Soft (compliant) curvature-changing UIs provide haptic feedback through changes in softness and curvature. Different softness can impact the deformation of UIs when worn and touched, and thus impact the users' perception of the curvature. To investigate how softness impacts users’ perception of curvature, we measured participants’ curvature perception accuracy and precision in different softness conditions. We found that participants perceived the curviest surfaces with similar precision in all different softness conditions. Participants lost half the precision of the rigid material when touching the flattest surfaces with the softest material. Participants perceived all curvatures with similar accuracy in all softness conditions. The results of our experiment lay the foundation for soft curvature perception and provide guidelines for the future design of curvature- and softness-changing UIs.