Redox flow batteries are an emerging electrochemical technology suitable for energy-intensive grid storage, but further cost reductions are needed for broad deployment. Overcoming cell performance limitations through improvements in the design and engineering of constituent components represent a promising pathway to lower system costs. Of particular relevance, but limited study, are the porous carbon electrodes whose surface composition and microstructure impact multiple aspects of cell behavior. Here, we systematically investigate woven carbon cloth electrodes based on identical carbon fibers but arranged into different weave patterns (plain, 8-satin harness, 2×2 basket) of different thicknesses to identify structure-function relations and generalizable descriptors. We first evaluate the physical properties of the electrodes using a suite of analytical methods to quantify structural characteristics, accessible surface area, and permeability. We then study the electrochemical performance in a diagnostic flow cell configuration to elucidate resistive losses through polarization and impedance analysis and to estimate mass transfer coefficients through limiting current measurements. Finally, we combine these findings to develop power-law relations between relevant dimensional and dimensionless quantities and to calculate extensive mass transfer coefficients. These studies reveal nuanced relationships between the physical morphology of the electrode and its electrochemical and hydraulic performance and suggest that the plain weave pattern offers the best combination of these attributes. More generally, this study provides physical data and experimental insights that support the development of purpose-built electrodes using a woven materials platform.