Tracking lava effusion rates during an eruption is critical for monitoring and assessing lava flow hazards and investigating controls on lava flow behavior. Flowing lava and water have dramatically different physical properties but can form similar hydraulic structures, including eddies, shock waves, and undular hydraulic jumps (UHJs), or standing wave trains. In water flows, UHJs are evidence of a transition from supercritical to subcritical flow, approaching critical flow, where the Froude number (U/√gd, where U and d are the flow velocity and depth, respectively, and g is gravity) is approximately equal to 1. In this regime, open-channel hydraulic theory provides a powerful tool for estimating flow depth and velocity. Monitoring these parameters in an active lava channel is inherently challenging, particularly because depth cannot be directly measured during eruption. However, they are essential for calculating lava effusion rate, a primary control on the rate of flow front advance and ultimate flow runout distance. We analyze UHJs in both water and lava flows to assess the conditions under which they form and, by extension, the potential use of critical flow theory to estimate, in real time, lava flow velocity, depth, and discharge. Experimental flume data for water flows show that UHJs mark the transition from supercritical to subcritical flow, and reveal relations among UHJ wavelength, flow depth, and velocity. Our analysis shows that UHJs in the near-vent lava channel of the 2018 lower East Rift Zone eruption of Kīlauea, Hawaiʻi also reflect critical flow conditions. UHJ wavelengths scale with flow depth and velocity in the lava channel, consistent with hydraulic theory. Calculated lava effusion rates are consistent with estimates made using more traditional approaches (Jeffreys equation based on lava viscosity, density, and channel slope), and with lava volumes derived from topographic-change mapping. These results demonstrate that lava effusion rate can therefore be accurately estimated solely from scaled imagery of a lava channel with UHJs. We therefore conclude that critical flow phenomena show great potential to track flow dynamics and inform hazard assessment for a wide range of geophysical fluids.