Localisation of simple stimuli such as angle vertices may contribute to a plethora of illusory effects. We focus on the Müller-Lyer illusion in an attempt to measure and characterise a more elementary effect that may contribute to the magnitude of said illusion. Perceived location error of angle vertices (a single set of Müller-Lyer fins) and arcs in a 2D plane was measured with the aim to provide clarification of ambiguous results from studies of angle localisation and expand the results to other types of stimuli. In three experiments, we utilised the method of constant stimuli in order to determine perceived locations of angle vertices (Experiments 1 and 2) as well as circular and elliptical arcs (Experiment 3). The results show significant distortions of perceived compared to objective vertex locations (all effect sizes d > 1.01, p < .001). Experiment 2 revealed strong effects of angle size and fin length on localisation error. Mislocalization was larger for more acute angles and longer angle fins (both ηp² = .43, p < .001). In Experiment 3, localisation errors were larger for longer arcs (ηp² = .19, p = .001) irrespective of shape (circular or elliptical). We discuss the effect in the context of modern trends in research of the Müller-Lyer illusion as well as the widely popular centroid theory. (PsycInfo Database Record (c) 2024 APA, all rights reserved).