Free-flowing rivers have been impacted by anthropogenic activity and extensive hydropower development. Despite this, many opportunities exist for context-specific energy extraction, at locations deemed undesirable for conventional hydropower plants, in ways that reduce the scale of operation and impact. Hydrokinetic energy conversion (HEC) is a renewable energy technology that requires accurate resource assessment to support deployment in rivers. We use global-scale modeled river discharge data, combined with a high-resolution vectorized representation of river networks, to estimate channel form, flow velocities, and hence global hydrokinetic potential. Our approach is based directly on the transfer of kinetic energy through the river network, rather than conventional, yet less realistic, assessments that are based on conversion from gravitational potential energy. We show that this new approach provides a more accurate global distribution of the hydrokinetic resource, highlighting the importance of the lower-courses of major rivers. The resource is shown to have great potential on the continents of South America, Asia, and Africa. We calculate that the mean hydrokinetic energy of global rivers (excluding Greenland and Antarctica) is \SI{5.911(9)}{\peta\joule}(\SI{1.642(3)}{\teraWattHour}).