The sense of limb position is crucial for movement control and environmental interactions. Our understanding of this fundamental proprioceptive process, however, is limited. For example, little is known about the accuracy of arm proprioception: Does it vary with changes in arm configuration, since some peripheral receptors are engaged only when joints move toward extreme angles? Are these variations consistent across different tasks? Does proprioceptive ability change depending on what we try to localize (e.g., fingertip position vs. elbow angle)? We used a robot exoskeleton to study proprioception in 14 arm configurations across three tasks, asking healthy subjects to 1) match a pointer to elbow angles after passive movements, 2) match a pointer to fingertip positions after passive movements, and 3) actively match their elbow angle to a pointer. Across all three tasks, subjects overestimated more extreme joint positions; this may be due to peripheral sensory signals biasing estimates as a safety mechanism to prevent injury. We also found that elbow angle estimates were more precise when used to judge fingertip position versus directly reported, suggesting that the brain has better access to limb endpoint position than joint angles. Finally, precision of elbow angle estimates improved in active versus passive movements, corroborating work showing that efference copies of motor commands and alpha-gamma motor neuron coactivation contribute to proprioceptive estimates. In sum, we have uncovered fundamental aspects of normal proprioceptive processing, demonstrating not only predictable biases that are dependent on joint configuration and independent of task but also improved precision when integrating information across joints.