Humans are able to adapt their motor commands in order to make accurate movements in novel sensorimotor environments, such as when wielding tools that alter limb dynamics. However, it is unclear to what extent sensorimotor representations obtained through experience with one limb are available to the opposite, untrained limb, and in which form they are available. Here we compared cross-limb transfer of force-field compensation after participants adapted to a velocity-dependent curl field oriented either in the sagittal or the transverse plane. Due to the mirror symmetry of the limbs, the force field had identical effects for both limbs in joint and extrinsic coordinates in the sagittal plane, but conflicting joint-based effects in the transverse plane. The degree of force-field compensation exhibited by the opposite arm in probe trials immediately after initial learning was significantly greater after sagittal (26 ± 5 %) than transverse plane adaptation (9 ± 4%; p < 0.001), irrespective of whether participants learned initially with the left or the right arm, or via abrupt or gradual exposure to the force field. Thus, transfer was impaired when the orientation of imposed dynamics conflicted in intrinsic coordinates for the two limbs. The data reveal that neural representations of novel dynamics are only partially available to the opposite limb, since transfer is incomplete even when force field perturbation is spatially compatible for the two limbs according to both intrinsic and extrinsic coordinates.