The Johnson-Mehl-Avrami (JMA) theory for nucleation and growth transformations is applied to isothermal and non-isothermal conditions as frequently used in differential scanning calorimetry (DSC) experiments. A model is derived with three kinetic parameters : activation energy, transformation order, and frequency factor. Analytical expressions are developed for the DSC heat-flow evolution as a function of time or temperature for both isothermal as well as constant heating rate conditions. They provide a variety of methods for the determination of the three kinetic parameters by fits to experimental DSC curves. The potential of the proposed model is demonstrated using the example of solid-state reactions in a Ti-Al multilayer thin film.