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Space weather events can negatively affect satellites, the electricity grid,satellite navigation systems and human health. As a consequence, extreme spaceweather has been added to the UK and other national risk registers. By theirvery nature, extreme space weather events occur rarely and, therefore,statistical methods are required to determine the probability of theiroccurrence. Space weather events can be characterised by a number of naturalphenomena such as X-ray (solar) flares, solar energetic particle (SEP) fluxes,coronal mass ejections and various geophysical indices (Dst, Kp, F10.7). Inthis paper extreme value theory (EVT) is used to investigate the probability ofextreme solar flares. Previous work has assumed that the distribution of solarflares follows a power law. However such an approach can lead to a poorestimation of the return times of such events due to uncertainties in the tailsof the probability distribution function. Using EVT and GOES X-ray flux data itis shown that the expected 150-year return level is approximately an X60 flarewhilst a Carrington-like flare is a one in a 100-year event. It is also shownthat the EVT results are consistent with flare data from the Kepler spacetelescope mission.

Using Extreme Value Theory for Determining the Probability of Carrington-Like Solar Flares