Phytoplankton blooms are ephemeral events of exceptionally high primary productivity that regulate the flux of carbon across marine food webs [1-3]. Quantification of bloom turnover  is limited by a fundamental difficulty to decouple between physical and biological processes as observed by ocean color satellite data. This limitation hinders the quantification of bloom demise and its regulation by biological processes [5, 6], which has important consequences on the efficiency of the biological pump of carbon to the deep ocean [7-9]. Here, we address this challenge and quantify algal blooms' turnover using a combination of satellite and in situ data, which allows identification of a relatively stable oceanic patch that is subject to little mixing with its surroundings. Using a newly developed multisatellite Lagrangian diagnostic, we decouple the contributions of physical and biological processes, allowing quantification of a complete life cycle of a mesoscale (?10-100 km) bloom of coccolithophores in the North Atlantic, from exponential growth to its rapid demise. We estimate the amount of organic carbon produced during the bloom to be in the order of 24,000 tons, of which two-thirds were turned over within 1 week. Complimentary in situ measurements of the same patch area revealed high levels of specific viruses infecting coccolithophore cells, therefore pointing at the importance of viral infection as a possible mortality agent. Application of the newly developed satellite-based approaches opens the way for large-scale quantification of the impact of diverse environmental stresses on the fate of phytoplankton blooms and derived carbon in the ocean.