Serum osmolality (calculated) and osmolar gap

Category: Renal and metabolic
Version: v1.0.1
Reviewed: Reviewed 6 Sep 2026
Validation: Validation pending

Sodium

mmol/LmEq/L

Glucose

mg/dLmmol/L

Blood urea nitrogen (BUN)

mg/dLmmol/L

Measured osmolality (optional)

Ethanol (optional)

mg/dLmmol/L

Calculated osmolality (Smithline–Gardner, the form Choy recommends and guidelines endorse) = 2 × sodium + glucose ÷ 18 + blood urea nitrogen ÷ 2.8 with mg/dL inputs, equivalently 2 × sodium + glucose + urea with every analyte in mmol/L. Osmolar gap = measured − calculated, and a normal gap is conventionally < 10 mOsm/kg. When a measured ethanol is entered the ethanol term is shown both ways, ÷ 3.7 (Purssell empiric) and ÷ 4.6 (ideal molar mass), and the abnormal-gap flag is replaced by “Accounted for by the measured ethanol” only when the raw gap was not negative to begin with and the residual is negative under both divisors. A negative raw gap needs no ethanol to explain it, so it keeps its ordinary band whatever the ethanol reading. BUN is not urea, the two differ by a factor of 2.8, and glucose and BUN must be in mg/dL for the divisors to apply.

A gap below 10 does not exclude toxic alcohol ingestion. The measured normal gap centres near −2 with an SD of about 6 (n = 321), spanning about −5 to +15 across equations, so an individual whose own baseline is negative can gain more than 20 mOsm/kg of unmeasured osmole and still read +10; early presentation before metabolism also keeps the gap low. The cutoff of 10 sits at the edge of the healthy distribution rather than outside it, and the test is never used in isolation. Paediatric normal gaps are wide, wider than the threshold itself: across 192 children the normal range spans about 22 mOsm whichever equation is used (McQuillen 1999), and children in chronic renal failure ran 13.7 ± 14.5 to 15.2 ± 17.6 mOsm/kg. A gap slightly above 10 in a child is weaker evidence than the sharpness of the cutoff implies, and the boundary stays at 10 because that is what the reference-limit literature supports. Below 3 months, measure rather than calculate: every calculated formula showed systematic and proportional error under 3 months (Berska 2023), and from 3 months to 2 years a different equation, which needs a potassium this score does not collect, agreed best with the osmometer. This calculator does not ask for age and will still compute for a neonate. Performance at the cutoff of 10 depends on the use case and on the ethanol coefficient, and every figure that follows is ADULT (Lynd 2008), as is the derivation of the 10 cutoff itself (Choy 2016) — the arithmetic is population-independent but this performance is not: for identifying the need for haemodialysis, sensitivity 1.0 and NPV 1.0 under both coefficients, at specificity 0.23 to 0.51; for identifying the need for antidotal therapy, sensitivity 0.90 with coefficient 1.0 (≡ ÷ 4.6) or 0.85 with coefficient 1.25 (≡ ÷ 3.7). The additive formula yields osmolarity while the osmometer yields osmolality, which is one reason a normal gap is non-zero, and a negative gap is ordinary variation rather than a finding. A raised gap does not identify the substance. Reference range for the osmolality value itself is 275–295 mOsm/kg, and the paediatric 280–295 mOsm/kg sits inside it.

osm_gap

Result

Interpretation

< 10

< 10 mOsm/kg — Below the reference limit of 10 mOsm/kg for the osmolar gap computed with the Smithline–Gardner formula (Choy 2016). The limit is partly conventional rather than a derived cut-point, and the spread behind it is wider than one number suggests: measured in 321 subjects the gap centres near −2 with an SD of about 6 mOsm, and across different equations the measured gaps ranged from about −5 to +15 (Hoffman 1993); secondary sources render the same distribution as a 95% population range of roughly −14 to +10, whose upper bound is where the cut-off of 10 sits (−2 + 2 SD). A gap below 10 does NOT exclude toxic alcohol ingestion, and the arithmetic above is the reason: an individual's own true baseline may be NEGATIVE, so a patient starting near −14 can acquire more than 20 mOsm/kg of unmeasured osmole and still measure only +10 — at the cut-off rather than far above it. An early presentation before metabolism does the same, and the test is not used in isolation (Lynd 2008). PAEDIATRIC DATA DOES EXIST — an earlier version of this page said none existed and called that absence settled; the claim is WITHDRAWN — and what it shows is a wide normal: across 192 children (median age 6.6 years, 7 days to 17.9 years) the range of normal osmolar gaps is about 22 mOsm whichever equation is used (McQuillen 1999), more than twice the width of the 10 mOsm/kg limit itself. A gap below 10 in a child is therefore unremarkable rather than reassuring. A negative gap is ordinary biological variation, measurement imprecision, or an artefact of an additive formula (which yields osmolarity) being compared with an osmometer (which yields osmolality); it is not a finding in itself.

≥ 10

≥ 10 mOsm/kg — At or above the reference limit of 10 mOsm/kg proposed for the Smithline–Gardner osmolar gap (Choy 2016) — the most common clinically applied cut-off (Lynd 2008). The threshold's performance depends on the question asked, and on which ethanol coefficient is used — the same fork this score already emits (1.0 ≡ ÷4.6 ideal; 1.25 ≡ ÷3.7 empiric). In Lynd 2008 a cut-off of 10 identified patients for whom HAEMODIALYSIS was recommended with sensitivity 1.0 (95% CI 0.80–1.00) and negative predictive value 1.0 under BOTH coefficients, at specificity 0.23 (coefficient 1.0) or 0.51 (coefficient 1.25), AUC 0.827 and 0.870. For identifying patients needing ANTIDOTAL THERAPY the same cut-off gave sensitivity 0.90 (95% CI 0.68–0.99) at specificity 0.22 with coefficient 1.0, and sensitivity 0.85 at specificity 0.50 with coefficient 1.25, AUC 0.736 and 0.785. (An earlier version of this page reported 0.90 and 0.85 as a sensitivity/NPV pair for the antidote question; they are two sensitivities, one per ethanol coefficient. Corrected here from the full text.) Suggests osmotically active solute not captured by sodium, glucose, and urea (e.g. a toxic alcohol, ethanol, mannitol, glycerol, propylene glycol, isopropanol, or a pseudo-gap from severe hyperlipidaemia/hyperproteinaemia). Some older sources use a wider normal up to ~14–15, and the measured normal range varies with the formula used: −2 ± 6 in 321 subjects, about −5 to +15 across equations (Hoffman 1993), and roughly −14 to +10 as a 95% population range in secondary renderings of the same data. A value just above 10 therefore sits at the edge of the healthy distribution rather than outside it. PAEDIATRIC DATA DOES EXIST, and this page's earlier claim that it did not — recorded as settled absent — is WITHDRAWN. It widens the same point: in 192 children (median age 6.6 years) the range of normal osmolar gaps is about 22 mOsm (McQuillen 1999), and in 101 children with chronic renal failure the gaps ran 13.7 ± 14.5 mOsm/kg on peritoneal dialysis and 15.2 ± 17.6 after haemodialysis (Dursun 2007). The boundary stays at 10 because that is what the reference-limit literature supports, not because paediatric normals are narrow — a gap a little above 10 in a child is weaker evidence of an unmeasured osmole than the sharpness of the cut-off suggests. The gap does not identify the substance; interpret with the full clinical picture.

osm_gap_ethanol_explained

Result

Interpretation

any value

Accounted for by the measured ethanol — The entered ethanol accounts for more than the whole measured-minus-calculated difference: that difference was zero or positive before the ethanol term, and with the term added the residual gap is negative under BOTH published divisors (÷3.7 empiric and ÷4.6 ideal). A gap that was already negative is never labelled this way — there was nothing for the ethanol to account for. The raw gap is shown for reference and is not read against the 10 mOsm/kg limit, which applies to a gap the ethanol term has not already absorbed. A negative residual is ordinary biological variation, measurement imprecision, or a formula artefact — the measured normal gap centres near −2, not 0 (Hoffman 1993). This does not exclude a co-ingested toxic alcohol; it says only that no unmeasured osmole is needed to explain this pair of numbers (Lynd 2008).

References

Smithline N, Gardner KD Jr. Gaps—anionic and osmolal. JAMA. 1976;236(14):1594–1597.Original Smithline–Gardner formula (default calculated osmolality).PMID 989132 DOI 10.1001/jama.236.14.1594
Choy KW, Wijeratne N, Lu ZX, Doery JCG. Harmonisation of Osmolal Gap — Can We Use a Common Formula? Clin Biochem Rev. 2016;37(3):113–119.Recommends Smithline–Gardner; proposes the gap reference limit of 10 mOsm/kg; healthy SD ≈ 4, uncertainty ≈ ±7.PMID 27872505
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.Empiric ethanol divisor 3.7 (factor 1.25 in SI).PMID 11719745 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;8:5.10 = most common cut-off; high sensitivity, low specificity; not to be used in isolation.PMID 18442409 DOI 10.1186/1471-227X-8-5
Dorwart WV, Chalmers L. Comparison of methods for calculating serum osmolality from chemical concentrations. Clin Chem. 1975;21(2):190–194.Alternate formula (1.86·Na + glucose/18 + BUN/2.8 + 9); not implemented — documented for cross-reference.PMID 1112025
Bhagat CI, Garcia-Webb P, Fletcher E, Beilby JP. Calculated vs measured plasma osmolalities revisited. Clin Chem. 1984;30(10):1703–1705.Alternate formula (Bhagat); not implemented — documented for cross-reference.PMID 6537784
Ranadive SA, Rosenthal SM. Pediatric Disorders of Water Balance. Pediatr Clin North Am. 2011;58(5):1271–1280.Pediatric normal plasma-osmolality range 280–295 mOsm/kg (the value's reference range, not the gap threshold).PMID 21981960 DOI 10.1016/j.pcl.2011.07.013
Hoffman RS, Smilkstein MJ, Howland MA, Goldfrank LR. Osmol gaps revisited: normal values and limitations. J Toxicol Clin Toxicol. 1993;31(1):81–93.N = 321. Measured normal gap centres at −2 with SD ≈ 6 mOsm and ranges about −5 to +15 depending on the equation — the basis for calling the 10 cut-off partly conventional (≈ mean + 2 SD), and for treating a negative gap as normal variation. The 95% population range of about −14 to +10 quoted alongside it is a secondary rendering of this distribution (and is arithmetically −2 ± 2 SD), not a figure this abstract prints.PMID 8433417
StatPearls [Internet]. Treasure Island (FL): StatPearls Publishing. Serum-osmolality chapter, NCBI Bookshelf ID NBK567764.Reference range 275–295 mOsm/kg for the osmolality VALUE. Tertiary/grey source cited with a retrieval date (retrieved 2026-08-03); the paediatric-specific 280–295 (Ranadive 2011) sits inside it.Source
Berska J, Bugajska J, Sztefko K. The accuracy of serum osmolarity calculation in small children. J Med Biochem. 2023;42(1):67–77.280 samples, first day of life to 2 years (mean age 8.2 ± 7.6 months); measured osmolality 285.8 ± 5.1 mOsm/kgH₂O. Below 3 months every calculated formula showed BOTH systematic and proportional error on Passing–Bablok regression, so osmolality should be measured rather than calculated in that group; from 3 months to 2 years 1.86·(Na+K) + 1.15·glucose + urea + 14 agreed best with the osmometer. RESOLVES a [NEEDS SOURCE]: this is the paper the round-2 pass carried by PMCID alone (PMC9920940) and described as an uncited 'Kraków cohort' — same 280 samples, same day-1-to-2-years range, same 285.8 ± 5.1, same equation. Full bibliographic record confirmed 2026-08-04.PMID 36819138 DOI 10.5937/jomb0-37490
McQuillen KK, Anderson AC. Osmol gaps in the pediatric population. Acad Emerg Med. 1999;6(1):27–30.PAEDIATRIC OSMOLAR-GAP DATA — the study whose existence this score previously denied. 192 children (median age 6.6 years, 7 days to 17.9 years) in a paediatric ED; mean measured osmolality 284.2 ± 6.9, range 265–311. Concludes that whichever equation is used, the range of normal paediatric osmol gaps is approximately 22 mOsm — more than twice the width of the 10 mOsm/kg limit. (The abstract prints the osmolality unit as mOsm/dL, which is not a unit of osmolality; the magnitude is unambiguously mOsm/kg and sits inside the 275–295 reference range.)PMID 9928973 DOI 10.1111/j.1553-2712.1999.tb00090.x
Dursun H, Noyan A, Cengiz N, et al. Changes in osmolal gap and osmolality in children with chronic and end-stage renal failure. Nephron Physiol. 2007;105(2):p19–21.101 children with chronic renal failure; osmolar gap 13.7 ± 14.5 mOsm/kg on peritoneal dialysis and 15.2 ± 17.6 after haemodialysis. Corroborates a wide paediatric spread, in a special population rather than a normal reference sample. Bibliographic record confirmed on PubMed 2026-08-04; PubMed carries no abstract for this article, so the numeric values come from the round-4 finding and were not independently re-read here.PMID 17139190 DOI 10.1159/000097604

Reproduction rights

Freely reproducible.The osmolality formulas (coefficients 2, ÷18, ÷2.8), the ethanol divisors (3.7, 4.6), the gap definition (measured − calculated), and the < 10 mOsm/kg reference limit are mathematical facts and numeric thresholds — outside copyright. No verbatim scale-item wording is embedded (serum-osmolality.md IP status).

Other renal and metabolic scores

Important. For use by qualified health professionals as an informational and educational aid. It supports clinical judgment and does not replace it. Verify every result independently before making a clinical decision. This is not a medical device.