The Pentland Firth is arguably the best-known candidate site for tidal stream power extraction worldwide. In this paper we estimate the maximum power that can be extracted by placing tidal stream power devices across the Pentland Firth and/or the individual sub-channels formed by the islands of Swona, Stroma and the Pentland Skerries. Using a depth-averaged numerical model, for the entire Firth we find that approximately 4.2 GW of power may be extracted, and this agrees reasonably well with predictions from an existing theoretical model. In contrast, for the sub-channels there is no single value to describe the power potential, but rather a range of power estimates because the extracted power from one sub-channel depends on the operation (or otherwise) of tidal devices placed in parallel sub-channels, or in series along the Firth. This range in output is of practical importance given present plans to lease separate sites within the Pentland to different device developers, and suggests that regulation of separate device developers will be crucial to achieve optimum performance across the entire Firth. Finally, we show that large scale energy extraction from the Pentland Firth does not lead to flow diversion around the Orkney Islands as a whole (as is sometimes assumed), however energy extraction in the Pentland Firth can augment the phase difference across smaller sub-channels in the Orkney Islands and this may increase their power potential.