A geometric tolerance factor τ proposed by Bartel et al. (2019) that predicts whether a given ABX3 composition will form a stable perovskite structure. Unlike the classical Goldschmidt tolerance factor t, τ incorporates the oxidation state of A-site cation and uses a different functional form: τ = r_X/r_B - n_A(n_A - r_A/r_B / ln(r_A/r_B)). Achieves 92% accuracy on experimental perovskite/non-perovskite classification.