The villous trees of human placentas delineate the fetomaternal border and are complex three-dimensional (3D) structures. Thus far, they have primarily been analyzed as thin, two-dimensional (2D) histological sections. However, 2D sections cannot provide access to key aspects such as branching nodes and branch order. Using samples taken from 50 normal human placentas at birth, in the present study we show that analysis procedures for 3D reconstruction of neuronal dendritic trees can also be used for analyzing trees of human placentas. Nodes and their branches (e.g., branching hierarchy, branching angles, diameters, and lengths of branches) can be efficiently measured in whole-mount preparations of isolated villous trees using high-end light microscopy. Such data differ qualitatively from the data obtainable from histological sections and go substantially beyond the morphological horizon of such histological data. Unexpectedly, branching angles of terminal branches of villous trees varied inversely with the fetoplacental weight ratio, a widely used clinical parameter. Since branching angles have never before been determined in the human placenta, this result requires further detailed studies in order to fully understand its impact.