Large turbine farms in strong tidal flows could contribute significantly to the global demand for renewable energy. Key to developing large scale power generation is determining how many turbines are required to deliver a given amount of power from proposed sites. Answering this question is computationally difficult, as large-scale power extraction changes the strength of the currents driving the turbines. As a consequence, the large hydrodynamic models used to assess the tidal current resource must be run many times to optimize power output for every potential site and farm size. This paper outlines an approach that can rapidly assess farm power output using an existing hydrodynamic model. This approach is aimed at rapidly determining the most promising farm sites, sizes and shapes within a region, enabling work with more detailed, realistic and slower models to focus on a smaller number of farms. The approach is used to assess how much of Cook Strait, New Zealand’s 15,000 MW potential could be realized with current generation turbines. A basic economic analysis suggests that a 90 MW farm with 95 20 m-diameter turbines might be viable in Cook Strait, if turbine manufacturing costs fall, or energy prices increase, by around 25%.