Three-stranded R-loop structures have been associated with genomic instability phenotypes. What underlies their wide-ranging effects on genome stability remains poorly understood. Here we combined biochemical and atomic force microscopy approaches with single molecule R-loop footprinting to demonstrate that R-loops formed at the model Airn locus in vitro adopt a defined set of three-dimensional conformations characterized by distinct shapes and volumes, which we call R-loop objects. Interestingly, we show that these R-loop objects impose specific physical constraints on the DNA, as revealed by the presence of stereotypical angles in the surrounding DNA. Biochemical probing and mutagenesis experiments revealed that the formation of R-loop objects at Airn is dictated by the extruded non-template strand, suggesting that R-loops possess intrinsic sequence-driven properties. Consistent with this, we show that R-loops formed at the fission yeast gene sum3 do not form detectable R-loop objects. Our results reveal that R-loops differ by their architectures and that the organization of the non-template strand is a fundamental characteristic of R-loops, which could explain that only a subset of R-loops is associated with replication-dependent DNA breaks.