The need for improved functionalities in extreme environments is fuelling interest in high-entropy ceramics1–3. Except for the computational discovery of high-entropy carbides, performed with the entropy-forming-ability descriptor4, most innovation has been slowly driven by experimental means1–3. Hence, advancement in the field needs more theoretical contributions. Here we introduce disordered enthalpy–entropy descriptor (DEED), a descriptor that captures the balance between entropy gains and enthalpy costs, allowing the correct classification of functional synthesizability of multicomponent ceramics, regardless of chemistry and structure. To make our calculations possible, we have developed a convolutional algorithm that drastically reduces computational resources. Moreover, DEED guides the experimental discovery of new single-phase high-entropy carbonitrides and borides. This work, integrated into the AFLOW computational ecosystem, provides an array of potential new candidates, ripe for experimental discoveries. DEED captures the balance between entropy gains and costs, allowing the correct classification of functional synthesizability of multicomponent ceramics, regardless of chemistry and structure, and provides an array of potential new candidates, ripe for experimental discoveries.