Enzyme reactions, both in Nature and technical applications, commonly occur at the interface of immiscible phases. Nevertheless, stringent descriptions of interfacial enzyme catalysis remain sparse, and this is partly due to a shortage of coherent experimental data to guide and assess such work. In this work, we produced and kinetically characterized 83 cellulases, which revealed a conspicuous linear free energy relationship (LFER) between the substrate binding strength and the activation barrier. The scaling occurred despite the investigated enzymes being structurally and mechanistically diverse. We suggest that the scaling reflects basic physical restrictions of the hydrolytic process and that evolutionary selection has condensed cellulase phenotypes near the line. One consequence of the LFER is that the activity of a cellulase can be estimated from its substrate binding strength, irrespectively of structural and mechanistic details, and this appears promising for in silico selection and design within this industrially important group of enzymes.