Context. One of the main discoveries from the first two orbits of Parker Solar Probe (PSP) was the presence of magnetic switchbacks, whose deflections dominated the magnetic field measurements. Determining their shape and size could provide evidence of their origin, which is still unclear. Previous work with a single solar wind stream has indicated that these are long, thin structures although the direction of their major axis could not be determined. Aims. We investigate if this long, thin nature extends to other solar wind streams, while determining the direction along which the switchbacks within a stream were aligned. We try to understand how the size and orientation of the switchbacks, along with the flow velocity and spacecraft trajectory, combine to produce the observed structure durations for past and future orbits. Methods. The direction at which the spacecraft cuts through each switchback depended on the relative velocity of the plasma to the spacecraft and the alignment direction for that stream. We searched for the alignment direction that produced a combination of a spacecraft cutting direction and switchback duration that was most consistent with long, thin structures. The expected form of a long, thin structure was fitted to the results of the best alignment direction, which determined the width and aspect ratio of the switchbacks for that stream. Results. We find that switchbacks consistently demonstrate a non-radial alignment in the same sense as the Parker spiral field, but not the background flow direction within each stream. This alignment direction varied between streams. The switchbacks had a mean width of 50 000 km, with an aspect ratio of the order of 10. Conclusions. We conclude that switchbacks are not aligned along the background flow direction, but instead aligned along the local Parker spiral, perhaps suggesting that they propagate along the magnetic field. Since the observed switchback duration depends on how the spacecraft cuts through the structure, the duration alone cannot be used to determine the size or influence of an individual event. For future PSP orbits, a larger spacecraft transverse component combined with more radially aligned switchbacks will lead to long duration switchbacks becoming less common.