In this paper, a novel quantitative measure of redundancy, called refined redundancy index (RRI), which is measured in the joint-rate level, is proposed. Based on the concept that a larger solution space of the inverse kinematics problem represents larger redundancy, the RRI is defined as the normalized magnitude of the solution spaces. The value of the RRI varies from 0 to 1, and larger RRI corresponds to larger redundancy. Unlike joint-angle-level approaches, our method does not have the problem that different regions of joint angles correspond to the same primary task. The proposed RRI is computationally efficient and easy to apply for real-time applications. Simulation results show that with RRI the manipulator can reduce the execution time of a given task significantly, compared to the conventional approach. The results also illustrate that motion failures can be avoided with RRI. It is believed that RRI can be applied to a variety of applications of redundant robots in the future.