In this study, a new concept of allowable velocity and force is proposed to precisely evaluate the maximum directional kinematic capability of a redundant manipulator. For a general redundant manipulator, an optimization problem is formulated to determine the maximum achievable velocity and force projected along the base direction at any target position in the workspace. This provides quantitative information on allowable (i.e., maximum directional) velocity and force to be precisely visualized in 2D and 3D complicated shapes, which conventional manipulability ellipsoid cannot provide. As application examples, allowable velocity and force are evaluated for a distributed actuation mechanism (DAM)-based three-link planar manipulator, 3RRR planar parallel manipulator, and the UR5 robot (a spatial manipulator with 6 degrees of freedom). The simulation and experimental results validate that the proposed method can precisely determine allowable velocity and force, thereby contributing to planning the optimal operation for a given task.