A review is made of the quantitative methods used in the NREFS project (Management of Nuclear Risks: Environmental, Financial and Safety) set up to consider how best to respond to a big nuclear accident. Those methods were: the Judgement- or J-value, optimal economic control and a combination of the computer codes PACE and COCO2 produced at Public Health England. The NREFS results show that the life expectancy lost through radiation exposure after a big nuclear accident can be kept small by the adoption of sensible countermeasures, while the downside risk is less severe than is widely perceived even in their absence. Nearly three quarters of the 116,000 members of the public relocated after the Chernobyl accident would have lost less than 9 months' life expectancy per person if they had remained in place, and only 6% would have lost more than 3 years of life expectancy. Neither figure is insignificant, but both are comparable with life expectancy differences resulting from the different day-to-day risks associated with living in different parts of the UK. It is clear in hindsight that too many people were relocated after both the Chernobyl and the Fukushima Daiichi accidents. Remediation methods can often be cost-effective, but relocation of large numbers following a big nuclear accident brings its own risks to health and well-being and should be used sparingly, a message coming from all three of the quantitative methods. There is a need to understand and hence demystify the effects of big nuclear accidents so that decision makers are not pressurised into instituting draconian measures after the accident that may do more harm than good. (c) 2017 Published by Elsevier B.V. on behalf of Institution of Chemical Engineers.