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Serum osmolality (calculated) and osmolar gap

Serum sodium in mmol/L (equivalently mEq/L — monovalent, 1:1).

Serum glucose. Accepts mg/dL (US) or mmol/L (SI, ×18).

Blood urea NITROGEN. Accepts mg/dL (US) or, if the lab reports whole-molecule urea (SI), mmol/L (×2.8). BUN ≠ urea — they differ by the ×2.8 factor.

Osmometer value in mOsm/kg. Enter it to compute the osmolar gap (measured − calculated).

Measured ethanol. Accepts mg/dL or mmol/L (×4.6). When entered, the calculated osmolality and residual gap are shown with both the ÷3.7 (empiric) and ÷4.6 (ideal) ethanol terms.

Independent clinical validation: pending

Two independent clinical validators will be named here once review is complete.

Validator slot open 1
Validator slot open 2

How it is calculated

Calculated osmolality (Smithline–Gardner) = 2 × sodium (mmol/L) + glucose (mg/dL) ÷ 18 + blood urea nitrogen (mg/dL) ÷ 2.8, in mOsm/kg. When a measured ethanol is entered, an ethanol term is added and shown two ways: ethanol (mg/dL) ÷ 3.7 (Purssell empiric) and ÷ 4.6 (ideal molar mass). Osmolar gap = measured osmolality − calculated osmolality; with an ethanol on board, the residual gap (ethanol accounted for) is also shown for each divisor. Normal gap is conventionally < 10 mOsm/kg.

Limitations and notes

Formula choice changes the number: this score uses Smithline–Gardner (2·Na + glucose/18 + BUN/2.8), the formula Choy 2016 recommends; Dorwart–Chalmers and Bhagat give slightly different values and are provided as references only, not computed. A gap threshold of 10 is valid only paired with the formula it was derived for. Ethanol divisor 3.7 vs 4.6 is a real fork (empiric Purssell vs ideal MW); both are emitted so the choice is explicit — using 4.6 when ethanol is present slightly over-states the residual gap. US vs SI unit traps: glucose and BUN must be mg/dL for the ÷18 and ÷2.8 divisors; the SI mmol/L alternates apply the factor once (entering already-SI values keeps the same result). BUN (nitrogen) ≠ urea (whole molecule) — they differ by ×2.8. The additive formula yields osmolarity (per L) while the osmometer yields osmolality (per kg water); this small structural mismatch is one reason a normal gap is non-zero, and severe hyperlipidaemia/hyperproteinaemia produce a pseudo-gap without true extra osmoles. The gap is a screening tool, not a rule-out: low specificity and wide baseline variation mean a gap < 10 does not exclude a toxic alcohol, and a raised gap does not identify the agent (Lynd 2008); early methanol/ethylene-glycol poisoning can show a normal gap. The gap requires a measured osmolality the app cannot compute. Pediatric applicability: the formula and threshold are population-independent arithmetic; the normal osmolality range in children matches adults (280–295 mOsm/kg, Ranadive & Rosenthal 2011). [NEEDS SOURCE]: the numeric input-validation bounds for sodium (100–200 mmol/L), glucose (10–2000 mg/dL), BUN (1–300 mg/dL), and measured osmolality (100–600 mOsm/kg) are engineering limits, not values from a specific publication. This is a training/reference calculator, not a clinical decision device.

Accepted input ranges

  • Sodium — 100–200 mmol/L
  • Glucose — 10–2000 mg/dL
  • Blood urea nitrogen (BUN) — 1–300 mg/dL
  • Measured osmolality (optional) — 100–600 mOsm/kg
  • Ethanol (optional) — 0–1000 mg/dL

References

  1. Smithline N, Gardner KD Jr. Gaps—anionic and osmolal. JAMA. 1976;236(14):1594–1597.PMID 989132DOI 10.1001/jama.236.14.1594
  2. 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.PMID 27872505
  3. 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.PMID 11719745DOI 10.1067/mem.2001.119455
  4. 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.PMID 18442409DOI 10.1186/1471-227X-8-5
  5. Dorwart WV, Chalmers L. Comparison of methods for calculating serum osmolality from chemical concentrations. Clin Chem. 1975;21(2):190–194.PMID 1112025
  6. Bhagat CI, Garcia-Webb P, Fletcher E, Beilby JP. Calculated vs measured plasma osmolalities revisited. Clin Chem. 1984;30(10):1703–1705.PMID 6537784
  7. Ranadive SA, Rosenthal SM. Pediatric Disorders of Water Balance. Pediatr Clin North Am. 2011;58(5):1271–1280.PMID 21981960DOI 10.1016/j.pcl.2011.07.013

Version and changelog

v1.0.0 · Renal and metabolic

  • 2026-07-25 v1.0.0 — Initial release: Smithline–Gardner calculated osmolality, osmolar gap, and both ethanol-divisor variants (÷3.7 / ÷4.6).

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.