Visual and somatosensory signals participate together in providing an estimate of the hand's spatial location. While the ability of subjects to identify the spatial location of their hand based on visual and proprioceptive signals has previously been characterized, relatively few studies have examined in detail the spatial structure of the proprioceptive map of the arm. Here, we reconstructed and analyzed the spatial structure of the estimation errors that resulted when subjects reported the location of their unseen hand across a 2D horizontal workspace. Hand position estimation was mapped under four conditions: with and without tactile feedback, and with the right and left hands. In the task, we moved each subject's hand to one of 100 targets in the workspace while their eyes were closed. Then, we either a) applied tactile stimulation to the fingertip by allowing the index finger to touch the target or b) as a control, hovered the fingertip 2 cm above the target. After returning the hand to a neutral position, subjects opened their eyes to verbally report where their fingertip had been. We measured and analyzed both the direction and magnitude of the resulting estimation errors. Tactile feedback reduced the magnitude of these estimation errors, but did not change their overall structure. In addition, the spatial structure of these errors was idiosyncratic: each subject had a unique pattern of errors that was stable between hands and over time. Finally, we found that at the population level the magnitude of the estimation errors had a characteristic distribution over the workspace: errors were smallest closer to the body. The stability of estimation errors across conditions and time suggests the brain constructs a proprioceptive map that is reliable, even if it is not necessarily accurate. The idiosyncrasy across subjects emphasizes that each individual constructs a map that is unique to their own experiences.