Serum osmolality calculator (with osmolal gap)
Calculate serum osmolality from sodium, glucose and BUN in mg/dL or urea in mmol/L, add ethanol if it was measured, and enter the lab's measured osmolality to see the osmolal gap.
Guides
- Osmolal gap: what a raised gap means and its causesWhat a raised osmolal gap means: the 10 and 20 cut-offs, causes from ethanol and toxic alcohols to ketoacidosis, and why a normal gap rules nothing out.
How this serum osmolality calculator works
This serum osmolality calculator adds up the three solutes that make up almost all of the osmolality of normal serum: sodium with its matching anions, glucose and urea. Kraut and Kurtz give the formula in their 2008 review in the Clinical Journal of the American Society of Nephrology as 2 × Na + BUN/2.8 + glucose/18, with sodium in mmol/L and glucose and blood urea nitrogen in mg/dL, and Lynd and colleagues call it the Smithline and Gardner equation, the one clinicians apply most often. Sodium is doubled to count chloride and bicarbonate. The divisors only change units: glucose has a molecular weight of 180, so mg/dL divided by 18 gives mmol/L, and BUN counts the 28 grams of nitrogen in each mole of urea, so mg/dL divided by 2.8 gives urea in mmol/L. With mmol/L results the formula becomes 2 × Na + glucose + urea, which Worthley and colleagues found came closest to measured osmolality of five formulas in 300 people.
mg/dL: calculated osmolality = 2 × Na + glucose ÷ 18 + BUN ÷ 2.8
mmol/L: calculated osmolality = 2 × Na + glucose + urea
With ethanol: add ethanol (mg/dL) ÷ 3.7, or 1.25 × ethanol (mmol/L)
Osmolal gap = measured osmolality − calculated osmolality
The ethanol term comes from Purssell and colleagues, who found in 98 observations that each 3.7 mg/dL of ethanol added about 1 mOsm/kg, with a correlation of 0.99. Hoffman's 1993 formula divided ethanol by 4.6, a tenth of its molecular weight. Under the result, the calculator also shows the formula Dorwart and Chalmers found most accurate in 715 hospital sera, 1.86 × Na + glucose/18 + BUN/2.8 + 9. Switching units converts the values you entered, so the result stays the same.
Serum osmolality and osmolal gap results
A serum osmolality calculator gives two numbers that mean different things. The calculated osmolality estimates how concentrated the serum is from sodium, glucose and urea; Kraut and Kurtz put normal serum osmolality at 285 to 290 mOsm/L, and each laboratory publishes its own reference range. The osmolal gap is the osmolality the lab measures with an osmometer minus the calculated value. Kraut and Kurtz state that measured osmolality is usually within 10 mOsm/L of the calculated value, and Lynd and colleagues tested a gap above 10 as the screening cut-off for ethylene glycol and methanol. A gap above 20, in Kraut and Kurtz's review, indicates that one of the alcohols has built up in the blood, because ketoacidosis, lactic acidosis, renal failure and critical illness with hyponatremia usually raise the gap only to 15 to 20 or less. The number is a clue for the laboratory work-up, not a diagnosis on its own, and the timing of the blood sample matters.
| Osmolal gap | Band | What it means |
|---|---|---|
| 10 or less | Within the usual range | Measured and calculated osmolality agree. A toxic alcohol is not excluded, especially late after exposure. |
| Above 10 to 20 | Raised | Unmeasured solutes are present. Causes include ethanol, toxic alcohols, ketoacidosis, lactic acidosis and renal failure. |
| Above 20 | Markedly raised | Points to an alcohol in the blood, per Kraut and Kurtz; check ethanol first, then ask the lab about toxic alcohols. |
The guide to the osmolal gap lists the causes of a raised gap and works through two examples, one explained by ethanol and one that is not.
Limits of calculated osmolality and the gap
The calculated osmolality and the osmolal gap both depend on which formula is used, and no single formula fits every patient. Hoffman and colleagues studied 305 adults at a large inner-city hospital and found a mean gap of −2 ± 6 mOsm with the formula 2 × Na + BUN/2.8 + glucose/18 + ethanol/4.6, while the other equations they tested gave gaps ranging from −5 to +15. They concluded that because the normal range is so wide, a small gap should not be used to rule out a toxic alcohol. Kraut and Kurtz add that alcohol levels high enough to cause harm may not raise osmolality much: methanol at 50 mg/dL adds about 15 mOsm/L, and ethylene glycol at 50 mg/dL only about 9. Lynd and colleagues found that a gap above 10, with the standard ethanol term, had a sensitivity of 0.90 but a specificity of only 0.22 for toxic alcohol levels above the treatment threshold in 131 patients. All values must come from one sample.
Dorwart and Chalmers also found that the difference between measured and calculated osmolality did not predict how long patients stayed in hospital or whether they died, so the gap is a diagnostic clue, not a prognostic score. Bhagat and colleagues later found Dorwart and Chalmers' formula less accurate than their own in 100 plasma samples, another sign that each formula fits its own population best.
Questions
What is the formula for calculated serum osmolality?
2 × Na + glucose ÷ 18 + BUN ÷ 2.8 with glucose and BUN in mg/dL, or 2 × Na + glucose + urea with all three in mmol/L. Sodium is in mmol/L either way.
Is the mmol/L formula the same as the mg/dL one?
Yes. Dividing glucose in mg/dL by 18 and BUN in mg/dL by 2.8 converts them to mmol/L, so the two formulas give the same answer for the same blood.
What is a normal osmolal gap?
Kraut and Kurtz state that measured osmolality is usually within 10 of the calculated value, and 10 is the usual cut-off. Hoffman 1993 found a mean of −2 ± 6, with a wide spread between people.
Should I include ethanol?
If ethanol was measured, yes. Ethanol raises measured osmolality, so leaving it out makes the gap look larger than what is left to explain.
Is my data sent anywhere?
No. The calculation runs in your browser, and the values you enter are not sent or stored.
Sources
- Kraut JA, Kurtz I. Toxic alcohol ingestions: clinical features, diagnosis, and management. Clin J Am Soc Nephrol. 2008;3(1):208–225. doi:10.2215/CJN.03220807
- Smithline N, Gardner KD Jr. Gaps—anionic and osmolal. JAMA. 1976;236(14):1594–1597. doi:10.1001/jama.1976.03270150028025
- 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. doi:10.1093/clinchem/21.2.190
- Worthley LI, Guerin M, Pain RW. For calculating osmolality, the simplest formula is the best. Anaesth Intensive Care. 1987;15(2):199–202. doi:10.1177/0310057X8701500214
- Bhagat CI, Garcia-Webb P, Fletcher E, Beilby JP. Calculated vs measured plasma osmolalities revisited. Clin Chem. 1984;30(10):1703–1705. doi:10.1093/clinchem/30.10.1703
- Hoffman RS, Smilkstein MJ, Howland MA, Goldfrank LR. Osmol gaps revisited: normal values and limitations. J Toxicol Clin Toxicol. 1993;31(1):81–93. doi:10.3109/15563659309000375
- 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
- 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