Relatively few studies have been reported that document how proprioception varies across the workspace of the human arm. Here we examined proprioceptive function across a horizontal planar workspace, using a new method that avoids active movement and interactions with other sensory modalities. We systematically mapped both proprioceptive acuity (sensitivity to hand position change) and bias (perceived location of the hand), across a horizontal-plane 2D workspace. Proprioception of both the left and right arms was tested at nine workspace locations and in 2 orthogonal directions (left-right and forwards-backwards). Subjects made repeated judgments about the position of their hand with respect to a remembered proprioceptive reference position, while grasping the handle of a robotic linkage that passively moved their hand to each judgement location. To rule out the possibility that the memory component of the proprioceptive testing procedure may have influenced our results, we repeated the procedure in a second experiment using a persistent visual reference position. Both methods resulted in qualitatively similar findings. Proprioception is not uniform across the workspace. Acuity was greater for limb configurations in which the hand was closer to the body, and was greater in a forward-backward direction than in a left-right direction. A robust difference in proprioceptive bias was observed across both experiments. At all workspace locations, the left hand was perceived to be to the left of its actual position, and the right hand was perceived to be to the right of its actual position. Finally, bias was smaller for hand positions closer to the body. The results of this study provide a systematic map of proprioceptive acuity and bias across the workspace of the limb that may be used to augment computational models of sensory-motor control, and to inform clinical assessment of sensory function in patients with sensory-motor deficits.