An important aspect of how viruses spread and infect is the viral burst size, or the number of new viruses produced by each infected cell. Surprisingly, this value remains poorly characterized for influenza A virus (IAV), commonly known as the flu. In this study, we screened tens of thousands of cells using a microfluidic method called droplet quantitative PCR (dqPCR). The high-throughput capability of dqPCR enabled the measurement of a large population of infected cells producing progeny virus. By measuring the fully assembled and successfully released viruses from these infected cells, we discover that the viral burst sizes for both the seasonal H3N2 and the 2009 pandemic H1N1 strains vary significantly, with H3N2 ranging from 101 to 104 viruses per cell, and H1N1 ranging from 101 to 103 viruses per cell. Some infected cells produce average numbers of new viruses, while others generate extensive number of viruses. In fact, we find that only 10% of the single-cell infections are responsible for creating a significant portion of all the viruses. This small fraction produced approximately 60% of new viruses for H3N2 and 40% for H1N1. On average, each infected cell of the H3N2 flu strain produced 709 new viruses, whereas for H1N1, each infected cell produced 358 viruses. This novel method reveals insights into the flu virus and can lead to improved strategies for managing and preventing the spread of viruses.