We tested the hypothesis that the performance of rapid movements represents body size-independent indices of muscle power. Physical education students (n = 159) were tested on various vertical jump (jump height and average power calculated from the ground reaction force) and muscle strength tests. When non-normalized data were used, a principal components analysis revealed a complex and inconsistent structure where jump height and muscle power loaded different components, while muscle strength and power partially overlapped. When the indices of muscle strength and power were properly normalized for body size, a simple and consistent structure of principal components supported the hypothesis. Specifically, the recorded height and muscle power calculated from the same jumps loaded the same components, separately for the jumps predominantly based on concentric actions and jumps based on a rapid stretch--shortening cycle of the leg extensors. The finding that the performance of rapid movements assesses the same physical ability as properly normalized tests of muscle power could be important for designing and interpreting the results of batteries of physical performance tests, as well as for understanding some basic principles of human movement performance.