Accurate measurements of the radiation delivered during the two largest solar flares ever observed are unavailable. In the case of the Carrington event (1858) the X-ray and UV radiation was not recorded, while in the case of the big flare which happened after the storm of 29-31 October 2003 we will call from now on as Halloween event (2003) the radiation saturated the X-ray radiometer. Despite many studies, a consensus regarding the real values of these events at the moment of maximum radiation has never been reached. In this paper, we used an alternative approach to try and determine these values. We estimated the values from the perturbations they produced in the Earth's magnetism -these are known as Solar Flare Effects (Sfe). Firstly, we established an empirical relationship between the variation in the radiation (cause) and its effect on the magnetism (consequence). Then, using the inverse function, we estimated the energy flux of both events. We found that both flares can actually be classified as being larger than X45. Finally, we also calculated the return period for a Carrington-like flare. Assuming that this event had an intensity of about X45 -according to our calculations -we estimated the return period to be 90 ± 60 years.