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A theoretical approach is presented for contingency allocation and management in building projects using the quantification of uncertainty of project cost. The uncertainty of input items to a bill of quantities, namely, quantities of bill items, usage of resources and their prices are quantified as two moments. From these, two moments for project cost are evaluated. The cumulative distribution function for project cost approximated from its two moments is used to determine the contingency allocation based on a desired probability of success. The management process of this allocation is developed using an approach that establishes initial bench-marks by distributing the allocation to individual bill item costs. By using these initial bench-marks for further distribution, sophistication is introduced to the management process.