Formulas for Calculated Osmolarity and Osmolal Gap: A Study of Diagnostic Accuracy

Am J Kidney Dis. 2017 Sep;70(3):347-356. doi: 10.1053/j.ajkd.2017.03.023. Epub 2017 May 31.


Background: The osmolal gap has been used for decades to screen for exposure to toxic alcohols. However, several issues may affect its reliability. We aimed to develop equations to calculate osmolarity with improved performance when used to screen for intoxication to toxic alcohols.

Study design: Retrospective cohort study.

Setting & participants: 7,525 patients undergoing simultaneous measurements of osmolality, sodium, potassium, urea, glucose, and ethanol or undergoing similar measurements performed within 30 minutes of a measurement of toxic alcohol levels at a single tertiary-care center from April 2001 to June 2016. Patients with detectable toxic alcohols were excluded.

Index test: Equations to calculate osmolarity using multiple linear regression.

Outcomes: The performance of new equations compared with published equations developed to calculate osmolarity, and to diagnose toxic alcohol intoxications more accurately.

Results: We obtained 7,525 measurements, including 100 with undetectable toxic alcohols. Among them, 3,875 had undetectable and 3,650 had detectable ethanol levels. In the entire cohort, the best equation to calculate osmolarity was 2.006×Na + 1.228×Urea + 1.387×Glucose + 1.207×Ethanol (values in mmol/L, R2=0.96). A simplified equation, 2.0×Na + 1.2×Urea + 1.4×Glucose + 1.2×Ethanol, had a similar R2 with 95% of osmolal gap values between -10.9 and 13.8. In patients with undetectable ethanol concentrations, the range of 95% of osmolal gap values was narrower than previous published formulas, and in patients with detectable ethanol concentrations, the range was narrower or similar. We performed a subanalysis of 138 cases for which both the toxic alcohol concentration could be measured and the osmolal gap could be calculated. Our simplified equation had superior diagnostic accuracy for toxic alcohol exposure.

Limitations: Single center, no external validation, limited number of cases with detectable toxic alcohols.

Conclusions: In a large cohort, coefficients from regression analyses estimating the contribution of glucose, urea, and ethanol were higher than 1.0. Our simplified formula to precisely calculate osmolarity yielded improved diagnostic accuracy for suspected toxic alcohol exposures than previously published formulas.

Keywords: Equation; diagnostic accuracy; ethanol; formula; glucose; osmolal gap (OG); osmolality; osmolarity; sodium; toxic alcohol; urea.

MeSH terms

  • Adult
  • Alcohols* / chemistry
  • Alcohols* / toxicity
  • Blood Glucose / analysis
  • Canada
  • Chemically-Induced Disorders* / blood
  • Chemically-Induced Disorders* / diagnosis
  • Chemically-Induced Disorders* / etiology
  • Dimensional Measurement Accuracy
  • Female
  • Humans
  • Linear Models
  • Male
  • Osmolar Concentration
  • Predictive Value of Tests
  • Reproducibility of Results
  • Retrospective Studies
  • Urea / blood


  • Alcohols
  • Blood Glucose
  • Urea