Interest in sources of renewable energy has led to increasing attention being paid to the potential of strong tidal currents. There is a limit to the available power, however, as too many turbines will merely block the flow, reducing the power generated. The maximum average power available from a tidal stream along a channel, such as that between an island and the mainland, is estimated and found to be typically considerably less than the average kinetic energy flux in the undisturbed state through the most constricted cross-section of the channel. A general formula gives the maximum average power as between 20 and 24\% of the peak tidal pressure head, from one end of the channel to the other, times the peak of the undisturbed mass flux through the channel. This maximum average power is independent of the location of the turbine ‘fences’ along the channel. The results may also be used to evaluate the power potential of steady ocean currents.