are different measurements. BUN counts only the nitrogen in urea.

The formulas

Calculated osmolality (default; Smithline–Gardner form) [1, 3, 9]

• US: 2 × Na + Glucose (mg/dL) ÷ 18 + BUN (mg/dL) ÷ 2.8
• SI: 2 × Na + Glucose (mmol/L) + Urea (mmol/L)

Effective osmolality (tonicity): 2 × Na + Glucose (mg/dL) ÷ 18 (SI: 2 × Na + glucose). Urea is left out because it crosses cell membranes freely and does not move water between compartments [11].

Ethanol term (optional)

• Default: + Ethanol (mg/dL) ÷ 3.7 (SI: + 1.25 × ethanol mmol/L). Purssell 2001 derived and validated this factor [4]. Lynd 2008 found that the 1.25 coefficient gave higher specificity and PPV with no loss of sensitivity [3].
• Alternative: + Ethanol (mg/dL) ÷ 4.6 (SI: + 1.0 × ethanol mmol/L). This is the theoretical one-osmole-per-mole value [5]. In a 2025 study of 22 healthy volunteers given ethanol (target peak > 200 mg/dL), correcting with ÷ 4.6 left the gap closer to each person’s pre-drinking baseline than ÷ 3.7 (mean difference 0.2 vs 11.0 mOsm/kg) and produced fewer gaps above 10 (21% vs 47% of 66 timepoints) [6]. Four of the 22 had a gap above 10 before drinking.
• The two factors are not equivalent. ÷ 3.7 pairs with × 1.25 in SI, and ÷ 4.6 pairs with × 1.0. At high ethanol levels they give noticeably different gaps, so name the one you used.

Dorwart–Chalmers (alternative, labelled): 1.86 × Na + Glucose ÷ 18 + BUN ÷ 2.8 + 9 [2]. A gap can be interpreted only against the equation used to set its reference range, so do not mix equations [5].

Unit conversions used

Output and rounding. Results are labelled mOsm/kg by clinical convention, but a calculated value is strictly an osmolarity estimate. Only an osmometer measures osmolality (osmolality vs osmolarity). The calculator keeps full precision and rounds only the displayed result, to 0 decimal places, half away from zero. It computes the gap from the unrounded calculated value.

Worked example 1: US units

Na 140 mmol/L, glucose 90 mg/dL, BUN 14 mg/dL.

1. Glucose: 90 ÷ 18 = 5.0 mmol/L
2. BUN → urea: 14 ÷ 2.8 = 5.0 mmol/L
3. Calculated: 2 × 140 + 5.0 + 5.0 = 290 mOsm/kg
4. Effective: 2 × 140 + 5.0 = 285 mOsm/kg (BUN does not change it)

With Dorwart–Chalmers, the same inputs give 1.86 × 140 + 5 + 5 + 9 = 279.4 → 279, about 11 lower. That difference alone is enough to move a gap across a threshold.

Worked example 2: SI units and the urea trap

Na 140, glucose 5.0 mmol/L, urea 5.0 mmol/L → 280 + 5 + 5 = 290 mOsm/kg, identical to example 1.

Now suppose a lab reports urea 30 mg/dL, not BUN. The right conversion is 30 ÷ 6.0 = 5.0 mmol/L, the same as BUN 14 mg/dL. Entering 30 in a BUN field (30 ÷ 2.8 = 10.7) adds almost 6 mOsm/kg that is not there. Pick the field that matches the report.

Worked example 3: ethanol and the gap

Example 1 inputs plus ethanol 100 mg/dL. Measured osmolality (freezing-point depression) is 350 mOsm/kg.

1. Ethanol term, default: 100 ÷ 3.7 = 27.03
2. Calculated with ethanol: 290 + 27.03 = 317.03 → 317 mOsm/kg
3. Gap: 350 − 317.03 = 32.97 → 33 mOsm/kg

With the ÷ 4.6 alternative: 100 ÷ 4.6 = 21.74, so the calculated value is 311.74 → 312, and the gap is 350 − 311.74 = 38.26 → 38. The patient is the same, but the gap is 5 mOsm/kg higher. Both displayed gaps (33 with ÷ 3.7, 38 with ÷ 4.6) are in the > 20 tier: even after ethanol is counted, it strongly suggests an unmeasured osmole such as a toxic alcohol [7]. It is not a diagnosis. Discuss with a clinician or poison center.

Why the gap uses the unrounded value. With Na 140, glucose 99 mg/dL and BUN 14 mg/dL, the calculated value is 280 + 5.5 + 5.0 = 290.5 (displayed 291). A measured 300 gives a raw gap of 300 − 290.5 = 9.5, displayed as 10 and flagged. Subtracting the rounded 291 would give 9 and miss the flag.

Worked example 4: an exact boundary

Na 125 mmol/L, glucose 900 mg/dL, BUN 56 mg/dL.

1. Glucose: 900 ÷ 18 = 50.0. Urea: 56 ÷ 2.8 = 20.0
2. Calculated: 250 + 50 + 20 = 320 mOsm/kg
3. Effective: 250 + 50 = 300 mOsm/kg

Among its criteria for hyperosmolar hyperglycemic state, the 2024 consensus lists effective osmolality > 300 or total osmolality > 320 mOsm/kg [10]. Here both values sit exactly on the line, so neither “greater than” is met. HHS also requires plasma glucose ≥ 600 mg/dL and the absence of significant ketonemia and acidosis [10], so the osmolality numbers are never the whole definition. The calculator reports the numbers without labelling a condition. Older guidance used an effective cut-off of > 320 [11], so check which edition a source follows. For the sodium side of this picture, see corrected sodium for hyperglycemia.

Reading the result

• Reference interval: 275–295 mOsm/kg is common [12, 13]. Some sources print narrower adult ranges, and ranges vary by laboratory. See normal osmolality range.
• Calculated vs measured: label every value. A measured osmolality comes from an osmometer. Use freezing-point depression for gap work, because vapor-pressure osmometers miss volatile alcohols [8, 14].
• Osmolal gap: a gap of 10 or more (Merck ≥ 10) is the commonly used threshold, a convention rather than a sharp boundary [3, 15]. The calculator flags a displayed (rounded) gap of 10 or more as elevated. Gaps up to about 15–20 occur in non-toxic states such as ketoacidosis, lactic acidosis and renal failure [7, 16]. A gap above 20 strongly suggests an unmeasured osmole such as a toxic alcohol, including ethanol if it was not entered [7, 16]. Every threshold depends on the equation used.
• A normal osmolal gap does not exclude toxic alcohol ingestion. Baseline gaps vary widely between people [5]. A toxic level can be too small to show [3]. As methanol or ethylene glycol is metabolized, the osmolal gap falls while the anion gap rises, so a late presentation can have a normal gap [17, 18].

Limitations

• The formula counts only sodium (doubled to stand in for its anions), glucose and urea. It ignores potassium, calcium, magnesium, proteins and lipids.
• It assumes no unmeasured osmoles. Mannitol, alcohols, glycols and other solutes show up only in a measured value.
• It is an estimate of osmolarity and does not adjust for plasma water. Severe hyperlipidemia or hyperproteinemia can distort the sodium result itself.
• Gap reference ranges belong to specific equations and populations [5, 9].

FAQs

Why is a calculated result given in mOsm/kg? By convention, so that it can be compared with the measured osmolality from the lab. Strictly, it is a calculated osmolarity [5, 8].

My lab reports urea in mmol/L. Which field do I use? Use the SI “Urea (mmol/L)” field with no conversion. Use “BUN (mg/dL)” only for a US BUN result. Urea in mg/dL is divided by 6.0, not 2.8.

Why does effective osmolality leave out urea? Urea crosses cell membranes and does not hold water in one compartment. Glucose (without insulin) and sodium do [11].

Should I enter the glucose-corrected sodium? No. Osmolality formulas use the measured sodium [11].

Which ethanol factor is right? The calculator defaults to ÷ 3.7 (Purssell), with ÷ 4.6 as a labelled alternative. Each has supporting data: Purssell derived and validated ÷ 3.7 [4], and a small 2025 volunteer study favoured ÷ 4.6 [6]. Report which one you used.

Can a normal gap rule out methanol or ethylene glycol? No. Small or normal gaps do not exclude toxic alcohol ingestion [5]. Suspected poisoning needs urgent clinical and poison-center input.

Educational content, not medical advice. Calculated values are estimates for learning and lab interpretation, not a diagnosis. Verify against your institution’s protocols and your laboratory’s reference ranges. In a suspected poisoning, contact poison control or emergency services. See our disclaimer and how we check content.

Related: Osmolar gap · Osmolality vs osmolarity · Normal osmolality range · Isotonic, hypotonic, hypertonic · Corrected sodium for hyperglycemia · IV fluid osmolarity

References

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2. Dorwart WV, Chalmers L. Comparison of methods for calculating serum osmolality from chemical concentrations, and the prognostic value of such calculations. Clin Chem. 1975;21(2):190–194. https://pubmed.ncbi.nlm.nih.gov/1112025/
3. Lynd LD, Richardson KJ, Purssell RA, et al. An evaluation of the osmole gap as a screening test for toxic alcohol poisoning. BMC Emerg Med. 2008;8:5. doi:10.1186/1471-227X-8-5. https://pmc.ncbi.nlm.nih.gov/articles/PMC2390580/
4. Purssell RA, Pudek M, Brubacher J, Abu-Laban RB. Derivation and validation of a formula to calculate the contribution of ethanol to the osmolal gap. Ann Emerg Med. 2001;38(6):653–659. doi:10.1067/mem.2001.119455. https://pubmed.ncbi.nlm.nih.gov/11719745/
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9. Choy KW, Wijeratne N, Lu ZX, Doery JC. Harmonisation of osmolal gap – can we use a common formula? Clin Biochem Rev. 2016;37(3):113–119. https://pmc.ncbi.nlm.nih.gov/articles/PMC5111243/
10. Umpierrez GE, Davis GM, ElSayed NA, et al. Hyperglycemic crises in adults with diabetes: a consensus report. Diabetes Care. 2024;47(8):1257–1275. doi:10.2337/dci24-0032. PMID 39052901. PMC11272983. https://pmc.ncbi.nlm.nih.gov/articles/PMC11272983/ Simultaneously published in Diabetologia 2024;67(8):1455–1479, doi:10.1007/s00125-024-06183-8, PMID 38907161 (open full text PMC11343900).
11. Kitabchi AE, Umpierrez GE, Miles JM, Fisher JN. Hyperglycemic crises in adult patients with diabetes. Diabetes Care. 2009;32(7):1335–1343. doi:10.2337/dc09-9032. PMID 19564476. https://pmc.ncbi.nlm.nih.gov/articles/PMC2699725/
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13. MedlinePlus Medical Encyclopedia. Osmolality blood test. US National Library of Medicine. https://medlineplus.gov/ency/article/003463.htm
14. Walker JA, Schwartzbard A, Krauss EA, Sherman RA, Eisinger RP. The missing gap: a pitfall in the diagnosis of alcohol intoxication by osmometry. Arch Intern Med. 1986;146(9):1843–1844. doi:10.1001/archinte.146.9.1843. https://pubmed.ncbi.nlm.nih.gov/3753127/
15. Merck Manual Professional Edition. Water and Sodium Balance. https://www.merckmanuals.com/professional/nephrology/fluid-metabolism/water-and-sodium-balance
16. Schelling JR, Howard RL, Winter SD, Linas SL. Increased osmolal gap in alcoholic ketoacidosis and lactic acidosis. Ann Intern Med. 1990;113(8):580–582. doi:10.7326/0003-4819-113-8-580. https://pubmed.ncbi.nlm.nih.gov/2400167/
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18. Chen RJ, Glagola JJ, Nappe TM. Ethylene Glycol Toxicity. In: StatPearls [Internet]. Treasure Island (FL): StatPearls Publishing. https://www.ncbi.nlm.nih.gov/books/NBK537009/