Accurate estimates of the prevalence of asymptomatic SARS-CoV-2 infections, ψ, have been important for understanding and forecasting the trajectory of the COVID-19 pandemic. Two-part population-based surveys, which test the infection status and also assess symptoms, have been used to estimate ψ. Here, we identified a widely prevalent confounding effect that compromises these estimates and devised a formalism to adjust for it. The symptoms associated with SARS-CoV-2 infection are not all specific to SARS-CoV-2. They can be triggered by a host of other conditions, such as influenza virus infection. By not accounting for the source of the symptoms, the surveys may misclassify individuals experiencing symptoms from other conditions as symptomatic for SARS-CoV-2, thus underestimating ψ. We developed a rigorous formalism to adjust for this confounding effect and derived a facile formula for the adjusted prevalence, ψadj. We applied it to data from 50 published serosurveys, conducted on the general populations from 28 nations. We found that ψadjwas significantly higher than the reported prevalence, ψc(P=3×10-8). The median ψadjwas ~60%, whereas the median ψcwas ~40%. In several instances, ψadjexceeded ψcby >100%. These findings suggest that asymptomatic infections have been far more prevalent than previously estimated. Our formalism can be readily deployed to obtain more accurate estimates of ψ from standard population-based surveys, without additional data collection. The findings have implications for understanding COVID-19 epidemiology and devising more effective interventions.