Hyperglycemia in hospitalized patients is associated with increased morbidity and mortality.We examined whether critical illness is more strongly associated with relative or absolute hyperglycemia.The study was an observational cohort study.A total of 2290 patients acutely admitted to a tertiary hospital.The relative hyperglycemia (stress hyperglycemia ratio [SHR]) was defined as admission glucose divided by estimated average glucose derived from glycosylated hemoglobin. The relationships between glucose and SHR with critical illness (in-hospital death or critical care) were examined.In univariable analyses, SHR (odds ratio, 1.23 per 0.1 increment [95% confidence interval, 1.18-1.28]; P < .001) and glucose (odds ratio, 1.18 per mmol/L [1.13-1.23]; P < .001) were associated with critical illness. In multivariable analysis, the association was maintained for SHR (odds ratio, 1.20 per 0.1 increment [1.13-1.28]; P < .001), but not glucose (odds ratio, 1.03 per mmol/L [0.97-1.11]; P = .31). Background hyperglycemia affected the relationship between glucose (P = .002) and critical illness, but not SHR (P = .35) and critical illness. In patients with admission glucose ≤ 10 mmol/L, the odds ratio for critical illness was higher in the fourth (2.4 [1.4-4.2]; P = .001) and fifth (3.9 [2.3-6.8]; P < .001) SHR quintiles than in the lowest SHR quintile.SHR controls for background glycemia and is a better biomarker of critical illness than absolute hyperglycemia. SHR identifies patients with relative hyperglycemia at risk of critical illness. Future studies should explore whether basing glucose-lowering therapy on relative, rather than absolute, hyperglycemia improves outcomes in hospitalized patients.