Since there is no authoritative, comprehensive and public historical record of nuclear power plant accidents, we reconstructed a nuclear accident data set from peer-reviewed and other literature. We found that, in a sample of five random years, the worldwide historical frequency of a nuclear major accident, defined as an INES level 7 event, is 14 %. The probability of at least one nuclear accident rated at level ≥4 on the INES scale is 67 %. These numbers are subject to uncertainties because of the fuzziness of the definition of a nuclear accident. © 2014 Springer Science+Business Media New York.