The 6-month-long 2014–2015 Holuhraun eruption was the largest in Iceland for 200 years, emitting huge quantities of sulfur dioxide (SO2) into the troposphere, at times overwhelming European anthropogenic emissions. Weather, terrain and latitude made continuous ground-based or UV satellite sensor measurements challenging. Infrared Atmospheric Sounding Interferometer (IASI) data are used to derive the first time series of daily SO2 mass present in the atmosphere and its vertical distribution over the entire eruption period. A new optimal estimation scheme is used to calculate daily SO2 fluxes and average e-folding time every 12 h. For the 6 months studied, the SO2 flux was observed to be up to 200 kt day−1 and the minimum total SO2 erupted mass was 4.4±0.8 Tg. The average SO2 e-folding time was 2.4±0.6 days. Where comparisons are possible, these results broadly agree with ground-based near-source measurements, independent remote-sensing data and values obtained from model simulations from a previous paper. The results highlight the importance of using high-resolution time series data to accurately estimate volcanic SO2 emissions. The SO2 mass missed due to thermal contrast is estimated to be of the order of 3 % of the total emission when compared to measurements by the Ozone Monitoring Instrument. A statistical correction for cloud based on the AVHRR cloud-CCI data set suggested that the SO2 mass missed due to cloud cover could be significant, up to a factor of 2 for the plume within the first kilometre from the vent. Applying this correction results in a total erupted mass of 6.7±0.4 Tg and little change in average e-folding time. The data set derived can be used for comparisons to other ground- and satellite-based measurements and to petrological estimates of the SO2 flux. It could also be used to initialise climate model simulations, helping to better quantify the environmental and climatic impacts of future Icelandic fissure eruptions and simulations of past large-scale flood lava eruptions.