In several real-world scenarios (e.g., in steel production), fast decisions about phases that may occur at certain temperatures and compositions in chemical systems are required. The classical approach of minimizing the Gibbs energy of the system numerically can be slow, wherefore this work aims to train and use neural networks to calculate phase equilibria for a given system. It is assumed that once trained, a neural network can provide answers quicker than the classical approach. It is the goal of this work to approximate phase equilibria in unary and binary systems with neural networks. For this aim, Gibbs energies, entropies, enthalpies, and heat capacities of unary systems are approximated. The network for predicting binary equilibria directly uses analytical Gibbs energy functions to determine the equilibrium compositions. Even though the approach for the unary system can be applied to approximate the Gibbs energy, entropy, enthalpy, and heat capacity functions of a unary system, it does not provide faster results for calculating phase equilibria when compared to classical methods. However, the presented approach for the binary equilibrium calculation is faster using neural networks than numerical methods. The approach using neural networks is an approximation and does not allow for exact calculations of the equilibrium compositions. It works best when applied to systems where the Gibbs energy curves do not have inflection points. This fact can be limiting for real-world applications. Therefore, an additional method to categorize phases is presented, which can classify measurements (e.g., for the heat capacity) into the phases the measurements are taken from. The presented network is trained on 78 pure elements. It can however easily be adapted to classify phases of binary systems by training it on the data of the desired systems. Whilst the calculation of binary phase equilibria using neural networks is faster than using numerical methods, the approach has restrictions. To make fast decisions about the phases present in a system, the approach to classifying measurements rather than calculating equilibrium conditions directly is more reliable.