ABSTRACT We present two approaches to determine the dynamical stability of a hierarchical triple-star system. The first is an improvement on the Mardling–Aarseth stability formula from 2001, where we introduce a dependence on inner orbital eccentricity and improve the dependence on mutual orbital inclination. The second involves a machine learning approach, where we use a multilayer perceptron (MLP) to classify triple-star systems as ‘stable’ and ‘unstable’. To achieve this, we generate a large training data set of 106 hierarchical triples using the N-body code MSTAR. Both our approaches perform better than previous stability criteria, with the MLP model performing the best. The improved stability formula and the machine learning model have overall classification accuracies of $93{{\ \rm per\ cent}}$ and $95{{\ \rm per\ cent}}$ respectively. Our MLP model, which accurately predicts the stability of any hierarchical triple-star system within the parameter ranges studied with almost no computation required, is publicly available on Github in the form of an easy-to-use python script.