The amount of glycated hemoglobin (HbA1c) in diabetic patients’ blood provides the best estimate of the average blood glucose concentration over the preceding 2 to 3 months. It is therefore essential for disease management and is the best predictor of disease complications. Nevertheless, substantial unexplained glucose-independent variation in HbA1c makes its reflection of average glucose inaccurate and limits the precision of medical care for diabetics. The true average glucose concentration of a nondiabetic and a poorly controlled diabetic may differ by less than 15 mg/dl, but patients with identical HbA1c values may have true average glucose concentrations that differ by more than 60 mg/dl. We combined a mechanistic mathematical model of hemoglobin glycation and red blood cell kinetics with large sets of within-patient glucose measurements to derive patient-specific estimates of nonglycemic determinants of HbA1c, including mean red blood cell age. We found that between-patient variation in derived mean red blood cell age explains all glucose-independent variation in HbA1c. We then used our model to personalize prospective estimates of average glucose and reduced errors by more than 50% in four independent groups of greater than 200 patients. The current standard of care provided average glucose estimates with errors >15 mg/dl for one in three patients. Our patient-specific method reduced this error rate to 1 in 10. Our personalized approach should improve medical care for diabetes using existing clinical measurements.