A measurement of novel event shapes quantifying the isotropy of collider events is performed in 140 fb−1 of proton-proton collisions with s = 13 TeV centre-of-mass energy recorded with the ATLAS detector at CERN’s Large Hadron Collider. These event shapes are defined as the Wasserstein distance between collider events and isotropic reference geometries. This distance is evaluated by solving optimal transport problems, using the ‘Energy-Mover’s Distance’. Isotropic references with cylindrical and circular symmetries are studied, to probe the symmetries of interest at hadron colliders. The novel event-shape observables defined in this way are infrared- and collinear-safe, have improved dynamic range and have greater sensitivity to isotropic radiation patterns than other event shapes. The measured event-shape variables are corrected for detector effects, and presented in inclusive bins of jet multiplicity and the scalar sum of the two leading jets’ transverse momenta. The measured distributions are provided as inputs to future Monte Carlo tuning campaigns and other studies probing fundamental properties of QCD and the production of hadronic final states up to the TeV-scale.