In chemical reaction engineering, not only a reactor type must be selected for the implementation of a specific chemical reaction, but often the reactor size must also be determined or statements about its operating behavior must be provided, given the operating conditions and production level. The relevant material and heat balance equations are used to model the material conversion in chemical reactors and their calculation. Based on this, mathematical models and design equations for three basic reactor types (batch and continuous stirred tank as well as tubular flow reactor) are derived, taking into account ideal flow and isothermal conditions. Mathematical modeling and design of ideal reactors lead overall to a better understanding of the functioning of reactors and enable the application of the calculation methods presented for the treatment of real reactors.