One of the purposes of reservoir engineering is to quantify the volumetric sweep efficiency for optimizing reservoir management decisions. The estimation of this parameter has always been a difficult task. Until now, sweep efficiency correlations and calculations have been limited to mostly homogeneous 2-D cases. Calculating volumetric sweep efficiency in a 3-D heterogeneous reservoir becomes difficult due to inherent complexity of multiple layers and arbitrary well configurations- In this paper, a new method for computing volumetric sweep efficiency for any arbitrary heterogeneity and well configuration is presented. The proposed method is based on Datta-Gupta and King's formulation of streamline time-of-flight (1995). Given the fact that the time-of-flight reflects the fluid front propagation at various times, then the connectivity in the time-of-flight represents a direct measure of the volumetric sweep efficiency. The proposed approach has been applied to synthetic as well as field examples. Synthetic examples are used to validate the volumetric sweep efficiency calculations using the streamline time-of-flight connectivity criterion by comparison with analytic solutions and published correlations. The field example, which illustrates the feasibility of the approach for large-scale field applications, is from the North Robertson Unit, a low permeability carbonate reservoir in West Texas.