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This paper develops a theoretical basis for three issues that are important in the quantification and management of uncertainty in activity duration networks. Firstly, the uncertainty in activity durations is quantified. Secondly, the quantification of uncertainty in project duration is developed. Thirdly, how these quantifications can be used for allocation and management of contingency in activity durations is demonstrated. A published numerical example is used to illustrate the application of this development to a construction project. While this idea challenges the popular longest path (PERT) approach, it provides a robust theoretical foundation and introduces a logical framework to the quantification and management of uncertainty in activity duration networks.